iMechanica - inverse problems
https://imechanica.org/taxonomy/term/1818
enOpen Postdoctoral Position - University of Pittsburgh
https://imechanica.org/node/24731
<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/73">job</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/12421">#Post-doc</a></div><div class="field-item odd"><a href="/taxonomy/term/162">computational mechanics</a></div><div class="field-item even"><a href="/taxonomy/term/1818">inverse problems</a></div><div class="field-item odd"><a href="/taxonomy/term/19">biomechanics</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" align="center">OPEN POSITION</p>
<p class="MsoNormal" align="center">POSTDOCTORAL RESEARCHER</p>
<p class="MsoNormal" align="center"><em>Computational Diagnostics and Inverse Mechanics</em></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">A <em>postdoctoral appointment </em>is available in the <em>Computational Diagnostics and Inverse Mechanics (CDIM) </em>research group under the supervision of Dr. John C. Brigham at the University of Pittsburgh Department of Civil and Environmental Engineering. </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">A highly motivated researcher is sought for this unique opportunity to develop existing research areas and help to build exciting new directions within the <em>CDIM </em>group. The <em>CDIM </em>group is actively involved in a number of projects covering a diverse array of applications, including shape and kinematic analysis of medical imaging data for diagnosis of cardiovascular disease, novel design concepts and optimal design strategies for smart material morphing structures, efficient and accurate computational nondestructive material characterization algorithms, and reduced-order modeling for simulating multi-physics behaviors.</p>
<p class="MsoNormal"><em> </em></p>
<p class="MsoNormal">A specific ongoing project involves development and implementation of shape-based methods to evaluate changes in the function of the human heart, including both direct statistical analysis as well as inverse estimation of heart wall mechanical properties. Another ongoing project is to develop complementary experimental and computational procedures to evaluate mechanical properties of cell/tissue constructs. The potential areas for further expansion include additional applications of inverse problems in mechanics of biological or artificial structures, with specifics depending upon the particular interests and capabilities of the candidate.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">The successful applicant will:</p>
<p class="MsoListParagraphCxSpFirst"><span>·<span> </span></span>possess or be on track to complete a PhD in a relevant STEM discipline and have an excellent academic record. </p>
<p class="MsoListParagraphCxSpMiddle"><span>·<span> </span></span>have expertise in computational mechanics and numerical methods.</p>
<p class="MsoListParagraphCxSpMiddle"><span>·<span> </span></span>have experience in coding with one or more software languages (e.g., Python, C++, Fortran, and/or MATLAB). </p>
<p class="MsoListParagraphCxSpLast"><span>·<span> </span></span>have a strong work ethic and time management skills along with the ability to work independently and within a multidisciplinary team as required.</p>
<p class="MsoNormal">Additional experience with pattern recognition and machine learning as well as numerical optimization is highly desirable. The candidate should have completed their Ph.D. prior to the start date of the position<span>.</span> Candidates from underrepresented minority groups and women are strongly encouraged to apply for this position. </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">The initial appointment will be for one year with the possibility of extension. The start date is flexible, with a preference for candidates capable of starting early in 2021 or <em>as soon as possible</em>. Review of applications will begin immediately and will continue until the position is filled.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Your application should include:</p>
<p class="MsoListParagraphCxSpFirst"><span>·<span> </span></span>Cover letter</p>
<p class="MsoListParagraphCxSpMiddle"><span>·<span> </span></span>Curriculum Vitae</p>
<p class="MsoListParagraphCxSpMiddle"><span>·<span> </span></span>1-page statement of your career goals and how this position will help you achieve your goals</p>
<p class="MsoListParagraphCxSpLast"><span>·<span> </span></span>Contact information for three references</p>
<p class="MsoNormal"><em> </em></p>
<p class="MsoNormal"><strong><em>Applications should be submitted at join.pitt.edu to faculty position 20005285.</em></strong></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">For further information or questions about this position you may contact: Dr. John Brigham directly (<a href="mailto:brigham@pitt.edu">brigham@pitt.edu</a>).</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">The University of Pittsburgh is an Affirmative Action/ Equal Opportunity Employer and values equality of opportunity, human dignity and diversity, EOE, including disability/vets.</p>
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</div></div></div>Tue, 17 Nov 2020 16:06:53 +0000johnbrigham24731 at https://imechanica.orghttps://imechanica.org/node/24731#commentshttps://imechanica.org/crss/node/24731Data-driven Biomechanics Simulations: Marie Curie Innovative Training Network RAINBOW announces 15 PhD positions open: Early Stage Researcher (ESR) positions for outstanding candidates
https://imechanica.org/node/22189
<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/73">job</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/539">phd</a></div><div class="field-item odd"><a href="/taxonomy/term/19">biomechanics</a></div><div class="field-item even"><a href="/taxonomy/term/5102">real-time</a></div><div class="field-item odd"><a href="/taxonomy/term/350">simulation</a></div><div class="field-item even"><a href="/taxonomy/term/885">modelling</a></div><div class="field-item odd"><a href="/taxonomy/term/1818">inverse problems</a></div><div class="field-item even"><a href="/taxonomy/term/11415">data-driven</a></div><div class="field-item odd"><a href="/taxonomy/term/11435">Big Data</a></div><div class="field-item even"><a href="/taxonomy/term/7126">data</a></div><div class="field-item odd"><a href="/taxonomy/term/11581">data science</a></div><div class="field-item even"><a href="/taxonomy/term/1499">surgical simulation</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><a href="https://euraxess.ec.europa.eu/jobs/283244">https://euraxess.ec.europa.eu/jobs/283244</a></p>
<ul><li>
<p>Candidates will be working as part of the Rapid Biomechanics Simulation for Personalized Clinical Design (RAINBOW) MSCA European Training Network, awarded by the European Union's Horizon 2020 research and innovation program. The network consists of 5 universities, 1 hospital, 8 industrial partners, located in Denmark, Spain, Luxembourg, England, France and Germany. The purpose of the network is to educate 15 ESRs through common dedicated training activities and research stays. The RAINBOW research objective is to realize the full potential of computational medicine and ICT to arrive at patient-specific simulation models that are rapidly set, are easy-to-use by clinical experts and do not require assistance from technicians. Candidates will be exposed to clinical practice and get close to patients and clinical experts while working both with theory and creating software, design tools, to be used by clinical experts</p>
</li>
<li><span>ESR1</span> Hip Growth Simulator (University of Copenhagen, DK)</li>
<li><span>ESR2</span> Hip Growth Simulator (Hvidovre Hospital, DK)</li>
<li><span>ESR3</span> Dynamic Jaw Simulator (3Shape, DK)</li>
<li><span>ESR4</span> Real-Time Physically-based Registration of Pre- and Intra Operative Medical Images (University of Copenhagen, DK)</li>
<li><span>ESR5</span> The Spinal Muscle Simulator (Aalborg University, DK)</li>
<li><span>ESR6</span> Breast Modelling and Simulation for Better Cancer Treatment (University of Luxembourg, LU)</li>
<li><span>ESR7</span> Spine Inverse Modelling for Scoliosis Brace Design (Universidad Rey Juan Carlos, ES)</li>
<li><span>ESR8</span> Biological Membrane Cutting and Tearing Simulation within Clinical Time Scales with Application to Cataract Surgery (University of Luxembourg, LU)</li>
<li><span>ESR9</span> Interactive Optimization-based Design of Cardiovascular Devices (Universidad Rey Juan Carlos, ES)</li>
<li><span>ESR10</span> Optimization-Based Fusion of Surgical Planning Data for Intraoperative Navigation (GMV, ES)</li>
<li><span>ESR11</span> Surgical Planning through Hands-on Medical Image Editing (Universidad Rey Juan Carlos, ES)</li>
<li><span>ESR12</span> Goal-oriented Error Controlled Super and Sub-geometric Finite and Boundary Element Methods for Patient-Specific Simulation of Cutting (Synopsys – Simpleware Product Group, UK)</li>
<li><span>ESR13</span> Identifying Patient Specific Material Models and Parameters using Adjoint-based Inverse Modelling Approaches: Model Selection and Parameter Identification on Phantom Gels (University of Luxembourg, LU)</li>
<li><span>ESR14</span> Meta Modelling for Soft Tissue Contact and Cutting Simulation (Cardiff University, UK)</li>
<li><span>ESR15</span> Baysian Geometrical Uncertainty Quantification for Soft Tissue Biomechanics Simulations (Synopsys – Simpleware Product Group, UK)</li>
<li>
<p>Starting date is 1 September 2018 or as soon as possible thereafter. Appointment is for a period of 36 months, includes enrollment in a Doctorate program and is expected to lead to a PhD dissertation. The scholarships requires a Master's degree in Computer Science or a field providing equivalent qualifications, at the time of taking up the position.</p>
<p><span><em>Further details on each position, requirements and submission of application via the hosting institution’s specific job add. Individual job adds available at </em></span><a href="http://rainbow.ku.dk/open-positions/"><span><em>http://rainbow.ku.dk/open-positions/</em></span></a></p>
<p><span>Benefits:</span> The ESRs will be employed by the host institution and have the benefits provided for in the MSCA-ITN early career fellowship regulations, including a competitive remuneration (exact salary will be calculated per country and will contemplate living and mobility allowances and possibly family allowances). They will receive scientific skills in biomechanics simulation and computational medicine and specialized courses and transferable skills. S/he will be supervised by a main supervisor and a co-supervisor. Also, all the students will participate in short term stays in collaborative organisations and industries within the network (secondments).</p>
<p><span>Mobility rule and eligibility criteria:</span> Since the scholarship is part of the MSCA European Training Network programme candidates must - at the date of recruitment – be an “Early Stage Researcher” (i.e. in the first 4 years of his/her research career and not have a doctoral degree) and cannot have resided in the country of their host organisation for more than 12 months in the three years immediately before the recruitment.</p>
</li>
</ul></div></div></div>Sat, 03 Mar 2018 12:41:03 +0000Stephane Bordas22189 at https://imechanica.orghttps://imechanica.org/node/22189#commentshttps://imechanica.org/crss/node/22189Postdoctoral position on: Inversion in nonlinear elastodynamics with application to the imaging of damaged media - CNRS & Aix-Marseille University, France
https://imechanica.org/node/21624
<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/73">job</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/11797">nonlinear waves</a></div><div class="field-item odd"><a href="/taxonomy/term/1818">inverse problems</a></div><div class="field-item even"><a href="/taxonomy/term/3982">imaging</a></div><div class="field-item odd"><a href="/taxonomy/term/11798">scientific computing</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>A one-year postdoctoral position is available at the Laboratory of Mechanics & Acoustics, CNRS & Aix-Marseille University, France.</p>
<p> </p>
<p>This project focuses on the propagation of waves in damaged solids, which involves nonlinear phenomena. The proposal aims at studying the inverse problem of parameter identification from elastodynamic data to quantify the nonlinear properties of the propagation medium. The work will address the theoretical and numerical aspects of the problem.</p>
<p>The fields of expertise of the candidate should include applied mathematics and theoretical mechanics.</p>
<p> </p>
<p>More information can be found in the attachment.
</p><p> </p>
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</div></div></div>Tue, 26 Sep 2017 08:51:37 +0000Cédric Bellis21624 at https://imechanica.orghttps://imechanica.org/node/21624#commentshttps://imechanica.org/crss/node/21624Postdoctoral Research Position in Computational Inverse Problems and Optimization at Duke University
https://imechanica.org/node/18802
<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/73">job</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/1818">inverse problems</a></div><div class="field-item odd"><a href="/taxonomy/term/3632">Optimization</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>This position is now closed.</p>
</div></div></div>Wed, 02 Sep 2015 19:47:26 +0000waquino18802 at https://imechanica.orghttps://imechanica.org/node/18802#commentshttps://imechanica.org/crss/node/18802Postdoctoral position on: Identification of elastic microstructures from full-field measurements - CNRS & Aix-Marseille University France
https://imechanica.org/node/17848
<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/73">job</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/1818">inverse problems</a></div><div class="field-item odd"><a href="/taxonomy/term/3982">imaging</a></div><div class="field-item even"><a href="/taxonomy/term/8753">identification</a></div><div class="field-item odd"><a href="/taxonomy/term/8754">full-field measurements</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>A one-year postdoctoral position is available at the Laboratory of Mechanics & Acoustics, CNRS & Aix-Marseille University, France.</p>
<p>The project focuses on image-based identification problems for physical quantities of interest in solid mechanics within the framework of optical measurement methods for complex manufactured materials. The guideline objective is to develop an identification framework for multiscale, heterogeneous and anisotropic media.</p>
<p>More information can be found in the attachment.</p>
<p>Application deadline: February 28th, 2015.</p>
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</div></div></div>Wed, 28 Jan 2015 14:09:31 +0000Cédric Bellis17848 at https://imechanica.orghttps://imechanica.org/node/17848#commentshttps://imechanica.org/crss/node/17848Journal Club Theme of January 2015: Topology Optimization for Materials Design
https://imechanica.org/node/17756
<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/2840">Topology optimization</a></div><div class="field-item odd"><a href="/taxonomy/term/8060">materials design</a></div><div class="field-item even"><a href="/taxonomy/term/10288">Inverse Homogenization</a></div><div class="field-item odd"><a href="/taxonomy/term/1818">inverse problems</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>Processing technologies are rapidly advancing and manufacturers now have the ability to control material architecture, or topology, at unprecedented length scales. This opens up the design space and provides exciting opportunities for tailoring material properties through design of the material’s topology. But as seen many times in history with advancements in materials and processing technologies, the natural default is to rely on familiar shapes and structure topologies. A new manufacturing process perhaps lets us create an existing shape at lower cost; increases in base material strength allows us to thin member sizes and reduce material usage in an existing design. But what is missed in defaulting to the familiar is that new processes may enable realization of previously unachievable topologies, or that thinning members to leverage higher base material strengths may ultimately lead to issues of stability that can be addressed more efficiently with new topologies. Technological advancements may thus not be fully leveraged unless we are willing to re-think design - similar evidence can be found in the evolution of structural forms [1]. </p>
<p>Topology optimization offers an alternative to ad hoc, intuition, and experience-driven design approaches, providing a systematic, rigorous framework for exploring the design space. The goal, put simply, is to identify whether or not material exists at each point in space within the design domain. For periodic materials, the design domain is the characteristic unit cell and one uses some form of upscaling to estimate the effective properties of the bulk material, which are the properties to be optimized and/or constrained. This upscaling is performed numerically, typically with finite elements, and the goal of determining material concentration at “every point in space” then becomes determining material concentration in every finite element. The connectivity of the elements containing material then ends up defining the topology. In this sense, one can think of topology optimization as the process of building the material unit cell from scratch out of white and black Legos, where the white bricks indicate voids and the black bricks indicate solid material. Computationally, we can change the color of any brick, from white to black or black to white, evolving topology as we do so. These “Legos” may also come in an array of colors (as in design of composite unit cells containing multiple materials) and need not be prismatic, but can be any shape or combination of shapes and sizes (as in unstructured meshes). </p>
<p>The capability to alter the connectivity is what differentiates topology optimization from shape and sizing optimization. Consider, for example, materials that can be characterized as micro-truss lattices, which have garnering significant interest [2-5]. For a given truss topology (pyramidal, tetrahedral, octet), one can optimize the size of the truss struts using sizing optimization, optimize the angle of struts with geometric optimization, or even add strut tapering with shape optimization. The goal of topology optimization, on all the other hand, is to consider all of these, in addition to the actual connectivity of the truss system. This of course adds computational expense, but also significant design freedom. </p>
<p>To fully leverage this freedom, the design problem is posed and solved as a formal optimization problem. The objective function is some scalar metric of material performance (effective modulus, effective thermal conduction, mass, etc.) and the constraints can include bounds on such metrics. Additionally, the governing mechanics are embedded in this optimization formulation - both the mechanics governing the unit cell behavior and the upscaling of these mechanics to estimate the material’s effective properties. </p>
<p>The resulting optimization problem is discrete - what material is located in each finite element - and one can imagine if we are allowing topological evolution and fine scale features we need a high dimension design space (lots and lots of design variables). Traditionally, the number of design variables scales with the number of finite elements (although this need not always be the case), and so hundreds of thousands of design variables is quite typical. Random search algorithms tend to fail in such high dimensions, giving strong preference for gradient-based optimizers. The Method of Moving Asymptotes, for example, is the most widely-used in the field [6]. This requires that the discrete condition on the design variables be relaxed (we must allow mixtures of materials in each element (grey Lego bricks)), we must approximate the constitutive behavior of such mixtures (interpolate the mechanics), and further must mathematically make discrete black-white solutions ‘more desirable’ than mixtures. The SIMP method, essentially a power-law approach, is the most popular approach for achieving this [7,8]. Gradient-based optimizers also require gradients (of course!), or a sensitivity analysis, which are typically estimated using adjoint methods or direct differentiation (see e.g., [9,10]). To add further challenge, optimization has the wonderful trait of revealing deficiencies in your problem formulation or underlying numerical instabilities [11], although we now have a good handle on many of these.</p>
<p>So, to summarize, we discretize the domain serving as the material's unit cell and construct the design variables to indicate each element’s composition. We perform an upscaling of the resulting unit cell design to estimate effective material properties, and perform a sensitivity analysis to indicate how each design variable will influence these effective properties. The output of these analyses are used by the gradient-based optimizer to change the design and evolve the topology. Figure 1 illustrates the general framework and illustrates that the design may evolve from an uneducated, ‘blurry’ guess to a clear representation of topology (note we’ve traded in greyscale Legos for color).</p>
<p> </p>
<p><img src="http://www.ce.jhu.edu/topopt/media/MaterialTopOpt_Guest.jpg" alt="" width="600" height="207" /></p>
<p> </p>
<p><strong>Examples in Literature</strong></p>
<p>The pioneering work of Ole Sigmund at Technical University of Denmark was the first to apply the topology optimization strategy to materials design. Sigmund discretized the design domain with truss and frame elements and optimized the connectivity of these elements (essentially building the unit cell out of K’nex, rather than Legos). He successfully designed materials with tailored elastic properties, including material topologies with negative Poisson’s ratio [12-14]. These ideas were later extended to continuum representations of material topology, where significantly more design freedom is introduced. This included porous materials with negative Poisson’s ratio ([12], and later fabricated and tested at -0.8 in [15]) and optimized elastic moduli [16]. It should be mentioned that elastic properties have also been optimized for composite materials [17] and functionally graded materials [18]. </p>
<p>Although its roots are in solid mechanics, topology optimization has undergone rapid expansion to consider other fields over the past decade. Material design examples include three-phase materials with negative thermal expansion [19], optimizing electric and thermal conduction of composites [20], fluid permeability of porous materials [21], and various combinations as may be needed in multifunctional materials, such as elastic moduli and thermal conduction [22,23] and elastic moduli and fluid permeability [24]. Various combinations of the latter have been manufactured and proposed for bone scaffolds [25-27]. A few additional examples include the design of electromagnetic metamaterials with negative permeability [28,29] and phononic materials [30,31]; a recent review of materials design with topology optimization can be found in [32].</p>
<p>It is important to also note these topology optimization problems are nonconvex, making it impossible to guarantee identification of a global minimum. There are, however, many examples of solutions being shown (computationally) to achieve theoretical bounds, such Hashin-Shtikman bounds for elastic moduli (e.g., [12,16,33]) and Gibiansky-Torquato stiffness-conductivity bounds in [22], giving confidence in the optimality of solutions. Interestingly, this design tool can also be used to influence the development of theoretical or estimated bounds. In [19], Sigmund and Torquato tell an interesting story that topology optimization was unable to identify solutions near the Schapery-Rosen-Hashin bounds on effective thermal strain coefficient for three-phase materials, ultimately motivating further study and development of new, tighter bounds [34]. Topology optimization was also recently used to probe the relationship between elastic stiffness and permeability in an attempt to estimate the upper bounds of this cross-property space [33]. </p>
<p><strong>Manufacturability</strong></p>
<p>The primary disadvantage of the design freedom inherent in topology optimization is that solutions may be complex structures that are quite challenging, or even impossible, to manufacture. This has been one of the major obstacles in bringing topology optimization into practice, and has garnered significant attention by topology optimization researchers. In the last ~10 years, various algorithms have been developed for controlling the minimum and maximum length scale of designed features in materials [35-39] so as to match manufacturing resolution capabilities, for handling size and shape restrictions in inclusion-based materials [40,41], and for materials manufactured by 3D weaving processes [42]. Algorithms have also been developed for other manufacturing processes (machining, casting, etc), but thus far have not been extended to 3D periodic material domains. It must be noted that while 3D printing has greatly opened up the space of what is realizable, manufacturing constraints will be omnipresent and require treatment within the optimization formulation if solutions are to be optimized for as-built conditions. </p>
<p><strong>Future Challenges </strong></p>
<p>As the fundamental need for topology optimization is computationally efficient upscaling of unit cell mechanics, it is not surprising that the above-mentioned material design works assume deterministic conditions and domains governed by linear continuum mechanics, enabling implementation of (for example) elastic homogenization [43,44]. However, topology optimization methods and algorithms for ‘structure’ design (where design is conducted at the same scale that performance is defined) are rapidly advancing, including algorithms for nonlinear mechanics [45-48] and designing robust structures in the presence of material and geometric uncertainties [49-55]. Some of these ideas have been implemented in the material domains recently, such as design for negative Poisson’s ratio under geometric uncertainties in the form of thinning or thickening of unit cell features [56] and optimizing energy absorption metrics in cellular materials [57], and it is fully expected that this trend will continue as computational methods for upscaling under these conditions advance. Driving design at even smaller scales, beyond continuum scale ‘architecture’, such as in [58], is another challenge that surely will be drawing interest in the future, particularly as our understanding of and control over processing continues to grow.</p>
<p>In summary, topology optimization is a systematic tool for guiding distribution of base materials within a design domain, such as the unit cell of a periodic material. Its power comes from the fact that (1) design decisions are driven by mathematical programming, rather than ad hoc rules, and (2) that design evolves in a ‘free-form’ manner, where structural connectivity (topology) is free to change during the design evolution. These properties enable exploration into new regions of the design space and, potentially, enable the discovery of new unit cell topologies offering previously unrealizable combinations of effective material properties. </p>
<p>For those that want to learn more, in addition to the above referenced works, you might consider a recent broad survey of applications and methods [59], an in-depth discussion of the properties of topology optimization methods and algorithms [60], and some basic MATLAB code [61] that is excellent to play with.</p>
<p> </p>
<p><strong>References</strong></p>
<p>1. Billington D.P. (1983). The Tower and The Bridge. Princeton University Press, Princeton, NJ.</p>
<p>2. Fleck N.A., Deshpande V.S., and Ashby M.F. (2011). Micro-architectured materials: past, present and future. Proceedings of the Royal Society A 466: 2495–2516.</p>
<p>3. Wadley H.N.G. (2006). Multifunctional periodic cellular metals. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364: 31-68.</p>
<p>4. Schaedler T.A., Jacobsen A.J., Torrents A., Sorensen A.E., Lian J., Greer J.R., Valdevit L., and Carter W. B. (2011). Ultralight metallic microlattices. Science 334: 962–965. </p>
<p>5. Torrents A., Schaedler T.A., Jacobsen A.J., Carter W.B., and Valdevit L. (2012). Characterization of nickel-based microlattice materials with structural hierarchy from the nanometer to the millimeter scale. Acta Materialia 60: 3511–3523.</p>
<p>6. Svanberg K. (1987). The method of moving asymptotes - a new method for structural optimization. International Journal for Numerical Methods in Engineering 24: 359-373.</p>
<p>7. Bendsøe M.P. (1989) Optimal shape design as a material distribution problem. Structural Optimization 1: 193– 202.</p>
<p>8. Zhou M., Rozvany G.I.N. (1991) The COC algorithm, part II: Topological, geometry and generalized shape optimization. Computer Methods in Applied Mechanics and Engineering 89: 309–336.</p>
<p>9. Michaleris P., Tortorelli D.A., and Vidal C.A. (1994) Tangent operators and design sensitivity formulations for transient non-linear coupled problems with applications to elastoplasticity. International Journal for Numerical Methods in Engineering 37: 2471–2499.</p>
<p>10. Jameson A. (2001). A perspective on computational algorithms for aerodynamic analysis and design. Progress in Aerospace Sciences 37: 197-243.</p>
<p>11. Sigmund O., and Petersson J. (1998). Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima, Structural Optimization 16: 68–75.</p>
<p>12. Sigmund O. (1994). Design of material structures using topology optimization. Ph.D. Thesis, Department of Solid Mechanics, Technical University of Denmark.</p>
<p>13. Sigmund O. (1994). Materials with prescribed constitutive parameters: an inverse homogenization problem. International Journal of Solids and Structures 31: 2313–2329. </p>
<p>14. Sigmund O. (1995). Tailoring materials with prescribed elastic properties. Mechanics of Materials 20: 351-368.</p>
<p>15. Larsen U. D., Sigmund O., and Bouwstra S. (1997). Design and fabrication of compliant mechanisms and material structures with negative Poissons ratio. Journal of MicroElectroMechanical Systems 6: 99-106.</p>
<p>16. Sigmund O. (2000). A new class of extremal composites. Journal of the Mechanics and Physics of Solids 48: 397–428. </p>
<p>17. Gibiansky L.V., and Sigmund O. (2000). Multiphase composites with extremal bulk modulus. Journal of the Mechanics and Physics of Solids 48: 461–498. </p>
<p>18. Paulino G.H., Silva E.C.N., and Le C.H. (2009). Optimal design of periodic functionally graded composites with prescribed properties. Structural and Multidisciplinary Optimization 38: 469-489.</p>
<p>19. Sigmund O., and Torquato S. (1997). Design of materials with extreme thermal expansion using a three-phase topology optimization method. Journal of the Mechanics and Physics of Solids 45(6): 1037–1067. </p>
<p>20. Torquato S., Hyun S., and Donev A. (2002). Multifunctional composites: optimizing microstructures for simultaneous transport of heat and electricity. Physical Review Letters 89: 266601-1–266601-4. </p>
<p>21. Guest J.K., and Prévost J.H. (2007). Design of maximum permeability material structures. Computer Methods in Applied Mechanics and Engineering 196: 1006–1017.</p>
<p>22. Challis V.J., Roberts A.P., and Wilkins A.H. (2008). Design of three dimensional isotropic microstructures for maximized stiffness and conductivity. International Journal of Solids and Structures 45: 4130–4146. </p>
<p>23. de Kruijf N., Zhou S., Li Q., and Mai Y.-W. (2007). Topological design of structures and composite materials with multiobjectives. International Journal of Solids and Structures 44: 7092–7109. </p>
<p>24. Guest J.K., and Prévost J.H. (2006). Optimizing multifunctional materials: design of microstructures for maximized stiffness and fluid permeability. International Journal of Solids and Structures 43: 7028–7047.</p>
<p>25. Hollister S.J. (2009). Scaffold design and manufacturing: from concept to clinic. Advanced Engineering Materials 21: 3330–3342. </p>
<p>26. Challis V.J., Roberts A.P., Grotowski J.F., Zhang L.C., and Sercombe, T.B. (2010). Prototypes for bone implant scaffolds designed via topology optimization and manufactured by solid freeform fabrication. Advanced Engineering Materials 12: 1106–1110.</p>
<p>27. Chen Y., Zhou S., and Li Q. (2011). Microstructure design of biodegradable scaffold and its effect on tissue regeneration. Biomaterials 32: 5003–5014. </p>
<p>28. Diaz A. and Sigmund O. (2010). A topology optimization method for design of negative permeability metamaterials. Structural and Multidisciplinary Optimization 41: 163–177.</p>
<p>29. Zhou S., Li W., Chen Y., Sun G., and Li Q. (2011). Topology optimization for negative permeability metamaterials using level-set algorithm. Acta Materialia 59: 2624-2636,</p>
<p>30. Sigmund O. and Jensen J.S. (2003). Systematic design of phononic band–gap materials and structures by topology optimization. Philosophical Transactions of the Royal Society A 361: 1001–1019.</p>
<p>31. Rupp C.J., Evgrafov A., Maute K., and Dunn M.L. (2007). Design of Phononic Materials/Structures for Surface Wave Devices Using Topology Optimization. Structural and Multidisciplinary Optimization, 34: 111-122.</p>
<p>32. Cadman J., Zhou S., Chen Y., and Li Q. (2013). On design of multi-functional microstructural materials. Journal of Materials Science 48: 51–66.</p>
<p>33. Challis V.J., Guest J.K., Grotowski J.F., and Roberts A.P. (2012). Computationally generated cross-property bounds for stiffness and fluid permeability using topology optimization, International Journal of Solids and Structures 49: 3397-3408.</p>
<p>34. Gibiansky L.V. and Torquato S. (1997) Thermal expansion of isotropic multi-phase composites and polycrystals. Journal of the Mechanics and Physics of Solids 45: 1223-1252. </p>
<p>35. Poulsen T.A. (2003). A new scheme for imposing minimum length scale in topology optimization. International Journal of Numerical Methods in Engineering 57: 741–760.</p>
<p>36. Guest J.K., Prévost J.H., and Belytschko T. (2004). Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International Journal for Numerical Methods in Engineering 61: 238-254.</p>
<p>37. Sigmund O (2007) Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33: 401–424 </p>
<p>38. Guest J.K. (2009). Topology optimization with multiple phase projection. Computer Methods in Applied Mechanics and Engineering 199: 123-135.</p>
<p>39. Guest J.K. (2009). Imposing maximum length scale in topology optimization. Structural and Multidisciplinary Optimization. 37: 463-473. </p>
<p>40. Guest J.K. (2015). Optimizing Discrete Object Layouts in Structures and Materials: A Projection-Based Topology Optimization Approach. Computer Methods in Applied Mechanics and Engineering 283: 330-351.</p>
<p>41. Ha S. and Guest J.K. (2014). Optimizing inclusion shapes and patterns in periodic materials using Discrete Feature Projection. Structural and Multidisciplinary Optimization 50: 65-80.</p>
<p>42. Zhao L., Ha S.H., Sharp K.W., Geltmacher A.B., Fonda R.W., Kinsey A., Zhang Y., Ryan S., Erdeniz D., Dunand D.C., Hemker K.J., Guest J.K., and Weihs T.P. (2014). Permeability measurements and modeling of topology-optimized metallic 3D woven lattices. Acta Materialia 81: 326-336.</p>
<p>43. Bensoussan A., Lions J., and Papanicolaou G. (1978). Asymptotic Analysis for Periodic Structures. Elsevier, North-Holland, Amsterdam. </p>
<p>44. Sanchez-Palencia, E. (1980). Non-homogeneous Media and Vibration Theory. Lecture Notes in Physics, vol. 127. Springer, Berlin. </p>
<p>45. Maute K., Schwarz S., and Ramm E. (1998) Adaptive topology optimization of elastoplastic structures. Structural Optimization 2: 81-91.</p>
<p>46. Buhl T., Pedersen C.B.W., and Sigmund O. (2000). Stiffness design of geometrically nonlinear structures using topology optimization. Structural and Multidisciplinary Optimization 19: 93-104.</p>
<p>47. Bruns T.E., and Tortorelli D.A. (2001). Topology optimization of non-linear elastic structures and compliant mechanisms, Computer Methods in Applied Mechanics and Engineering 190: 3443–3459.</p>
<p>48. Wang F., Lazarov B.S., Sigmund O., Jensen J.S. (2014). Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems. Computer Methods in Applied Mechanics and Engineering 276: 453-472.</p>
<p>49. Guest J.K. and Igusa T. (2008). Structural optimization under uncertain loads and nodal locations. Computer Methods in Applied Mechanics and Engineering, 198(1):116-124.</p>
<p>50. Sigmund O (2009) Manufacturing tolerant topology optimization. Acta Mechanica Sinica 25: 227–239.</p>
<p>51. Chen S., Chen W., Lee S., (2010). Level set based robust shape and topology optimization under random field uncertainties, Structural and Multidisciplinary Optimization 41: 507–524. </p>
<p>52. Wang F., Jensen J.S., and Sigmund O. (2011). Robust topology optimization of photonic crystal waveguides with tailored dispersion properties. Journal of the Optical Society of America B: Optical Physics 28(3): 387–397.</p>
<p>53. M. Schevenels, B. S. Lazarov, and O. Sigmund (2011). Robust topology optimization accounting for spatially varying manufacturing errors. Computer Methods in Applied Mechanics and Engineering 200: 3613–3627.</p>
<p>54. Tootkaboni M., Asadpoure A., and Guest J.K. (2012). Topology Optimization of Continuum Structures under Uncertainty – A Polynomial Chaos Approach. Computer Methods in Applied Mechanics and Engineering 201-204(1): 263-275.</p>
<p>55. Jalalpour M., Guest J.K., and Igusa T. (2013). Reliability-based topology optimization of trusses with stochastic stiffness matrix. Journal of Structural Safety 43: 41-49.</p>
<p>56. Andreassen E., Lazarov B.S., Sigmund O. (2014). Design of manufacturable 3D extremal elastic microstructure. Mechanics of Materials 69: 1-10.</p>
<p>57. Lotfi R., Ha S., Carstensen J.V., and Guest J.K. (2014). Topology Optimization for Cellular Material Design. Proceedings of 2013 MRS Fall Meeting, Boston, MA, 1-6.</p>
<p>58. Evgrafov A., Maute K., Yang R.G., and Dunn M.L. (2009). Topology optimization for nano-scale heat transfer. International Journal for Numerical Methods in Engineering 77: 285-300.</p>
<p>59. Deaton J.D., Grandhi R.V. (2014). A survey of structural and multidisciplinary continuum topology optimization: post 2000. Structural and Multidisciplinary Optimization 49: 1-38.</p>
<p>60. Sigmund O. and Maute K. (2013). Topology optimization approaches: A comparative review. Structural and Multidisciplinary Optimization 48: 1031-1055.</p>
<p>61. Andreassen E., Clausen A., Schevenels M., Lazarov B.S., Sigmund O. (2011). Efficient topology optimization in MATLAB using 88 lines of code. Structural and Multidisciplinary Optimization 43: 1-16.</p>
<p> </p>
</div></div></div>Fri, 09 Jan 2015 19:41:20 +0000Jamie Guest17756 at https://imechanica.orghttps://imechanica.org/node/17756#commentshttps://imechanica.org/crss/node/17756One PhD student position at Department of Civil Engineering, The University of Akron, OH
https://imechanica.org/node/13300
<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/128">education</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/934">Composites</a></div><div class="field-item odd"><a href="/taxonomy/term/1818">inverse problems</a></div><div class="field-item even"><a href="/taxonomy/term/2106">PHD position</a></div><div class="field-item odd"><a href="/taxonomy/term/4050">multiscale stochastic finite element method</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>
Recruiting PhD students at University of Akron, Department of Civil Engineering. Intelligent Structural Engineering and Health Monitoring Group
</p>
<p>
Our website: <a href="http://isehm.mech.uakron.edu/">http://isehm.mech.uakron.edu/</a>
</p>
<p>
Research Area:Stochastic Modeling of Composite Materials, Inverse Problems, Experimental Mechanics.
</p>
<p>
Scholarship program is available for suitable candidate.
</p>
<p>
Applications including CV and PS can be sent to <a href="mailto:gy3@uakron.edu">gy3@uakron.edu</a> Dr. Gunjin Yun
</p>
</div></div></div>Fri, 28 Sep 2012 17:17:02 +0000ShenShang13300 at https://imechanica.orghttps://imechanica.org/node/13300#commentshttps://imechanica.org/crss/node/13300Ph.D. in seismology and geodynamics at ETH Zurich
https://imechanica.org/node/10063
<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/1124">Seismology</a></div><div class="field-item odd"><a href="/taxonomy/term/1552">computation</a></div><div class="field-item even"><a href="/taxonomy/term/1818">inverse problems</a></div><div class="field-item odd"><a href="/taxonomy/term/2656">geology</a></div><div class="field-item even"><a href="/taxonomy/term/5149">geophysics</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>The institute of Geophysics of ETH Zurich is seeking a highly motivated Ph.D. candidate to be working in the domain of seismic imaging of the Earth's interior. Global seismic tomography is a relatively young discipline that rose to prominence in the 1980s and<br />
early 90s, when it consolidated many aspects of plate tectonics and lead to the discovery of lower-mantle subduction and lowermost-mantle large-scale low-shear-velocity provinces. While in the past global tomographers have been concerned with the isotropic velocity of shear or compressional waves, the successful candidate will focus on imaging of seismic anisotropy and of compositional heterogeneity, based on a particularly large and diverse database. A key aspect of the project is its multidisciplinary nature: the student will interact closely with researchers in seismology (<a href="http://www.seg2.ethz.ch/boschil">Lapo Boschi</a> , <a href="http://n.ethz.ch/~tarjen/">Tarje Nissen-Meyer</a> , <a href="http://www.seg.ethz.ch/people/professors/giardind">Domenico Giardini</a> ), mineral physics (<a href="http://www.geopetro.ethz.ch/people/scarmen">Carmen Sanchez-Valle</a> ) and geodynamics (<a href="http://jupiter.ethz.ch/~pjt/">Paul Tackley</a> ). Knowledge of all these disciplines will be gained to then properly interpret seismic imaging results in terms of the Earth's nature, origin and history. Time permitting, computational aspects of the inverse problem (i.e., the adjoint method) will be explored. Applicants must hold a M. Sc., Diploma or equivalent in the geosciences, physics, applied mathematics, computer sciences or related fields. Some familiarity with computer programming and a solid knowledge of English are mandatory. The Institute of Geophysics at ETH Zurich boasts a strong research and teaching environment covering a<br />
wide array of disciplines and Zurich is consistently ranked as one of the cities with highest life quality worldwide. Please consult the<a href="http://www.seg.ethz.ch"> Seismology and Geodynamics</a> web pages or contact Dr.<a href="http://www.seg2.ethz.ch/boschil"> Lapo Boschi</a> for further information. Complete applications must include a curriculum vitae and contact details of two referees familiar with the academic ability of the candidate, and should be emailed to Dr. Boschi: <a href="mailto:lapo@erdw.ethz.ch">lapo@erdw.ethz.ch</a> (electronic PDF format preferred). The search starts now (April 2011) and will continue until the position is filled. Tentative starting date: September 2011.</p>
</div></div></div>Sat, 09 Apr 2011 08:11:47 +0000pippo10063 at https://imechanica.orghttps://imechanica.org/node/10063#commentshttps://imechanica.org/crss/node/10063Journal Club Theme of March 1: Measuring Cellular Tractions
https://imechanica.org/node/2786
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>
Cell tractions are the outcome of the complex process of cytoskeletal force generation that cell uses to maintain structural stability, to sense the physical environment and to propel itself. We are only now beginning to understand the process of cytoskeletal force generation, and we cannot yet say much about the losses in transmission through focal adhesion/integrin complexes (attachment ‘islands’ at the cell-substrate interface), but we can definitely measure the tractions that result from cytoskeletal force generation. The mechanics behind the measurement method might be of interest to the wider audience of iMechanica, as it involves an interesting inverse problem and different solution methods that have incited lively discussions in past years.
</p>
<p>
The main idea is to calculate tractions from the measurement of the deformation they caused in a substrate to which the cell is attached. It is assumed that the in-plane forces and out-of-plane displacements are not coupled, and that, effectively, the out-of-plane forces are negligible.
</p>
<p>
Among the discrete methods, the simplest one uses arrays of microfabricated elastomeric posts whose protein-coated tips act as attachment points for the cells:
</p>
<p>
Tan JL, Tien J, Pirone DM, Gray DS, Bhadriraju K and Chen CS. Cells lying on a bed of micro-needles: An approach to isolate mechanical force. PNAS 100 (4): 1484-1489 (2003).
</p>
<p>
<a href="http://www.pnas.org/cgi/content/full/100/4/1484">http://www.pnas.org/cgi/content/full/100/4/1484</a>
</p>
<p>
Force at the post tip is calculated using Euler-Bernoulli beam theory, but the post's short length (compared to diameter) and considerable deflection do not warrant EB theory’s neglect of transverse shear strain, so using EB overestimates the force. Also, the inward forces bring post tips in contact with each other and EB theory breaks down—that this happens frequently can be seen in the recent movie [1]. Optimizing the post stiffness to prevent contact while providing measurable deflection, involves repeated expensive microfabrication procedure, which is the main drawback for this technique.
</p>
<p>
In contrast, the substrate for all the continuum methods is an isotropic linearly elastic solid, usually a hydrogel or a silicon rubber film. Fluorescent markers (beads) are embedded in the substrate surface and their motions are recorded using fluorescence microscopy. Substrate thickness (usually ~100 microns) is at least order of magnitude greater than the maximum surface displacement in order to satisfy the key assumption: that the substrate is a semi-infinite body. This assumption was needed in order to use the Boussinesq Equations, which simplify the solution of this inverse problem. Displacements are given as the convolution of Green’s tensor and traction and the challenge is to solve the inverse problem given the limitation of the noisy displacement field obtained from the measurements.
</p>
<p>
In the first method that launched the cell traction assays, tractions are explicitly set to 0 outside the cell boundary while the noisy displacement field is specified everywhere, effectively providing for an ill-posed inverse problem that requires somewhat arbitrary smoothing in order to obtain stable solution:
</p>
<p>
Dembo M and Wang Y-L. Stresses at the cell-to-substrate interface during locomotion of fibroblasts. Biophys J 76: 2307-2316 (1999).
</p>
<p>
<a href="http://www.biophysj.org/cgi/content/full/76/4/2307">http://www.biophysj.org/cgi/content/full/76/4/2307</a>
</p>
<p>
Furthermore, the problem kernel is not diagonal in real space, which leads to bulky matrices and computationally intensive inversion.
</p>
<p>
In the competing traction calculation method, inversion is performed in Fourier space because the kernel is diagonal in Fourier space and inversion is exact and considerably less computationally intensive:
</p>
<p>
Butler JP, Tolić-Nørrelykke IM, Fabry B and Fredberg JJ. Traction fields, moments, and strain energy that cells exert on their surroundings. Am J Physiol Cell Physiol 282: C595-C605 (2002).
</p>
<p>
<a href="http://ajpcell.physiology.org/cgi/content/full/282/3/C595">http://ajpcell.physiology.org/cgi/content/full/282/3/C595</a>
</p>
<p>
Lack of periodicity in measured data results in artifact tractions at the boundary of the computational region, but these artifacts are contained only at the boundary and do not affect tractions in the region of interest (cell-covered area) provided that the distance to the boundary is equal to several cell lengths.
</p>
<p>
When tested on identical data set, the real-space and the Fourier-space method provided reasonably similar results [2].
</p>
<p>
An interesting detail remains unnoticed by cell biologists: the small-strain assumption is implied in the Boussinesq Equations but apparently unsupported by the experimental data. Substrate stiffness is fine-tuned to allow measurable displacements at given imaging conditions but that results with large strains which can be easily inferred from the time-lapse movies of substrate deformations (strain data is not reported in the references). It seems that the error of small-strain assumption should be considerable but it is not clear if it results in overestimates of tractions, as my intuition suggests, or it is of a more complex nature. iMechanica is perhaps the best forum for discussions of this specific issue and this class of inverse problems in elasticity.
</p>
<p>
REFERENCES
</p>
<p>
[1] Supporting Movie 1 for: du Roure O, Saez A, Buguin A, Austin RH, Chavrier P, Silberzan P and Ladux B. Force mapping in epithelial cell migration. PNAS 102 (7): 2390-2395 (2005).
</p>
<p>
[2] Ning Wang, personal communication
</p>
</div></div></div><div class="field field-name-taxonomy-forums field-type-taxonomy-term-reference field-label-above"><div class="field-label">Forums: </div><div class="field-items"><div class="field-item even"><a href="/forum/417">Journal Club Forum</a></div></div></div><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-above"><div class="field-label">Free Tags: </div><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/1818">inverse problems</a></div><div class="field-item odd"><a href="/taxonomy/term/1967">cellular tractions</a></div></div></div>Sat, 01 Mar 2008 04:52:42 +0000Vesna Damljanovic2786 at https://imechanica.orghttps://imechanica.org/node/2786#commentshttps://imechanica.org/crss/node/2786