Teng zhang's blog
http://imechanica.org/blog/1694
enSymplectic Analysis of Wrinkles in Elastic Layers with Graded Stiffnesses
http://imechanica.org/node/22715
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/8234">wrinkles</a></div><div class="field-item odd"><a href="/taxonomy/term/942">gradient</a></div><div class="field-item even"><a href="/taxonomy/term/12236">symplectic analysis</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span>Wrinkles in layered neo-Hookean structures were recently formulated as a Hamiltonian system by taking the thickness direction as a pseudo-time variable. This enabled an efficient and accurate numerical method to solve the eigenvalue problem for onset wrinkles. Here, we show that wrinkles in graded elastic layers can also be described as a time-varying Hamiltonian system. The connection between wrinkles and the Hamiltonian system is established through an energy method. Within the Hamiltonian framework, the eigenvalue problem of predicting wrinkles is defined by a series of ordinary differential equations with varying coefficients. By modifying the boundary conditions at the top surface, the eigenvalue problem can be efficiently and accurately solved with numerical solvers of boundary value problems. We demonstrated the accuracy of the symplectic analysis by comparing the theoretically predicted displacement eigenfunctions, critical strains, and wavelengths of wrinkles in two typical graded structures with finite element simulations.</span></p>
<p><span><span><a href="http://appliedmechanics.asmedigitalcollection.asme.org/article.aspx?articleid=2706318">http://appliedmechanics.asmedigitalcollection.asme.org/article.aspx?arti...</a></span></span></p>
</div></div></div>Wed, 03 Oct 2018 15:12:13 +0000Teng zhang22715 at http://imechanica.orghttp://imechanica.org/node/22715#commentshttp://imechanica.org/crss/node/22715Journal Club for October 2018: Ruga mechanics of thin sheets: wrinkling, crumpling, and folding
http://imechanica.org/node/22701
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/17">thin film</a></div><div class="field-item odd"><a href="/taxonomy/term/12231">ruga mechanics</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Teng Zhang</p>
<p>Department of Mechanical and Aerospace Engineering, Syracuse University</p>
<p><strong>Introduction</strong></p>
<p class="MsoNormal"><span><span>As indicated by the title, we will discuss Rgua (1) and thin films (2, 3). For “Ruga”, I directly borrowed the opening introduction from previous Journal club “<a href="http://imechanica.org/node/17889">The Ruga mechanics</a>” organized by Dr. Mazen Diab, Dr. Ruike Zhao and Prof. Kyung-Suk Kim. “The ‘ruga’, a Latin term, means a single state of various corrugated material configurations, which form diverse 2D-patterns on solid surfaces, interfaces and in thin films. Typical ruga configurations include large-amplitude wrinkles, creases, folds, ridges, wrinklons, crinkles and crumples.” Thin films are ubiquitous in nature and engineering structures, from nanoscale graphene films to millimeter scale polymer films, from centimeter scale clothes to kilometer space balloon and floating ice sheet (Fig. 1). In this club discussion, we will focus on the intersection between thin films and mechanics of ruga configurations, which definitely is only a subset of the thin film mechanics and ruga mechanics. Further, this discussion is motivated by our recent collaboration on instability of floating thin films with Dr. Joseph Paulsen in Physics department at Syracuse University. Therefore, I will start from the wrinkling, crumpling, and folding in thin films floating on water surfaces and use them as representative examples to explore the nonlinear coupling of gravity, surface tension, curvature, and bending deformation in determining various ruga patterns in general thin film structures.</span></span></p>
<p><img src="http://imechanica.org/files/Slide1.png" alt="" width="760" height="331" /></p>
<p class="MsoNormal"><em><span><span>Figure. 1. (a) Wrinkles in a stretched graphene sheet (4), (b) torsion induced wrinkles in an annular graphene sheet (5), (c) wrapping liquid droplet with thin films (6), (d) folding of a floating thin film (7), (e) wrinkles and folds in cylindrical shell (8, 9), (f) wrinkles in clothes based on numerical simulations (10), (g) google balloon, and (f) floating ice sheet. Pictures in (g) and (f) are from internet. </span></span></em></p>
<p class="MsoNormal"><span><span>This is a long post, although I did not expect it at beginning. So I try to make each section self-contained. I only have a short time to prepare this club discussion, and will very likely miss some interesting and related studies. <strong>Please do point out these studies and participate in the discussion</strong>. Please also excuse typos in my writing.</span></span></p>
<p class="MsoNormal"><strong><span><span>A universal scaling law for thin sheet wrinkles</span></span></strong></p>
<p class="MsoNormal"><span><span>Before we start discussing wrinkles in specific thin films, we would like to review a universal law for thin film wrinkling. Taking the wrinkles in a stretched polyethylene sheet as an example, Cerda and Mahadevan (11) derived a universal law for he wrinkle wavelength in thin sheets as</span></span></p>
<p class="MsoNormal"><span><span> λ=2π(B/K_eff )^(1/4), (1)</span></span></p>
<p class="MsoNormal"><span><span>where B and K_eff represent the bending modulus of thin sheets and effective stiffness, respectively. For the stretched sheets, the K_eff comes from the tension stress. Another simple example is the liquid substrate, the stiffness is just K_eff=ρg. The scaling law in Eq. (1) is also applicable to solid substrate, the effective stiffness of which will depend on the wavelength (12). </span></span></p>
<p class="MsoNormal"><img src="http://imechanica.org/files/Slide2.png" alt="" width="406" height="182" /></p>
<p class="MsoNormal"><span>Figure. 2. (a) geometry and physics of wrinkling (11), (b) the curvature effect on wrinkles in thin films (13).</span></p>
<p class="MsoNormal"><span>Recently, wrinkles in curved structures, either with intrinsic curvature or deformation induced curvature, have attracted a lot attentions. Paulsen et al., (13) extended Eq. (1) to include the effect of deformation curvature,</span></p>
<p class="MsoNormal"><span>K_eff (r)=K_sub+σ_|| (x) [Φ'(x)/</span>Φ<span>(x) ]^2+(Et) R_|| (x)^(-2), (2)</span></p>
<p class="MsoNormal"><span>where is the substrate’s stiffness (e.g., K_sub=</span><span>ρ</span><span>g for a liquid substrate), </span>σ_||<span> (x) and </span>R_||<span> (x) are, respectively, the tensile stress and radius of curvature along the wrinkles, Et is the stretching modulus of the sheet, and </span>Φ<span>^2 (x) is proportional to the fractional length Δ absorbed by the wrinkles. We will review the applications of Eq. (2) in the following sections. Matteo and Dominic (14) further discussed the effective stiffness due to intrinsic curvature in spherical shell.</span></p>
<p class="MsoNormal"><span>Therefore, an important task of analyzing wrinkles becomes deriving K_eff in different situations, which depend on substrate (e.g., liquid or solid), stress field, and the curvature of wrinkles. We will highlight this question in a few set up and try to answer some of them. It should also be pointed out that the scaling laws in Eq. (1) and (2) are determined by local properties, which may not be always true. But these general relations between the wrinkles and material and geometry properties can still provide an important guide in analyzing the problems. </span></p>
<p><strong><span>Droplet on film-the coupling between gravity and surface tension</span></strong></p>
<p><span>Huang et al., (15) show that wrinkles form when placing a droplet on top of a floating thin polymer film (Fig. 3a). A recent study by Chang et al., (16) further reveal complicated wrinkles (e.g., two Fourier modes) in very thin films (Fig. 3b). These wrinkles were found to be effective to measure the mechanical properties of nanoscale thin films. Schroll et al., (17) found that this droplet on film problem can be nicely formed as an annular thin sheet subject to tension difference on the inner and outer edge (Fig. 3c). This simple set up turns out to have very rich wrinkling behaviors, which cannot be described by perturbation theory and eigenvalue analysis for very thin sheets. Focusing on this far-from threshold regime, Benny et al., (18) propose a compression free theory and apply energy minimization method to derive a scaling law for the wrinkle number, which is governed by the so-called bendability ε^(-1)=(T_out R_in^2)/B (Fig. 3d). </span></p>
<p><img src="http://imechanica.org/files/Slide3.png" alt="" width="467" height="238" /></p>
<p><em><span>Figure. 3. (a) wrinkles in floating thin film induced by a water droplet (15), (b) more complicated wrinkles in floating thin film induced by a water droplet (16), (c) theoretical models for these wrinkles (17), (d) phase diagram of different wrinkles (i.e., near threshold and far-from threshold wrinkles) (18).</span><span><img src="https://www.dropbox.com/home/imechanica?preview=Slide3.PNG" alt="" /></span></em></p>
<p><span>Parallel effort has also been devoted to understanding the wrinkling, buckling and folding in a real annular sheet. Working with PDMS sheet, Pineirua et al., (19) created surface tension difference in the inner and outer boundaries of the annular structure by adding surfactant (e.g., liquid soap) to the water outside of the annulus (Fig. 4a). Their results showed the wrinkles (e.g., wavelength) are governed the gravity and can be well described by the universal scaling in Eq. (1). Paulsen et al., (20) applied a similar set up to very thin PS films and observed folding (Fig. 4b) and developed a geometry model to explain their findings. Although the wrinkle numbers were not directly measured, it is expected that the surface tension will play an important role and the structures are likely in the FFT regimes. Before we highlight a few open questions, we would like to point out the numerical challenges in simulating wrinkles in ultra-thin sheets. Taylor et al., (21) compared several numerical methods and found the dynamical relaxation method can give general very good results (Fig. 4c), although geometry perturbations are still required. </span></p>
<p><img src="http://imechanica.org/files/Slide4.png" alt="" width="432" height="165" /></p>
<p><em><span>Figure. 4. (a) capillary annular wrinkles in thick polymer films (t~10µm) (19), (b) capillary annular buckling and folding in thin polymer films (t~100 nm) (20), (c) numerical simulations for wrinkles in the FFT regime (21).</span></em></p>
<p><span><em><strong>Interesting questions</strong></em><span>:</span></span></p>
<p><span>a)We already can understand the two limiting cases: (1) gravity dominant wrinkles and (2) tension dominant wrinkles. However, there is still a lack of understanding of the general cases where both gravity and tension are important.</span></p>
<p><span>b)Folding can happen in very thin annular sheets, but the exact transition from wrinkles to folding is still not known. </span></p>
<p><span>c)The “two Fourier modes” wrinkles observed in very thin sheets are not fully understood yet.</span></p>
<p><span>d)For such complicated wrinkle configurations, what numerical simulations will be better (Newton-Raphson method or dynamics-like method)? </span></p>
<p><span>e)Either in experiments and simulations, do we only observe local minimum configurations? </span></p>
<p><strong><span>Film on droplet-the coupling of curvature, tension, and gravity</span></strong></p>
<p><span>Let us take a look at another opposite set up by placing an initially flat thin sheet on top of a liquid droplet. King et al., (22) revealed the wrinkling and crumpling as symmetry-breaking instabilities in such as experimental set up (Fig. 5a-b). Except the bendability, the wrinkles are also influenced by another dimensionless variable, named as confinement α=YW/2γR^2, where Y is the stretching stiffness, γ is the surface tension, W is the radius of the thin film, and R is the droplet of the liquid. Bendability (ε^(-1)) and confinement (a) determine whether the wrinkles are in the NT or FFT regimes. Note that wrinkles in NT regimes can be generally understood from linear perturbation and eigenvalue analysis, while wrinkles in FFT usually far exceed the onset instabilities, and require post-buckling analysis. Paulsen et al., (13) successfully applied the universal scaling law in Eq. (2) to explain the wrinkle numbers in the film on droplet set up. In addition, they also compared the theoretical prediction with wrinkle numbers measured in a floating thin film under poke.</span></p>
<p><img src="http://imechanica.org/files/Slide5.png" alt="" width="426" height="218" /></p>
<p><span>Figure. 5. (a) wrinkles in film on a droplet (22), (b) the unwrinkled and wrinkled regions as a function of confinement (22), (c) Wrinkles in a floating thin film under poke (13). </span></p>
<p><span>For poking a floating thin film, the resultant force is another very interesting quantity to measure and study, except for the wrinkling configuration. Holmes and Crosby (23) found the transition from wrinkling folding and also reported a force drop when folding happens (Fig. 6a). Hysteresis loop in force can also be seen. By carefully examining the geometry nonlinear deformation and wrinkle formation and evolution, Benny, Dominic and their collaborators (24-27) revealed several deform regimes that the force-indentation depth relations follow different rules. Very recently, my collaborators Joseph Paulsen and Vincent Démery, using experiments and geometry model, identified another nonlinear regime for large indentation, where the force is constant and linear proposal to the surface tension and film radius (28). </span></p>
<p><img src="http://imechanica.org/files/Slide6.png" alt="" width="390" height="272" /></p>
<p><em><span>Figure. 6. (a)Wrinkling and folding in thin film under poke (23)(b) 4 nonlinear regimes of force-indentation depth in floating thin films under poke (28).</span></em></p>
<p><span>To better understand the different nonlinear deformation regimes in poking a floating thin film, we developed a lattice model to simulate the problem (28), where elastic thin sheets and liquid surface tension were described by a triangle lattice model (29) and a spring with zero-rest length (30), respectively (Fig. 7a). The gravity force was directly applied to the particles in the elastic sheet, F_g=v3/2 r_0^2 ρgz, where the force was only along z direction, and the coefficient represented the effective area of a particle in the triangle lattice model. For large indentation, the gravity force is applied to each triangle with tilt deformation taken into account. A typical wrinkling configuration of the film under poke is shown in Fig. (7b). Our numerical simulations and experiments can well capture the first three nonlinear deformation regimes, compared to previous theory (27) (Fig. 7c). More detailed analysis of the regime 4 will be posted on line very soon (28). </span></p>
<p> <img src="http://imechanica.org/files/Slide7.png" alt="" width="420" height="267" /></p>
<p><span><em>Figure. 7. (a) Lattice mode for simulating floating thin film under poke, (b) Simulated wrinkle configuration, and (c) force-indentation depths from simulations and experiments (28). </em></span></p>
<p><span><em><strong>Interesting questions</strong></em>:</span></p>
<p><span>f)The coupling effects of gravity, tension, and curvature on wrinkle numbers, profiles, and system stiffness (resultant force).</span></p>
<p><span>g)The roles of contact, friction, and adhesion in the folding of thin films. </span></p>
<p><span>h)Our preliminary results show crumpling does not alter the force response, but why?</span></p>
<p><strong><span>Intrinsic curvature effect on the wrinkling and folding in shells</span></strong></p>
<p><span>Our previous discussion mostly focused on initially flat thin films, very rich wrinkling behaviors are also found in thin shells with intrinsic curvatures. Aharoni et al., (31) investigated wrinkles in a floating spherical shells (Fig. 8a), which is to overcome the geometry incompatibility. Albarran et al., (32) further extended the studies to more general curved shell with combined experiments and ABAQUS simulations (Fig. 8b). It should be noticed that surface tension does not play an important role in these two studies. Except the floating curved shell, a large number of studies have been conducted on the wrinkles/buckles of cylindrical (8, 9, 33-35) and spherical shells (36). </span></p>
<p><img src="http://imechanica.org/files/Slide8.png" alt="" width="432" height="270" /></p>
<p><em><span>Figure. 8. (a) wrinkles in a spherical shell laid atop a flat body of water (31), (b)more general studies on the curvature controlled patterns in floating shells (32), (c) cylindrical shell buckling (34), (d) surface texturing through cylindrical buckling (35), (e) wrinkling to folding transition in cylindrical buckling (9), (f) reversible patterning of spherical shells through constrained buckling (36).</span></em></p>
<p><span><em><strong>Interesting questions</strong></em>:</span></p>
<p><span>i)Will and how surface tension will modify the wrinkling patterns of floating shells? </span></p>
<p><span>j)Some geometry models have been proposed to understand the patterning in cylinder and sphere under constraints, can one develop more sophisticated theatrical models for these patterns? </span></p>
<p><strong><span>Multiple stability </span></strong></p>
<p> A following up question of the curvatures is multiple stable configurations in thin films or shells. Even for the 1D floating thin film, Diaman and Witten (37) showed both symmetric and anti-symmetric solutions can exist in an infinite long system (Fig. 9a). Demery et al., (38) investigated the energy of the large fold in the same system with numerical simulations, and found the anti-symmetric folding has lower energy than the symmetric folding (Fig. 9b). Rivetti and Neukirch (39) studied the mode branching route to localization of the finite-length floating elastica (Fig. 9c). </p>
<p><img src="http://imechanica.org/files/Slide9.png" alt="" width="450" height="200" /></p>
<p><span><em>Figure. 9. (a)Exact solutions for wrinkling and folding in a floating thin film (37), (b) mechanics of large folds in interfacial thin films (38), (c) The mode branching route in a finite-length floating elastica (39). Figure. 9. (a)Exact solutions for wrinkling and folding in a floating thin film (37), (b) mechanics of large folds in interfacial thin films (38), (c) The mode branching route in a finite-length floating elastica (39).</em> </span></p>
<p><span>More structures with bistable or multiple stable configurations can be found in curved shells, bi-layer film with strain mismatch and metastructures, such as origami structures (40-46). Taffetani et al., (41) showed bistable configurations for a spherical cap (Fig. 10a). Chen et al., (42) demonstrated the bistablity in a pre-stressed bilayer structure (Fig. 10b). Silverberg et al., (43) revealed a bistability in origami structures due to hidden degrees of freedom (Fig. 10c). Chung et al., (44) showed that long cylindrical elastic plate can, when loaded appropriately, serve to store elastic bits, localized dimples and bumps that can be written and erased at will anywhere along it (Fig. 10d). Fu et al., (45) introduced a set of concepts for morphable 3D mesostructures in diverse materials and fully formed planar devices spanning length scales from micrometres to millimetres (Fig. 10e). </span></p>
<p><span><img src="http://imechanica.org/files/Slide10.png" alt="" width="438" height="212" /></span></p>
<p><em><span>Figure. 10. (a) static bistability of spherical caps (41), (b) bistable morphing structures based on pre-stressed bi-layer (42), (c) bistable origami structure (43), (d) reprogrammable braille on an elastic shell (44), (e) Morphable 3D mesostructures based on multisable buckling mechanics (45).</span></em></p>
<p><span>One of the important applications of the multiple stability is to understand the knock-down factor of forces in cylindrical shell buckling (47, 48). It is well known that the maximum force a cylindrical shell can sustain is usually smaller than the theoretical prediction based on eigenvalue analysis (48), which is due to shell buckling and sensitive to imperfections. This geometry sensitivity can be attributed to the exist of multiple stable configurations, the energy barrier of which can determine the buckling stress (48). This classical problem recently attracts a lot attentions from both novel experiments and theoretical modeling. With a single local probe, Virot et al., (49) explored the energy landscape of the cylindrical shell under compression. Marthelot et al., (50) performed combined experiments and simulations to assess the shell instability via probing a hemi-spherical shell with point force. From the theoretical side, Horak et al., (51) applied the mountain pass theorem to search the energy barriers of cylindrical shell buckling. Hutchinson and Thomson (52) computed the energy barriers of a spherical shell with the framework of Maxwell load and identified the lowest the buckling load.</span></p>
<p><span><img src="http://imechanica.org/files/Slide11.png" alt="" width="441" height="265" /></span></p>
<p><em><span>Figure. 11. (a) Experimental data of the shell buckling stress (47), (b) poke of a cylindrical shell (49), (c) local probe of a spherical shell (50), (d) the Maxwell load method (52) and (e) the mountain pass theorem (51) for searching energy barrier in shell buckling.</span></em></p>
<p><span><em><strong>Interesting questions</strong></em>:</span></p>
<p><span>k)For a given structure, how can one predict the multiple stabile configurations? This is a question to find as many as possible local energy minimum configuration of a system with complicated energy landscapes. </span></p>
<p><span>l)Suppose we can find the local minimum configurations, what are the energy minimum paths to move from one to another local minimum location? </span></p>
<p><span>m)What are the new functions and/or devices we can achieve from these structures with multiple stability?</span></p>
<p><span>n)Can we understand the geometry sensitivity in the buckling stress of shells with the information of energy barriers between different local minimum configurations? </span></p>
<p><strong><span>Highly stretchable thin sheets</span></strong></p>
<p> Most previous discussion focused on thin sheets/shells with geometrical nonlinear deformation. A substantial effort has also been devoted to study the wrinkles in highly stretchable thin sheets, where both geometry and material nonlinearities are important (53). Zheng et al., (54) used simulations and experiments to show that wrinkles can form and disappear in elastomer membranes under stretch (Fig. 12a). Nayyar et al., (55, 56) conducted experiments and modeling to understand the stress patterns and wrinkles in hyperelastic sheets (Fig. 12b). Taylor et al., (57) considered the finite strain effect on the wrinkle patterns in thin elastic sheets. Li and Healey (58) examined different hyperelastic model for the elastic thin sheets and computed the wrinkle evolution path via continuation for an inflated system (Fig. 12c). Zhang et al., (59) investigated the wrinkling patterns in soft spherical shell under poke with both experiments and simulations (Fig. 12d). Except for the pure elastic thin sheets, Feher found very interesting wrinkling behavior in highly stretched thin films with Mullins effect (60). </p>
<p><img src="http://imechanica.org/files/Slide12.png" alt="" width="461" height="263" /></p>
<p><em><span>Figure. 12. (a) FEM simulations of the formation and disappearing of wrinkles in elastomer membranes (54), (b) experiments on the wrinkles in hyperelastic thin sheets (56), (c) wrinkle pattern evolution in neo-Hookean elastic thin sheet (58), (d) wrinkling patterns in soft spherical shell under poke (59), (e) the Mulins effect in the wrinkling behavior of highly stretched thin films (60).</span></em></p>
<p><span><em><strong>Interesting questions</strong></em>:</span></p>
<p><span>o)Theoretical proof of the wrinkling in these highly stretched thin sheet is important, but challenging. </span></p>
<p><span>p)What wrinkling behavior we can have in thin metal sheet with plasticity?</span></p>
<p><span>q)The current FEM software (i.e., ABAQUS) can handle geometry and material nonlinear very well, but there seems still a lack of general and powerful tool for nonlinear instability problem and tracking the instability path. In addition, geometry imperfections are still needed for most simulations of post-buckling analysis. A question may be how to integrate the well-tested and robust FEM software with novel continuation methods for instability analysis? </span></p>
<p><strong><span>Who will care?</span></strong></p>
<p><span>Thanks for reading this long post. You may wonder “Interesting patterns, so what?”. This is a tough question, but also very important. I try to answer it in a general and vague way. I think most of the studies can be summarized as “<strong>to wrinkled, or not to wrinkled</strong>”. Here I list two examples, and am sure there are many others. You are very welcomed to add to the discussion.</span></p>
<p><span><strong>To wrinkled</strong></span></p>
<p><span>Very recently, Chen et al., (61) showed the hierarchical micro-channels in Sarracenia trichome are keys for the ultrafast water harvesting and transport (Fig. 13a). We can see hierarchical wrinkles on the Sarracenia trichome (Fig. 13b). Wrinkles are myself interpretation, which can be wrong. Even they are wrinkles, they may be seen as films bonded on solid substrate, which is very important, but not discussed in the previous sections. I choose this structure mainly because it beautifully contains several key features discussed above: (1) varied curvature of the cone-like surface, (2) two or more Fourier modes wrinkles, (3) wrinkle bifurcation, likely indicating wrinkle number change.</span></p>
<p><img src="http://imechanica.org/files/Slide13.png" alt="" width="645" height="263" /></p>
<p><span>Figure. 13. (a) In situ optical microscope images of the Sarracenia trichome and its water transport process, (b) Appearance and surface wrinkled structure of the Sarracenia trichome (61).</span></p>
<p><strong><span>Not to wrinkled</span></strong></p>
<p><span>In some cases, we do not want to have wrinkles in thin sheets. One example is thin glass sheet produced by redrawing (Fig. 14a) (62-65). Filippov and Zheng (62) analyzed the dynamics and shape instability of these thin viscous sheets and used the elliptic and hyperbolic zones to define stable and unstable zones (Fig. 14b). Srinivasan et al., (65) determine the conditions for the onset of an out-of-plane wrinkling instability stated in terms of an eigenvalue problem for a linear partial differential equation governing the displacement of the midsurface of the sheet (Fig. 14c).</span></p>
<p><img src="http://imechanica.org/files/Slide14.png" alt="" width="566" height="315" /></p>
<p><em><span>Figure. 14. (a) example and modeling set up of a heated thin glass sheet during the redraw process (65), (b) theoretical model and maps of elliptic and hyperbolic zones (62), (c) eigenmodes of the midplane deformation (65).</span></em></p>
<p><strong><span>Acknowledgements</span></strong></p>
<p>I am grateful to Joseph D. Paulsen, Halim Kusumaatmaja, Vincent Demery, and Timothy J. Healey for helpful discussion.</p>
<p> </p>
<p><strong><span>References</span></strong></p>
<p><span>1. Diab M, Zhang T, Zhao R, Gao H, & Kim K-S (2013) Ruga mechanics of creasing: from instantaneous to setback creases. Proc. R. Soc. A 469(2157):20120753.</span></p>
<p><span>2.Witten TA (2007) Stress focusing in elastic sheets. Reviews of Modern Physics 79(2):643.</span></p>
<p><span>3.Audoly B & Pomeau Y (2010) Elasticity and geometry: from hair curls to the non-linear response of shells (Oxford University Press).</span></p>
<p><span>4.Bao W, et al. (2009) Controlled ripple texturing of suspended graphene and ultrathin graphite membranes. Nature nanotechnology 4(9):562.</span></p>
<p><span>5.Qin Z, Taylor M, Hwang M, Bertoldi K, & Buehler MJ (2014) Effect of wrinkles on the surface area of graphene: toward the design of nanoelectronics. Nano letters 14(11):6520-6525.</span></p>
<p><span>6.Paulsen JD, et al. (2015) Optimal wrapping of liquid droplets with ultrathin sheets. Nature materials 14(12):1206.</span></p>
<p><span>7.Pocivavsek L, et al. (2008) Stress and fold localization in thin elastic membranes. Science 320(5878):912-916.</span></p>
<p><span>8.Stoop N & Müller MM (2015) Non-linear buckling and symmetry breaking of a soft elastic sheet sliding on a cylindrical substrate. International Journal of Non-Linear Mechanics 75:115-122.</span></p>
<p><span>9.Yang Y, Dai H-H, Xu F, & Potier-Ferry M (2018) Pattern Transitions in a Soft Cylindrical Shell. Physical review letters 120(21):215503.</span></p>
<p><span>10.Jin N, Lu W, Geng Z, & Fedkiw RP (2017) Inequality cloth. Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, (ACM), p 16.</span></p>
<p><span>11.Cerda E & Mahadevan L (2003) Geometry and physics of wrinkling. Physical review letters 90(7):074302.</span></p>
<p><span>12.Brau F, Damman P, Diamant H, & Witten TA (2013) Wrinkle to fold transition: influence of the substrate response. Soft Matter 9(34):8177-8186.</span></p>
<p><span>13.Paulsen JD, et al. (2016) Curvature-induced stiffness and the spatial variation of wavelength in wrinkled sheets. Proceedings of the National Academy of Sciences 113(5):1144-1149.</span></p>
<p><span>14.Taffetani M & Vella D (2017) Regimes of wrinkling in pressurized elastic shells. Phil. Trans. R. Soc. A 375(2093):20160330.</span></p>
<p><span>15.Huang J, et al. (2007) Capillary wrinkling of floating thin polymer films. Science 317(5838):650-653.</span></p>
<p><span>16.Chang J, Toga KB, Paulsen JD, Menon N, & Russell TP (2018) Thickness Dependence of the Young’s Modulus of Polymer Thin Films. Macromolecules.</span></p>
<p><span>17.Schroll R, et al. (2013) Capillary deformations of bendable films. Physical review letters 111(1):014301.</span></p>
<p><span>18.Davidovitch B, Schroll RD, Vella D, Adda-Bedia M, & Cerda EA (2011) Prototypical model for tensional wrinkling in thin sheets. Proceedings of the National Academy of Sciences.</span></p>
<p><span>19.Pineirua M, Tanaka N, Roman B, & Bico J (2013) Capillary buckling of a floating annulus. Soft Matter 9(46):10985-10992.</span></p>
<p><span>20.Paulsen JD, et al. (2017) Geometry-driven folding of a floating annular sheet. Physical review letters 118(4):048004.</span></p>
<p><span>21.Taylor M, Davidovitch B, Qiu Z, & Bertoldi K (2015) A comparative analysis of numerical approaches to the mechanics of elastic sheets. Journal of the Mechanics and Physics of Solids 79:92-107.</span></p>
<p><span>22.King H, Schroll RD, Davidovitch B, & Menon N (2012) Elastic sheet on a liquid drop reveals wrinkling and crumpling as distinct symmetry-breaking instabilities. Proceedings of the National Academy of Sciences 109(25):9716-9720.</span></p>
<p><span>23.Holmes DP & Crosby AJ (2010) Draping films: A wrinkle to fold transition. Physical review letters 105(3):038303.</span></p>
<p><span>24.Vella D, Huang J, Menon N, Russell TP, & Davidovitch B (2015) Indentation of ultrathin elastic films and the emergence of asymptotic isometry. Physical review letters 114(1):014301.</span></p>
<p><span>25.Vella D & Davidovitch B (2017) Indentation metrology of clamped, ultra-thin elastic sheets. Soft matter 13(11):2264-2278.</span></p>
<p><span>26.Box F, Vella D, Style RW, & Neufeld JA (2017) Indentation of a floating elastic sheet: geometry versus applied tension. Proc. R. Soc. A 473(2206):20170335.</span></p>
<p><span>27.Vella D & Davidovitch B (2018) Regimes of wrinkling in an indented floating elastic sheet. arXiv preprint arXiv:1804.03341.</span></p>
<p><span>28.Ripp MM, Démery V, Zhang T, & Paulsen JD (2018) Geometric stiffening and softening of an indented floating thin film. arXiv preprint arXiv:1804.02421.</span></p>
<p><span>29.Seung H & Nelson DR (1988) Defects in flexible membranes with crystalline order. Physical Review A 38(2):1005.</span></p>
<p><span>30.Giomi L & Mahadevan L (2012) Minimal surfaces bounded by elastic lines. Proc. R. Soc. A 468(2143):1851-1864.</span></p>
<p><span>31.Aharoni H, et al. (2017) The smectic order of wrinkles. Nature Communications 8:15809.</span></p>
<p><span>32.Albarrán O, Todorova DV, Katifori E, & Goehring L (2018) Curvature controlled pattern formation in floating shells. arXiv preprint arXiv:1806.03718.</span></p>
<p><span>33.Wohlever J & Healey T (1995) A group theoretic approach to the global bifurcation analysis of an axially compressed cylindrical shell. Computer Methods in Applied Mechanics and Engineering 122(3-4):315-349.</span></p>
<p><span>34.Lord G, Champneys A, & Hunt GW (1999) Computation of localized post buckling in long axially compressed cylindrical shells. Localization and Solitary Waves in Solid Mechanics, (World Scientific), pp 271-284.</span></p>
<p><span>35.Seffen K & Stott S (2014) Surface texturing through cylinder buckling. Journal of Applied Mechanics 81(6):061001.</span></p>
<p><span>36.Marthelot J, Brun P-T, Jiménez FL, & Reis PM (2017) Reversible patterning of spherical shells through constrained buckling. Physical Review Materials 1(2):025601.</span></p>
<p><span>37.Diamant H & Witten TA (2011) Compression induced folding of a sheet: An integrable system. Physical review letters 107(16):164302.</span></p>
<p><span>38.Démery V, Davidovitch B, & Santangelo CD (2014) Mechanics of large folds in thin interfacial films. Physical Review E 90(4):042401.</span></p>
<p><span>39.Rivetti M & Neukirch S (2014) The mode branching route to localization of the finite-length floating elastica. Journal of the Mechanics and Physics of Solids 69:143-155.</span></p>
<p><span>40.Holmes DP (2018) Elasticity and Stability of Shape Changing Structures. arXiv preprint arXiv:1809.04620.</span></p>
<p><span>41.Taffetani M, Jiang X, Holmes DP, & Vella D (2018) Static bistability of spherical caps. Proc. R. Soc. A 474(2213):20170910.</span></p>
<p><span>42.Chen Z, et al. (2012) Nonlinear geometric effects in mechanical bistable morphing structures. Physical review letters 109(11):114302.</span></p>
<p><span>43.Silverberg JL, et al. (2015) Origami structures with a critical transition to bistability arising from hidden degrees of freedom. Nature materials 14(4):389.</span></p>
<p><span>44.Chung JY, Vaziri A, & Mahadevan L (2018) Reprogrammable Braille on an elastic shell. Proceedings of the National Academy of Sciences 115(29):7509-7514.</span></p>
<p><span>45.Fu H, et al. (2018) Morphable 3D mesostructures and microelectronic devices by multistable buckling mechanics. Nature materials 17(3):268.</span></p>
<p><span>46.Overvelde JT, et al. (2016) A three-dimensional actuated origami-inspired transformable metamaterial with multiple degrees of freedom. Nature communications 7:10929.</span></p>
<p><span>47.Seide P, Weingarten V, & Morgan E (1960) The development of design criteria for elastic stability of thin shell structures. (TRW Space Technology Labs Los Angeles CA).</span></p>
<p><span>48.Hutchinson JW & Thompson JMT (2018) Imperfections and energy barriers in shell buckling. International Journal of Solids and Structures.</span></p>
<p><span>49.Virot E, Kreilos T, Schneider TM, & Rubinstein SM (2017) Stability landscape of shell buckling. Physical review letters 119(22):224101.</span></p>
<p><span>50.Marthelot J, JimÃŠnez FL, Lee A, Hutchinson JW, & Reis PM (2017) Buckling of a pressurized hemispherical shell subjected to a probing force. Journal of Applied Mechanics 84(12):121005.</span></p>
<p><span>51.Horák J, Lord GJ, & Peletier MA (2006) Cylinder buckling: the mountain pass as an organizing center. SIAM Journal on Applied Mathematics 66(5):1793-1824.</span></p>
<p><span>52.Hutchinson JW & Thompson JMT (2017) Nonlinear buckling behaviour of spherical shells: barriers and symmetry-breaking dimples. Phil. Trans. R. Soc. A 375(2093):20160154.</span></p>
<p><span>53.Wong W & Pellegrino S (2006) Wrinkled membranes I: experiments. Journal of Mechanics of Materials and Structures 1(1):3-25.</span></p>
<p><span>54.Zheng L (2009) Wrinkling of dielectric elastomer membranes (California Institute of Technology).</span></p>
<p><span>55.Nayyar V, Ravi-Chandar K, & Huang R (2011) Stretch-induced stress patterns and wrinkles in hyperelastic thin sheets. International journal of solids and structures 48(25-26):3471-3483.</span></p>
<p><span>56.Nayyar V, Ravi-Chandar K, & Huang R (2014) Stretch-induced wrinkling of polyethylene thin sheets: Experiments and modeling. International Journal of Solids and Structures 51(9):1847-1858.</span></p>
<p><span>57.Taylor M, Bertoldi K, & Steigmann DJ (2014) Spatial resolution of wrinkle patterns in thin elastic sheets at finite strain. Journal of the Mechanics and Physics of Solids 62:163-180.</span></p>
<p><span>58.Li Q & Healey TJ (2016) Stability boundaries for wrinkling in highly stretched elastic sheets. Journal of the Mechanics and Physics of Solids 97:260-274.</span></p>
<p><span>59.Zhang C, Hao Y-K, Li B, Feng X-Q, & Gao H (2018) Wrinkling patterns in soft shells. Soft matter 14(9):1681-1688.</span></p>
<p><span>60.Feher E, Healey TJ, & Sipos AA (2018) The Mullins effect in the wrinkling behavior of highly stretched thin films. arXiv preprint arXiv:1806.00060.</span></p>
<p><span>61.Chen H, et al. (2018) Ultrafast water harvesting and transport in hierarchical microchannels. Nature Materials 17(10):935.</span></p>
<p><span>62.Filippov A & Zheng Z (2010) Dynamics and shape instability of thin viscous sheets. Physics of Fluids 22(2):023601.</span></p>
<p><span>63.Perdigou C & Audoly B (2016) The viscous curtain: General formulation and finite-element solution for the stability of flowing viscous sheets. Journal of the Mechanics and Physics of Solids 96:291-311.</span></p>
<p><span>64.O'Kiely D (2017) Mathematical models for the glass sheet redraw process.).</span></p>
<p><span>65.Srinivasan S, Wei Z, & Mahadevan L (2017) Wrinkling instability of an inhomogeneously stretched viscous sheet. Physical Review Fluids 2(7):074103.</span></p>
<p> </p>
</div></div></div><div class="field field-name-upload field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><table class="sticky-enabled">
<thead><tr><th>Attachment</th><th>Size</th> </tr></thead>
<tbody>
<tr class="odd"><td><span class="file"><img class="file-icon" alt="Image icon" title="image/png" src="/modules/file/icons/image-x-generic.png" /> <a href="http://imechanica.org/files/Slide1.png" type="image/png; length=851560">Slide1.png</a></span></td><td>831.6 KB</td> </tr>
<tr class="even"><td><span class="file"><img class="file-icon" alt="Image icon" title="image/png" src="/modules/file/icons/image-x-generic.png" /> <a href="http://imechanica.org/files/Slide2.png" type="image/png; length=442954">Slide2.png</a></span></td><td>432.57 KB</td> </tr>
<tr class="odd"><td><span class="file"><img class="file-icon" alt="Image icon" title="image/png" src="/modules/file/icons/image-x-generic.png" /> <a href="http://imechanica.org/files/Slide3.png" type="image/png; length=846148">Slide3.png</a></span></td><td>826.32 KB</td> </tr>
<tr class="even"><td><span class="file"><img class="file-icon" alt="Image icon" title="image/png" src="/modules/file/icons/image-x-generic.png" /> <a href="http://imechanica.org/files/Slide4.png" type="image/png; length=679639">Slide4.png</a></span></td><td>663.71 KB</td> </tr>
<tr class="odd"><td><span class="file"><img class="file-icon" alt="Image icon" title="image/png" src="/modules/file/icons/image-x-generic.png" /> <a href="http://imechanica.org/files/Slide5.png" type="image/png; length=538401">Slide5.png</a></span></td><td>525.78 KB</td> </tr>
<tr class="even"><td><span class="file"><img class="file-icon" alt="Image icon" title="image/png" src="/modules/file/icons/image-x-generic.png" /> <a href="http://imechanica.org/files/Slide6.png" type="image/png; length=662260">Slide6.png</a></span></td><td>646.74 KB</td> </tr>
<tr class="odd"><td><span class="file"><img class="file-icon" alt="Image icon" title="image/png" src="/modules/file/icons/image-x-generic.png" /> <a href="http://imechanica.org/files/Slide7.png" type="image/png; length=496978">Slide7.png</a></span></td><td>485.33 KB</td> </tr>
<tr class="even"><td><span class="file"><img class="file-icon" alt="Image icon" title="image/png" src="/modules/file/icons/image-x-generic.png" /> <a href="http://imechanica.org/files/Slide8.png" type="image/png; length=707610">Slide8.png</a></span></td><td>691.03 KB</td> </tr>
<tr class="odd"><td><span class="file"><img class="file-icon" alt="Image icon" title="image/png" src="/modules/file/icons/image-x-generic.png" /> <a href="http://imechanica.org/files/Slide9.png" type="image/png; length=302071">Slide9.png</a></span></td><td>294.99 KB</td> </tr>
<tr class="even"><td><span class="file"><img class="file-icon" alt="Image icon" title="image/png" src="/modules/file/icons/image-x-generic.png" /> <a href="http://imechanica.org/files/Slide10.png" type="image/png; length=607803">Slide10.png</a></span></td><td>593.56 KB</td> </tr>
<tr class="odd"><td><span class="file"><img class="file-icon" alt="Image icon" title="image/png" src="/modules/file/icons/image-x-generic.png" /> <a href="http://imechanica.org/files/Slide11.png" type="image/png; length=417972">Slide11.png</a></span></td><td>408.18 KB</td> </tr>
<tr class="even"><td><span class="file"><img class="file-icon" alt="Image icon" title="image/png" src="/modules/file/icons/image-x-generic.png" /> <a href="http://imechanica.org/files/Slide12.png" type="image/png; length=745689">Slide12.png</a></span></td><td>728.21 KB</td> </tr>
<tr class="odd"><td><span class="file"><img class="file-icon" alt="Image icon" title="image/png" src="/modules/file/icons/image-x-generic.png" /> <a href="http://imechanica.org/files/Slide13.png" type="image/png; length=733046">Slide13.png</a></span></td><td>715.87 KB</td> </tr>
<tr class="even"><td><span class="file"><img class="file-icon" alt="Image icon" title="image/png" src="/modules/file/icons/image-x-generic.png" /> <a href="http://imechanica.org/files/Slide14.png" type="image/png; length=432882">Slide14.png</a></span></td><td>422.74 KB</td> </tr>
<tr class="odd"><td><span class="file"><img class="file-icon" alt="Image icon" title="image/png" src="/modules/file/icons/image-x-generic.png" /> <a href="http://imechanica.org/files/Balloons_0.png" type="image/png; length=927010">Balloons.png</a></span></td><td>905.28 KB</td> </tr>
</tbody>
</table>
</div></div></div>Mon, 01 Oct 2018 03:47:26 +0000Teng zhang22701 at http://imechanica.orghttp://imechanica.org/node/22701#commentshttp://imechanica.org/crss/node/22701Deriving a lattice model for neo-Hookean solids from finite element methods
http://imechanica.org/node/22670
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/3950">soft materials</a></div><div class="field-item odd"><a href="/taxonomy/term/8687">lattice model</a></div><div class="field-item even"><a href="/taxonomy/term/4819">Neo-Hookean</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span>Lattice models are popular methods for simulating deformation of solids by discretizing continuum structures into spring networks. Despite the simplicity and efficiency, most lattice models only rigorously converge to continuum models for lattices with regular shapes. Here, we derive a lattice model for neo-Hookean solids directly from finite element methods (FEM). The proposed lattice model can handle complicated geometries and tune the material compressibility without significantly increasing the complexity of the model. Distinct lattices are required for irregular structures, where the lattice spring stiffness can be pre-calculated with the aid of FEM shape functions. Multibody interactions are incorporated to describe the volumetric deformation. We validate the lattice model with benchmark tests using FEM. The simplicity and adoptability of the proposed lattice model open possibilities to develop novel numerical platforms for simulating multiphysics and multiscale problems via integrating it with other modeling techniques.</span></p>
<p><span><span><a href="https://arxiv.org/abs/1809.02030">https://arxiv.org/abs/1809.02030</a></span></span></p>
</div></div></div>Sat, 22 Sep 2018 01:58:59 +0000Teng zhang22670 at http://imechanica.orghttp://imechanica.org/node/22670#commentshttp://imechanica.org/crss/node/22670ABAQUS files of coupled Mullins effect and cohesive zone model for fracture and adhesion of soft tough materials
http://imechanica.org/node/22162
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/3950">soft materials</a></div><div class="field-item odd"><a href="/taxonomy/term/31">fracture</a></div><div class="field-item even"><a href="/taxonomy/term/27">adhesion</a></div><div class="field-item odd"><a href="/taxonomy/term/879">cohesive element</a></div><div class="field-item even"><a href="/taxonomy/term/3552">mullins effect</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p class="MsoNormal"> </p>
<p class="MsoNormal"><a name="OLE_LINK21" id="OLE_LINK21"></a><a name="OLE_LINK20" id="OLE_LINK20"></a><a name="OLE_LINK19" id="OLE_LINK19"></a><a name="OLE_LINK18" id="OLE_LINK18"></a><a name="OLE_LINK17" id="OLE_LINK17"></a><span><span><span><span><span>Soft materials including elastomers and gels are pervasive in biological systems and technological applications. Robust mechanical properties, such as high toughness and tough bonding, are crucial to realize the potentials of soft materials. It has been well recognized that building energy dissipation into an elastic network is </span><span>one important toughening mechanism</span><span>. </span><span>However, it is still challenging to </span></span></span></span></span><a name="OLE_LINK16" id="OLE_LINK16"></a><a name="OLE_LINK15" id="OLE_LINK15"></a><span><span><span><span><span><span><span>quantitatively</span></span></span></span></span></span></span><span><span><span><span><span><span> predict the synergistic effect of the intrinsic fracture energy and mechanical dissipation </span><span>in process zone due to the highly nonlinear deformations. We recently showed that a coupled Mullins effect and cohesive zone model can accurately predict the fracture toughness and adhesion of tough hydrogels. The coupled simulation model can be carried out with finite element software ABAQUS. With the new experimental techniques, material fabrication and numerical methods, it is very promising to rationally design novel soft tough materials and quantitatively predict the designed materials with simulations. To further promote research on fracture and adhesion of soft tough materials, we share the ABAUQS input files for simulating fracture and 90 degree peeling of tough hydrogels. Please change the files to ".inp" after you download them to run the simulations with ABAQUS. </span></span></span></span></span></span></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><span>Zhang, Teng, Shaoting Lin, Hyunwoo Yuk, and Xuanhe Zhao. "Predicting fracture energies and crack-tip fields of soft tough materials." </span><em>Extreme Mechanics Letters</em><span> 4 (2015): 1-8.</span></p>
<p class="MsoNormal"><span>Yuk, Hyunwoo, Teng Zhang, Shaoting Lin, German Alberto Parada, and Xuanhe Zhao. "Tough bonding of hydrogels to diverse non-porous surfaces." </span><em>Nature materials</em><span> 15, no. 2 (2016): 190.</span></p>
<p class="MsoNormal"><span>Zhang, Teng, Hyunwoo Yuk, Shaoting Lin, German A. Parada, and Xuanhe Zhao. "Tough and tunable adhesion of hydrogels: experiments and models." </span><em>Acta Mechanica Sinica</em><span> 33, no. 3 (2017): 543-554.</span></p>
</div></div></div><div class="field field-name-upload field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><table class="sticky-enabled">
<thead><tr><th>Attachment</th><th>Size</th> </tr></thead>
<tbody>
<tr class="odd"><td><span class="file"><img class="file-icon" alt="Plain text icon" title="text/plain" src="/modules/file/icons/text-plain.png" /> <a href="http://imechanica.org/files/gel_h20_ogden1_s080md100_k2000_v125.txt" type="text/plain; length=2547299">gel_h20_ogden1_s080md100_k2000_v125.txt</a></span></td><td>2.43 MB</td> </tr>
<tr class="even"><td><span class="file"><img class="file-icon" alt="Plain text icon" title="text/plain" src="/modules/file/icons/text-plain.png" /> <a href="http://imechanica.org/files/gel_h20_ogden1_s080md100_k2000_v0625.txt" type="text/plain; length=2547301">gel_h20_ogden1_s080md100_k2000_v0625.txt</a></span></td><td>2.43 MB</td> </tr>
<tr class="odd"><td><span class="file"><img class="file-icon" alt="Plain text icon" title="text/plain" src="/modules/file/icons/text-plain.png" /> <a href="http://imechanica.org/files/gel_peeling_2d_ogden2_s200d30_h32.txt" type="text/plain; length=734933">gel_peeling_2d_ogden2_s200d30_h32.txt</a></span></td><td>717.71 KB</td> </tr>
<tr class="even"><td><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="http://imechanica.org/files/User%20guides_0.pdf" type="application/pdf; length=443349">User guides.pdf</a></span></td><td>432.96 KB</td> </tr>
</tbody>
</table>
</div></div></div>Fri, 23 Feb 2018 04:40:15 +0000Teng zhang22162 at http://imechanica.orghttp://imechanica.org/node/22162#commentshttp://imechanica.org/crss/node/22162EMI 2018 Mini-Symposium MS20 “Nonlinear mechanics of highly deformable solids and structures”
http://imechanica.org/node/21944
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/584">mechanics</a></div><div class="field-item odd"><a href="/taxonomy/term/151">Conference</a></div><div class="field-item even"><a href="/taxonomy/term/10034">EMI</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span>Dear Colleague,</span></p>
<p><span>The next Engineering Mechanics Institute Conference (EMI) will take place from May 29th to June 1st, 2018, at MIT.</span></p>
<p><span>As organizers of the Mini-Symposium MS20 “Nonlinear mechanics of highly deformable solids and structures”, it is our pleasure to invite you and your students to participate in our mini symposium.</span><br /><span>The deadline for abstract submission is January 31st, 2018.</span></p>
<p><span>A link to the conference website and abstract submission portal is: </span><a href="https://umi.mit.edu/EMI2018" target="_blank">https://umi.mit.edu/EMI2018</a></p>
<p><span>We are looking forward to your contribution and to seeing you at the meeting.</span></p>
<p><span>MS Description:</span></p>
<p><span>Advancements in design and application of materials and structures that can perform at large deformations, together with the increasing interest in deformation of biological materials, are continually revealing new mechanical phenomena that are beyond explanation by classical theories. This has led to a renewed interest in failure mechanisms that appear at large strains such as fracture, cavitation and delamination, and the identification of reversible instability patterns such as fingering, fringing, creasing and elastic necking, that can possibly be exploited for future engineering applications. The objective of this symposium is to provide a forum for researchers from academia, industry and national labs to present, discuss and exchange the latest development in theoretical, computational, and experimental studies on nonlinear solid mechanics across a wide range of length-scales. Both fundamental research and practical applications are welcome. Topics invited for this symposium include but are not limited to:</span></p>
<p><span> Failure – fracture and cavitation</span><br /><span> Rate-dependent material response</span><br /><span> Material characterization</span><br /><span> Instabilities in solids and structures</span><br /><span> Interface phenomena – adhesion and peeling</span><br /><span> Biological materials and bio inspired systems</span><br /><span> Mechanics of 3D printed materials and structures</span><br /><span> Wave propagation phenomena</span></p>
<p><span>Best regards,</span><br /><span> </span><br /><span>Teng Zhang, Syracuse University</span><br /><span>Stephan Rudykh, Technion</span><br /><span>Qiming Wang, University of Southern California</span><br /><span>Tal</span><span> Cohen, MIT</span></p>
</div></div></div>Thu, 14 Dec 2017 17:59:12 +0000Teng zhang21944 at http://imechanica.orghttp://imechanica.org/node/21944#commentshttp://imechanica.org/crss/node/21944Tenure-Track Assistant Professor Position in Mechanical and Aerospace Engineering at Syracuse University
http://imechanica.org/node/21664
<div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/541">job</a></div><div class="field-item odd"><a href="/taxonomy/term/127">Faculty Position</a></div><div class="field-item even"><a href="/taxonomy/term/11811">Syracuse University</a></div><div class="field-item odd"><a href="/taxonomy/term/800">mechanical engineering</a></div><div class="field-item even"><a href="/taxonomy/term/4457">Aerospace engineering</a></div><div class="field-item odd"><a href="/taxonomy/term/8286">cyber-physical systems</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p> </p>
<p>The Department of Mechanical and Aerospace Engineering at Syracuse University invites applications for a faculty position at the rank of tenure-track assistant professor. Applications in all subject areas of mechanical and aerospace engineering will be considered, particularly those with primary research interests in engineered systems that seamlessly integrate computational algorithms and physical components (cyber-physical systems). The successful candidate will participate in all aspects of the Department’s mission, including development of an independent, externally funded research program; teaching undergraduate and graduate courses in mechanical and aerospace engineering; supervision of graduate and undergraduate students; and service responsibilities.</p>
<p>The department has close ties with other departments and on-campus multidisciplinary centers, including the Syracuse Center of Excellence in Environmental and Energy Systems (SyracuseCoE), the Center for Advanced Systems and Engineering (CASE), Syracuse Biomaterials Institute (SBI) and Green Data Center. Researchers working at these centers are involved in several federally funded projects on topics that include unmanned systems, biomimetic systems, intelligent building control, data fusion and mining, communication systems and networks. In addition, New York state opportunities include the recent investment of $250 million for unmanned systems and cross-connected platforms in the central New York state region as part of the Upstate Revitalization Initiative, and the New York State Energy and Research Development Authority (NYSERDA) funding opportunities to develop smart building technologies.</p>
<p>For full consideration, applicants must complete an online Application at <a href="http://www.sujobopps.com">www.sujobopps.com</a> and attach the application file to job number 073512. Required application materials consist of:</p>
<p>1) cover letter,</p>
<p>2) detailed resume or curriculum vitae,</p>
<p>3) a statement of teaching and research interests,</p>
<p>4) names and contact information of three references.</p>
<p>The initial screening of applications will begin on December 1, 2017; applications will be accepted until the position is filled. For information about the department, please visit <a href="http://eng-cs.syr.edu/our-departments/mechanical-and-aerospace-engineering/">http://eng-cs.syr.edu/our-departments/mechanical-and-aerospace-engineering/</a>.</p>
<p>Syracuse and its surrounding areas offer a vibrant intellectual and cultural atmosphere, a diverse community, excellent public education systems, affordable homes, and many other assets that make it a great place to live and work. Syracuse University is an affirmative action/equal opportunity employer and is dedicated to enhancing community and scholarly pursuits through gender and ethnic diversity. Women and members of historically underrepresented groups are especially encouraged to apply.</p>
</div></div></div>Thu, 05 Oct 2017 19:23:57 +0000Teng zhang21664 at http://imechanica.orghttp://imechanica.org/node/21664#commentshttp://imechanica.org/crss/node/21664Symplectic analysis for wrinkles: a case study of layered neo-Hookean structures
http://imechanica.org/node/21198
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/8234">wrinkles</a></div><div class="field-item odd"><a href="/taxonomy/term/634">perturbation</a></div><div class="field-item even"><a href="/taxonomy/term/11624">Symplectic</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><strong>Abstract</strong></p>
<p class="MsoNormal"><span>Wrinkles are widely found in natural and engineering structures, ranging from skins to stretchable electronics. However, it is nontrivial to predict wrinkles, especially for complicated structures, such as multilayer or gradient structures. Here we establish a symplectic analysis framework for the wrinkles and apply it to a layered neo-Hookean structures. The symplectic structure enables us to accurately and efficiently solve the eigenvalue problems of wrinkles via the extended Wittrick–Williams algorithm. The symplectic analysis is able to exactly predict wrinkles in bi- and triple-layer structures, compared with the benchmark results and finite element simulations. Our findings also shed light on the formation of hierarchical wrinkles.</span></p>
<p class="MsoNormal"><span><span>(<a href="http://appliedmechanics.asmedigitalcollection.asme.org/article.aspx?articleid=2625793">http://appliedmechanics.asmedigitalcollection.asme.org/article.aspx?arti...</a>)</span></span></p>
</div></div></div>Tue, 02 May 2017 16:58:27 +0000Teng zhang21198 at http://imechanica.orghttp://imechanica.org/node/21198#commentshttp://imechanica.org/crss/node/21198Predicting fracture energies and crack-tip fields of soft tough materials
http://imechanica.org/node/18796
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/10657">soft tough materials</a></div><div class="field-item odd"><a href="/taxonomy/term/31">fracture</a></div><div class="field-item even"><a href="/taxonomy/term/6720">dissipation</a></div><div class="field-item odd"><a href="/taxonomy/term/5449">cohesive zone</a></div><div class="field-item even"><a href="/taxonomy/term/846">FEM</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><span>Soft materials including elastomers and gels are pervasive in biological systems and technological applications. Whereas it is known that intrinsic fracture energies of soft materials are relatively low, how the intrinsic fracture energy cooperates with mechanical dissipation in process zone to give high fracture toughness of soft materials is not well understood. In addition, it is still challenging to predict fracture energies and crack-tip strain fields of soft tough materials. Here, we report a scaling theory that accounts for synergistic effects of intrinsic fracture energies and dissipation on the toughening of soft materials. We then develop a coupled cohesive-zone and Mullins-effect model capable of quantitatively predicting fracture energies of soft tough materials and strain fields around crack tips in soft materials under large deformation. The theory and model are quantitatively validated by experiments on fracture of soft tough materials under large deformations. We further provide a general toughening diagram that can guide the design of new soft tough materials.</span></p>
<p> </p>
<p><span><a href="http://www.sciencedirect.com/science/article/pii/S2352431615000899">http://www.sciencedirect.com/science/article/pii/S2352431615000899</a></span></p>
</div></div></div>Wed, 02 Sep 2015 01:09:56 +0000Teng zhang18796 at http://imechanica.orghttp://imechanica.org/node/18796#commentshttp://imechanica.org/crss/node/18796Stroh formalism and hamilton system for 2D anisotropic elastic
http://imechanica.org/node/3671
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/669">Stroh formalism</a></div><div class="field-item odd"><a href="/taxonomy/term/670">anisotropic elasticity</a></div><div class="field-item even"><a href="/taxonomy/term/2720">hamilton system</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
</p>
<p>
<span>We have read some papers of stroh formalism and the textbook of Tom Ting, and found that the stroh formalism and the hamilton system proposed by prof.zhong wanxie had some relation. We want to know whether the stroh formalism is enough for the analysis of the anisotropic elastic? Thus's to say, for some problems could not give the satisfied answer which we may try the hamilton framework. I briefly compare the two methods as follows:</span>
</p>
<p>
<span>On one hand, I noted that the stroh formalism is widely used in the anisotropic elastic, both static and wave propagation. Stroh formalism is powerful and elegant. In some sense, the stroh formalism may be regarded as the generalization of the complex function method for 2D isotropic elastic, this formalism reveals simple structures hidden in the equations of anisotropic elasticity and provides a systematic approach to these equations.</span>
</p>
<p>
<span>On another hand, Prof.zhong wanxie had established a new system for elastic under the hamilton framework. For the isotropic elastic, we can derive the exact solution which is usually in the series solution, without assumptions of the solutions, for the strip domain and sectorial domain via the new system. The key idea of this new system is the introdution of the dual variables---stresses; then one direction is modelled as the time coordinate and using the method of separation variables, we can get the </span><span>eigenvalue problem of Hamiltonian matrix</span><span>: H*phi=miu*phi, where H is a operator matrix and also hamiltonian matrix, next we can get eigenfunction of lamda for the other direction. We found that the ratios lamda/miu has the same meaning of the eigenvalue p; finally, we established the eigenfunction via induced the boundary condition. </span><span> </span>
</p>
<p>
<span>Most the solutions having been obtained are isotropic elastic, however, this system can be extened to anisotropic elastic too. Unfortunately, this extention is invalid for sectorial domain, since, the solutions of sectorial domain need to do coordinates transformation which are only found for the situation that the elastic constants are rotation invariant.</span>
</p>
<p>
<span>Compare the two methods, the stroh formalism give the general solution and the final solution for some problems need to be determined by the boundary condition; while the hamilton system give the final solution directly in the series solution without the assumption of the solution. However, the hamilton system has a restriction in the shape--strip domain, it may be overcome this by the conformal tranformation, but, in that case, the solution may become so complex that it loses the advantage of the closed-form solution. </span>
</p>
<p>
<span>Thank you for your attention, any comments is appreciated.</span><span> </span>
</p>
</div></div></div><div class="field field-name-upload field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><table class="sticky-enabled">
<thead><tr><th>Attachment</th><th>Size</th> </tr></thead>
<tbody>
<tr class="odd"><td><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="http://imechanica.org/files/Hamiltonian%20system%20based%20Saint%20Venant%20solutions%20for%20multi-layered%20composite%20plane%20anisotropic%20plates.pdf" type="application/pdf; length=132840" title="Hamiltonian system based Saint Venant solutions for multi-layered composite plane anisotropic plates.pdf">Hamiltonian system based Saint Venant solutions for multi-layered composite plane anisotropic plates.pdf</a></span></td><td>129.73 KB</td> </tr>
<tr class="even"><td><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="http://imechanica.org/files/Plane%20elasticity%20in%20sectorial%20domain%20and%20the%20Hamiltonian%20system%20.pdf" type="application/pdf; length=482125" title="Plane elasticity in sectorial domain and the Hamiltonian system .pdf">Plane elasticity in sectorial domain and the Hamiltonian system .pdf</a></span></td><td>470.83 KB</td> </tr>
<tr class="odd"><td><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="http://imechanica.org/files/A%20state%20space%20formalism%20for%20anisotropic%20elasticity.%20Part%20I%20Rectilinear%20anisotropy%20.pdf" type="application/pdf; length=134677" title="A state space formalism for anisotropic elasticity. Part I Rectilinear anisotropy .pdf">A state space formalism for anisotropic elasticity. Part I Rectilinear anisotropy .pdf</a></span></td><td>131.52 KB</td> </tr>
<tr class="even"><td><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="http://imechanica.org/files/A%20state%20space%20formalism%20for%20anisotropic%20elasticity.%20Part%20II%20Cylindrical%20anisotropy%20.pdf" type="application/pdf; length=166593" title="A state space formalism for anisotropic elasticity. Part II Cylindrical anisotropy .pdf">A state space formalism for anisotropic elasticity. Part II Cylindrical anisotropy .pdf</a></span></td><td>162.69 KB</td> </tr>
</tbody>
</table>
</div></div></div>Sun, 10 Aug 2008 13:28:29 +0000Teng zhang3671 at http://imechanica.orghttp://imechanica.org/node/3671#commentshttp://imechanica.org/crss/node/3671wave propagation in Hamilton Systems
http://imechanica.org/node/3400
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/2524">wave propagation Hamilton Systems</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
I am a junior graduate student now, and very interesting in wave motion. My advisor Prof. Zhong wanxie and his PHD student qiang Gao have developed a precise numerical technique to solve the Rayleigh wave frequency equation, which can avoid the missing root. They did a systematic work involving surface wave propagation in a transversely isotropic stratified solid resting on an elastic semi-infinte space, wave propagation in the anisotropic layered media and the propagation of stationary and non-stationary random waves in a viscoelastic, transversely isotropic and stratified half space.
</p>
<p>
The essence of these work is the idea of introducing dual variables, then tranforming them into duality system. The surface wave frequency equation was solved via the precise integration method (PIM) and the extended Wittrick-Williams (W-W) algorithm. As for the third problem, they transformed the random wave problems into deterministic problems and transformed governing equations of viscoelastic materials into Hamilton equations in which the dual variables were specially chosen due to the viscoelastic. And pseudo-excitation method (PEM) was used for the random waves solution.
</p>
<p>
I am just following their work and maybe do some work based on that in the future. We have some puzzles now. Although we think our numerical technique has advantage, we find that it is a little difficult in extension--not many people used these methods. So I want to discuss the advantage and disadvantage of these symplectic methods and the traditional methods, and hope to hearing the discussion from others.
</p>
<p>
Advantage
</p>
<p>
1. precise and avoid the missing root for the surface wave frequency equation
</p>
<p>
2. the same simple formula and uniform steps for anisotropic layered media and the isotropic
</p>
<p>
3. high efficent for random wave problems owe to PEM
</p>
<p>
Disadvantage
</p>
<p>
1. strict restriction of the geometric shape--only for layered structure now
</p>
<p>
2. only for the linear elastic now, most time the traditional methods are efficient enough in these areas
</p>
<p>
3. people are not very used to these, so they maybe not want to change their familiar method to these new ones
</p>
<p>
I think the last two disadvantages may be the reason for the less use of these new methods. We are trying to find new areas to use these methods such as piezoelectric crystals, phononic/photonic crystals now, however, we have not found a clear idea by now. I want to know the main weakness of the traditional methods of the wave propagation, how can we improved our methods for more widely used and some potential use of these methods.
</p>
<p>
That is just my own opinion. Thank you for your attention and I really look forward to listening to your opinions.
</p>
</div></div></div><div class="field field-name-upload field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><table class="sticky-enabled">
<thead><tr><th>Attachment</th><th>Size</th> </tr></thead>
<tbody>
<tr class="odd"><td><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="http://imechanica.org/files/A%20precise%20method%20for%20solving%20wave%20propagation%20problems%20in%20layered%20anisotropic%20media%20.pdf" type="application/pdf; length=301850" title="A precise method for solving wave propagation problems in layered anisotropic media .pdf">A precise method for solving wave propagation problems in layered anisotropic media .pdf</a></span></td><td>294.78 KB</td> </tr>
</tbody>
</table>
</div></div></div>Wed, 25 Jun 2008 12:40:23 +0000Teng zhang3400 at http://imechanica.orghttp://imechanica.org/node/3400#commentshttp://imechanica.org/crss/node/3400Questions about symplectic conservation of MD
http://imechanica.org/node/2849
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
MD method is widely employed in different areas. However, as we all known that the limitation in timescales and length scales and the stiffness problem due to high frequency molecular vibrations are still important and difficult issues to be solved. While, characteristics of symplectic conservation is important for numerical methods. I found that only a few leteratures discussed this issue, and seldom new symplectic methods were widely adopted expect for the classical leap-frog Verlet algorithm whose characteristics of symplectic conservation was proofed later.
</p>
<p>
I have several questios as fellows:
</p>
<p>
Which are the key issues of the development of MD?
</p>
<p>
Whether symplectic conservation is still not paid enough attention for the reason that the time scales limitation is so short that the dissipative effect is still not obvious?
</p>
<p>
Can the symplectic algorithm paly an important role in the development of MD.
</p>
<p>
I am not familiar with this area , if anything wrong, please point it out.
</p>
<p>
Best regards
</p>
<p>
teng zhang
</p>
</div></div></div>Fri, 07 Mar 2008 11:17:43 +0000Teng zhang2849 at http://imechanica.orghttp://imechanica.org/node/2849#commentshttp://imechanica.org/crss/node/2849