iMechanica - biomedical devices
https://imechanica.org/taxonomy/term/13580
enJournal Club for September 2022: Mechanics of soft network materials
https://imechanica.org/node/26194
<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/18">micromechanics</a></div><div class="field-item odd"><a href="/taxonomy/term/9428">mechanical metamaterials</a></div><div class="field-item even"><a href="/taxonomy/term/6667">tissue engineering</a></div><div class="field-item odd"><a href="/taxonomy/term/13579">soft network materials</a></div><div class="field-item even"><a href="/taxonomy/term/13580">biomedical devices</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">Renheng Bo, Shunze Cao, and Yihui Zhang</p>
<p class="MsoNormal">Department of Engineering Mechanics, Tsinghua University</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><strong>1. Introduction</strong></p>
<p class="MsoNormal">Soft network materials are a family of artificial materials consisting of strategically engineered microstructures, through which a tunable “softness” could always be achieved, regardless of the nature of constituent materials. For example, soft networks made of rigid materials can still offer a high level of stretchability and a low effective modulus. The conceptual design of network roots in nature – the ubiquitous fractal networks touching nearly every corner of living biosystems. Similar to the abundant biological diversity created by natural networks, the unparalleled design flexibility[1-6] of man-made soft networks enables the precision engineering of a huge family of structured materials with outstanding mechanical/physical properties[1, 2, 7-9], such as high stretchability, tunable porosity, high air permeability, defect-insensitive behavior, among others. </p>
<p class="MsoNormal">According to the geometry of the network microstructure, the existing soft network materials could be basically classified into two categories, including network materials with periodic microstructures and those with randomly distributed microstructures. Given the large variety of network designs and their prominent mechanical/physical properties, soft network materials are intensively explored for numerous applications (<strong>Figure 1a-d</strong>), including the cellular encapsulation of stretchable electronics (<strong>Figure 1a</strong>)[5, 10, 11], self-cooling emitter[12], mechanical metamaterials (<strong>Figure 1b</strong>)[1], regenerative medicine (<strong>Figure 1c</strong>)[13], and artificial tissues with biomimetic mechanical properties (<strong>Figure 1d</strong>)[13-15]. In this journal club, we discuss structural designs and mechanics modeling of soft network materials, and provide our perspectives on future research opportunities in this exciting area. </p>
<p><img title="Figure 1" src="https://imechanica.org/files/Figure%201_4.jpg" alt="" width="1141" height="501" /></p>
<p><strong>Figure 1 Applications of soft network materials.</strong> <strong>a)</strong> Encapsulation of stacked flexible electronics[10]. <strong>b)</strong> Mechanical metamaterials with tunable Poisson’s ratios[1]. <strong>c)</strong> Soft LCE networks for wound healing, scale bars = 1 cm[13]. <strong>d)</strong> 3D soft networks mimicking the J-shaped stress-strain curve of natural biological tissues, scale bars = 5 mm[16]. </p>
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<p class="MsoNormal"><strong>2. Design principles of soft network materials</strong></p>
<p class="MsoNormal"><strong>2D Soft Network Materials</strong></p>
<p class="MsoNormal"><strong>Figure 2a</strong> shows a representative random soft network prepared by electrospinning. This sort of network design originates mainly from simply replicating disorder natural structures. By taking advantage of the specific mechanical/biocompatible properties of synthetic/natural elastic polymer fibers, such designs can offer an excellent stretchability, and tunable effective modulus. This type of network materials usually consists of randomly oriented fibers with diameters varying from few nanometers (e.g., 2 nm) to micrometer scale (e.g., 10 mm), and micropores of dimensions ranging from 50 to 250 mm. Such relatively dense microstructures with additional growth factor would mimic extracellular matrix (ECM) in nature, providing a comfortable environment for spreading, proliferation, and differentiation of cells, thereby holding promising applications as tissue scaffolds. To be noted, the microstructure dimensions and physical properties of such networks (e.g., pore size, fiber diameters, stretchability, modulus, conductivity, and etc.) could be tuned by varying the precursor concentration, extruding velocity, applied voltage and other parameters.</p>
<p class="MsoNormal">Inspired by wavy microstructures found in many collagen tissues, 2D network design with periodic topologies consisting of curved filaments were derived from straight-beamed networks (<strong>Figure 2b i</strong>) to offer biomimetic J-shaped stress-strain response and strain-limiting behavior[17]. In particular, the curved building-block structures enable a bending-dominated deformation mode at small strains, with a transition into a stretching-dominated mode at high strains, which is close to that of biological tissues in nature. <strong>Figure</strong> <strong>2b</strong> <strong>ii</strong> shows a typical periodic 2D soft network design with horseshoe microstructures formed by two identical circular arcs. For a prescribed constituent material, tunable nonlinear mechanical responses could be achieved via adjusting its geometric parameters including the arc angle, and normalized width. Therefore, such network materials can be used in flexible electronics to allow its integration with skins in a mechanically-invisible manner[18]. </p>
<p class="MsoNormal">To further increase the stretchability, artificial fractals were introduced to the design of 2D networks (<strong>Figure 2c i</strong>)[19]. The fractal-inspired design harnesses the unique deformation mechanism of ordered unraveling (of the fractal microstructure) to offer a significantly enhanced elastic stretchability than the transitional pattern (without the fractal design). <strong>Figure 2c ii</strong> presents an example of network materials with fractal horseshoe microstructures and the deformation under uniaxial stretching. Introducing rotatable structural nodes (e.g., in the forms of ring or disk, as shown in <strong>Figure 2d i</strong>)[20] represents another design strategy to achieve an increased stretchability in the soft network material. Specifically, assuming an unvaried area of the topological unit, the use of rotatable nodes would reduce the bending strain of curved filaments by increasing their curvature radius and allowing the rotation to occur (<strong>Figure 2d ii</strong>). For a unit cell with structural node (i.e., composed of six identical circular arcs), its key geometric parameters include the arc angle, radius, normalized ligament width and node radius. The normalized ligament width plays a crucial role on the utmost strength of network, while the arc angle and normalized nodal radius mainly affect the stretchability. </p>
<p> </p>
<p class="MsoNormal"><strong>3D Soft Network Materials</strong></p>
<p class="MsoNormal">The burgeoning of additive manufacturing (AM) spurs rapid developments of 3D soft network materials in recent years. Amongst them, cylindrical networks stand as a typical 3D derivative of 2D soft networks with tunable mechanical properties[21]. Such cylindrical designs could take advantage of the relatively mature 2D designs to expand them into steric configurations. For instance, <strong>Figure 2e</strong> presents a 3D tube-like network consisting of three types of zigzag microstructures at different locations, enabling an unusual Poisson effect, as manifested by the various cross-sectional deformations. </p>
<p>To better replicate the real 3D configuration of natural collagenous fibers and their nonlinear mechanical responses, 3D soft network materials with engineered helical microstructures were developed, as shown in <strong>Figure 2f i </strong>(with an octahedral topology in this example). To avoid the geometric overlap of differently aligned microstructures at the connective nodes, an unconventional helical microstructure consisting of three segments is designed, including a central part that corresponds to an ideal helical structure and two joint parts that are modified to ensure a tangential attachment to the nodal regions of the network (<strong>Figure 2f ii</strong>). The central line of this helical microstructure can be characterized by parametric equations in analytical forms. The key geometrical parameters of helical microstructures include the fiber diameter, helix radius, the number of coils, pitch as well as joint length. </p>
<p><img title="Figure 2" src="https://imechanica.org/files/Figure%202_6.jpg" alt="" width="1140" height="644" /></p>
<p class="MsoNormal"><strong>Figure 2 Structural designs of soft network materials.</strong> <strong>a)</strong> SEM images of the soft network material with randomly distributed fibers: left side, non-oriented; right side, oriented, scale bar = 2μm. <strong>b)</strong> Representative configurations of rationally designed network materials containing straight (<strong>i</strong>) and curved horseshoe microstructures (<strong>ii</strong>)[17]. <strong>c)</strong> Schematical illustrations of 2D soft network with fractal horseshoe microstructures (<strong>i</strong>), and unravelling sequences of a second-order horseshoe microstructure with an arc angle of 240o under uniaxial stretching, scale bars = 5mm (<strong>ii</strong>)[19]. <strong>d) </strong>Schematical illustrations of 2D soft network with rotatable structural nodes (<strong>i</strong>), and the deformation sequence of a building-block structure under uniaxial stretching (<strong>ii</strong>)[20]. <strong>e)</strong> 3D printed cylindrical shells with engineered Poisson effects, where the left segment, middle segment, and right segment possess negative, zero (middle), and positive Poisson’s ratios, respectively, scale bars = 20μm.[21]. <strong>f) </strong>Schematical illustrations of 3D network materials with octahedral topology (<strong>i</strong>) and the geometric configurations of a representative helical microstructure (<strong>ii</strong>)[16].</p>
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<p class="MsoNormal"><strong>3. Mechanics modeling of soft network materials</strong></p>
<p class="MsoNormal"><strong>Mechanical responses of soft network materials</strong></p>
<p class="MsoNormal">For random 2D network materials, the alignment of its composing fibers would gradually occur under uniaxial stretching. For instance, <strong>Figure 3a </strong>shows the true stress-strain curve of an electrospun amorphous PI network material with randomly distributed fibers, and the SEM images of its microstructures at initial state (0% strain) and deformed state (41% strain)[22]. Due to a lack of control over the microstructure topology, the nonlinear mechanical response can be adjusted only in a limited range.</p>
<p class="MsoNormal">For conventional lattice material with straight microstructures, the typical elastic-plastic responses under tension and compression before failure are presented in<strong> Figure 3b</strong>[23]. Obviously, it is quite difficult for such designs to replicate the nonlinear J-shaped stress-strain curves of biological tissues. </p>
<p class="MsoNormal">In terms of well-organized 2D soft networks (<strong>Figure 3c i</strong>)[18], its typical uniaxial stress-strain curve (<strong>Figure 3c ii</strong>) presents three phases, which is in line with that of soft biological tissues. The first phase (i.e., ‘toe’ region) is attributed to bending-dominated deformations of the curved filaments, yielding a low effective modulus. During the second phase (i.e., ‘heel’ region), the continuous stretching causes the curved filaments to rotate, bend and align to the loading direction, leading to a gradually increased modulus. When entering the third phase (i.e., ‘linear’ region), the stretching of constituent materials dominates the structural response. As a result, the soft network material shows a J-shaped stress-strain curve, which combines high levels of stretchability with a natural ‘strain-limiting’ mechanism that protects tissues from excessive strains. It is also notable that the effective modulus of the network material in the third phase could be 1-2 orders of magnitude higher than that seen in the first phase. </p>
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<p class="MsoNormal"><strong>Mechanics modeling of 2D soft network materials</strong></p>
<p class="MsoNormal">Given rapid developments of various 2D soft network materials, mechanics modeling has been attracting more and more attentions, aiming to provide theoretical basis of rapid network designs. Both micromechanics and phenomenological models have been established.</p>
<p class="MsoNormal">A micromechanics model of soft networks with horseshoe microstructures was developed through combining a <a title="Learn more about finite deformation from ScienceDirect's AI-generated Topic Pages" href="https://www.sciencedirect.com/topics/engineering/finite-deformation">finite deformation</a> constitutive relation of the building-block structure (i.e., horseshoe microstructure), with the analysis of equilibrium and deformation compatibility[17]. The mechanics analysis of the horseshoe microstructure is schematically illustrated in<strong> Figure 3d i</strong>, where the nonlinear load-displacement relationship can be obtained by the finite-deformation theory of curved beams. Considering the structural periodicity, a unit cell composed of three differently oriented horseshoe microstructures is further analyzed to establish the equilibrium equations and deformation compatibility of the entire network, as schematically shown in <strong>Figure</strong> <strong>3d</strong> <strong>ii</strong>. The equilibrium equations can be derived by considering the equilibrium of the unite cell and the connective node. The deformation compatibility requires that the side lengths and interior angles of the deformed triangle should satisfy a set of geometric equations. Besides, the angle between the tangent lines of different horseshoe microstructures keeps unchanged during the deformation. By solving these sets of equations, the nonlinear stress-strain curves and deformed patterns can be predicted, which agree well with both finite element analyses (FEA) results and experiments, for a wide range of geometric parameters, as shown in <strong>Figure 3e i </strong>and<strong> ii</strong>.</p>
<p class="MsoNormal">Later on, this micromechanics model was extended to study nonlinear mechanical behaviors of soft networks with fractal-inspired horseshoe microstructures (<strong>Figure 2c</strong>)[19], <a title="Learn more about anisotropic from ScienceDirect's AI-generated Topic Pages" href="https://www.sciencedirect.com/topics/engineering/anisotropic">anisotropic</a> mechanical responses of soft networks with horseshoe microstructures[24], and stretchability enhancement in soft networks with rotatable nodes and horseshoe microstructures[20]. Recently, the model was further extended to consider soft networks with a wide range of microstructures (with varying curvatures) whose central lines can be depicted by parametric functions in polygonal forms[25].</p>
<p class="MsoNormal">Despite the progress, the above micromechanics models are applicable only to soft network materials with a certain type of geometric constructions. A more general micromechanics model allowing the prediction of arbitrarily architected soft networks remain challenging. The phenomenological model can overcome this limitation to some extent, however, by sacrificing a certain degree of prediction accuracy. Based on this concept, a single-parameter phenomenological framework, incorporating a two-segment model that exploits simple, explicit expressions to capture the J-shaped stress-strain relationship, was proposed. Additionally, the machine learning (ML) approach was introduced to enable the determination of the single phenomenological parameter (<strong>Figure 3f i</strong>)[26]. The mechanical responses of several randomly generated 2D soft networks were well predicted via the phenomenological framework, and the results were validated through FEA and experimental measurements (<strong>Figure 3f ii</strong>). </p>
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<p class="MsoNormal"><strong>Mechanics modeling of 3D soft network materials</strong></p>
<p class="MsoNormal">Recently, a micromechanics model was established to investigate the nonlinear anisotropic mechanical properties of the soft 3D network materials consisting of helical microstructures[27]. The model starts with the mechanics analyses of an ideal helix under uniaxial stretching, where the deformed structure was assumed to maintain an ideal helical configuration, as schematically shown in<strong> Figure 3g i</strong>. The constitutive relation of the loading force (<em>F</em>) and the elongation (<em>p</em>/<em>p_</em>0) of the helix along the helical axis could be obtained based on this assumption. Then, every unit segment (d<em>S</em>) of the helical microstructure (including two joint parts) undergoes a similar deformation to that of an ideal helical structure, as schematically shown in<strong> Figure 3g ii</strong>. This allowed us to exploit the theory of the ideal helical structure to analyze the deformation of every unit segment in the helical microstructure, and resort to the concept of calculus to determine the elongation of the entire structure. As the force components of load-bearing microstructures along the loading direction mainly contribute to the effective stress (<em>σ</em>) of soft 3D network materials, the contributions from the other helical microstructures are neglected for simplicity. Based on the connection of mechanical responses of building-block structures (i.e., helical microstructures) and that of 3D soft network materials, a theoretical model can be developed to predict effective stress-strain (<em>σ</em>–<em>ɛ</em>applied) curves of 3D soft network materials. For instance, for 3D soft cubic network materials consist of helical microstructures under the uniaxial stretching along a principal direction, only the group of helical microstructures parallel with the loading direction is straightened, and thereby contributes to the stress of the entire 3D network. The other two groups of helical microstructures perpendicular to the loading direction mainly undergo rigid body translation to ensure the connectivity, and experience negligible stretching/compression deformations. Due to the lattice periodicity, a representative unit cell can be used to establish the equilibrium equations and deformation compatibility of the entire 3D soft cubic network materials, as schematically shown in <strong>Figure 3g iii</strong>. The stress-strain curves obtained from theoretical model show good agreements with FEA and experimental results, as shown in <strong>Figure 3g iv</strong>.</p>
<p><img title="Figure 3" src="https://imechanica.org/files/Figure%203_6.jpg" alt="" width="1141" height="645" /></p>
<p><strong>Figure 3 Mechanical properties of soft network materials.</strong> <strong>a)</strong> Representative uniaxial tensile characterization of electrospun PI membrane, and the SEM images showing the microstructural network at the initial and deformed states[22]. <strong>b)</strong> Tensile and compressive stress-strain curves of 3D network materials with straight beams[23]. <strong>c)</strong> optical images of soft network materials with horseshoe microstructures at different tensile strain (<strong>i</strong>), a representative J-shaped stress-strain curve of soft network material with horseshoe microstructures with three distinct phases (<strong>ii</strong>). <strong>d)</strong> Schematic illustration of a mechanics model for the horseshoe microstructure (<strong>i</strong>), schematic illustration of the theoretical model of the hierarchical triangular lattice subject to a uniform tensile stress along horizontal stretching (<strong>ii</strong>)[17]. <strong>e) </strong>Theoretical, FEA, and experimental results of stress–strain curves for the triangular network materials with horseshoe microstructure: (i) theoretical and experimental results of stress-strain curves for a wide range of arc angle, and fixed normalized width, (ii) theoretical and FEA results of stress-strain curves for a wide range of normalized width, and fixed arc angle (<strong>iii</strong>)[17]. <strong>f)</strong> Flow chart for acquiring nonlinear stress-strain curves of soft network materials with randomly curved microstructures based on the phenomenological framework (<strong>i</strong>), uniaxial tensile responses of two types of random soft networks predicted by the phenomenological framework, and their corresponding validation via FEA and experiments (<strong>ii</strong>)[26]. <strong>g)</strong> Schematic illustration of mechanics model for helical microstructure under uniaxial stretching, initial and deformed configurations of an ideal helical structure (<strong>i</strong>), deformation of a unit element for a helical microstructure with nonuniform curvature (<strong>ii</strong>), deformation analyses of soft cubic network materials with helical microstructure under horizontal stretching (<strong>iii</strong>), the representative stress-strain curves of 3D cubic network material obtained from theoretical model, FEA, and experiments (<strong>iv</strong>)[27].</p>
<p class="MsoNormal"><strong> </strong></p>
<p class="MsoNormal"><strong>4. Summaries and perspectives </strong></p>
<p class="MsoNormal">Overall, we have briefly discussed the structural designs and mechanics modeling of soft network materials, covering network materials with both randomly and periodically distributed microstructures, either in 2D or 3D constructions. </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><strong>Perspectives on mechanics</strong></p>
<p class="MsoNormal">In practical applications, soft network materials would often undergo biaxial tension or coupled tension/shear loadings, instead of the uniaxial tension. Therefore, to understand the intricate deformation and failure behaviors of soft network materials under these complex loading conditions, developing a new micromechanics model in a general stress space is highly desirable. </p>
<p class="MsoNormal">In addition, functionalities and performances of soft network materials rely on both their structural design and the nature of constituent materials. Therefore, strategic integration of soft active materials (under external thermal, electric, magnetic or optical stimuli) with the network design could allow access to active mechanical metamaterials that offer exotic mechanical behavior or mechanical properties that surpass those of conventional materials in nature, such as negative Poisson’s ratios, unusual swelling and thermal expansion responses, programmable multistability, and abnormal acoustic properties[1,2,8,13,28]. This would offer great opportunities for future device designs and applications. For instances, the use of LCEs[29] in soft network materials might give reversible biaxial deformation capability inaccessible previously. Soft network materials composed of supramolecular polymers[30] might present extreme stretchability exceeding 4000% strain under uniaxial stretching[31]. Soft network materials affording rapid reversible transformation of topologies could be prepared thanks to the uncover of a liquid-induced mechanism[32]. Developing coupled multifield mechanics model for active network materials is more challenging, yet of pivotal importance in the network designs.</p>
<p class="MsoNormal">Last but not least, as mentioned previously, we have preliminarily used machine learning (i.e., to obtain phenomenological parameters) to assist the phenomenological framework to predict the J-shaped stress-strain curves of arbitrary network materials. Considering its strong capability, machine learning could be further used to resolve the inverse design problems of soft network materials for any targeted nonlinear mechanical responses. Future opportunities might lie in establishment of the mapping relation from one desired stress-strain curve to several potential network configurations, by providing additional key factors such as the microstructure geometry, and topological information (e.g., number of microstructures connecting to each structural node). </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><strong>Perspective on synthesis and fabrication</strong></p>
<p class="MsoNormal">Well-organized 2D and 3D networks show an extraordinary level of design flexibility, and thus, their properties (i.e., not only mechanical properties but also others, such as electrical and optical properties) could be customized on demands. This makes them promising candidates for emerging biomedical applications such microtissues scaffolds and organoid culture, which often require densely distributed nanostructures. However, due to current fabrication limits, preparation approaches for macroscopic network materials with well-defined nanostructures have not yet been developed. Meanwhile, random 2D network materials, usually in the form of films or membranes, feature densely distributed self-assembled nanostructures, which are similar to naturally developed ECMs. This makes them ideal for both <em>in vitro</em> and <em>in vivo</em> biomedical applications. However, the lack of structural control hinders their practical applications. Therefore, hybrid architectures consisting of active surfaces (i.e., random network materials with nanostructures) supported by well-designed network materials could be of great interest for future explorations.</p>
<p class="MsoNormal">The blossoms of flexible electronics and materials sciences have enabled the integration of functional devices with advanced artificial structures. The highly designable soft network materials with tunable physical/chemical properties stand as very suitable candidates for such purpose, which would offer unprecedented opportunities for applications spanning real-time monitoring of growing tissues, <em>in</em> <em>situ</em> study of organisms regeneration, smart patch for regenerative medicine, and continuously shaping of organoids among others.</p>
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</div></div></div>Tue, 30 Aug 2022 15:54:35 +0000Yihui Zhang26194 at https://imechanica.orghttps://imechanica.org/node/26194#commentshttps://imechanica.org/crss/node/26194