User login


You are here

Journal Club for September 2022: Mechanics of soft network materials

Yihui Zhang's picture


Renheng Bo, Shunze Cao, and Yihui Zhang

Department of Engineering Mechanics, Tsinghua University


1. Introduction

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.  

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 (Figure 1a-d), including the cellular encapsulation of stretchable electronics (Figure 1a)[5, 10, 11], self-cooling emitter[12], mechanical metamaterials (Figure 1b)[1], regenerative medicine (Figure 1c)[13], and artificial tissues with biomimetic mechanical properties (Figure 1d)[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. 

Figure 1 Applications of soft network materials. a) Encapsulation of stacked flexible electronics[10]. b) Mechanical metamaterials with tunable Poisson’s ratios[1]. c) Soft LCE networks for wound healing, scale bars = 1 cm[13]. d) 3D soft networks mimicking the J-shaped stress-strain curve of natural biological tissues, scale bars = 5 mm[16]. 


2. Design principles of soft network materials

2D Soft Network Materials

Figure 2a 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.

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 (Figure 2b i) 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.  Figure 2b ii 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]. 

To further increase the stretchability, artificial fractals were introduced to the design of 2D networks (Figure 2c i)[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). Figure 2c ii 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 Figure 2d i)[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 (Figure 2d ii).  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. 


3D Soft Network Materials

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, Figure 2e 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. 

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 Figure 2f i (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 (Figure 2f ii).  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. 

Figure 2 Structural designs of soft network materials. a) SEM images of the soft network material with randomly distributed fibers: left side, non-oriented; right side, oriented, scale bar = 2μm. b) Representative configurations of rationally designed network materials containing straight (i) and curved horseshoe microstructures (ii)[17]. c) Schematical illustrations of 2D soft network with fractal horseshoe microstructures (i), and unravelling sequences of a second-order horseshoe microstructure with an arc angle of 240o under uniaxial stretching, scale bars = 5mm (ii)[19]. d) Schematical illustrations of 2D soft network with rotatable structural nodes (i), and the deformation sequence of a building-block structure under uniaxial stretching (ii)[20]. e) 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]. f) Schematical illustrations of 3D network materials with octahedral topology (i) and the geometric configurations of a representative helical microstructure (ii)[16].


3. Mechanics modeling of soft network materials

Mechanical responses of soft network materials

For random 2D network materials, the alignment of its composing fibers would gradually occur under uniaxial stretching.  For instance, Figure 3a 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.

For conventional lattice material with straight microstructures, the typical elastic-plastic responses under tension and compression before failure are presented in Figure 3b[23].  Obviously, it is quite difficult for such designs to replicate the nonlinear J-shaped stress-strain curves of biological tissues. 

In terms of well-organized 2D soft networks (Figure 3c i)[18], its typical uniaxial stress-strain curve (Figure 3c ii) 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.  


Mechanics modeling of 2D soft network materials

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.

A micromechanics model of soft networks with horseshoe microstructures was developed through combining a finite deformation 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 Figure 3d i, 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 Figure 3d ii.  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 Figure 3e i and ii.

Later on, this micromechanics model was extended to study nonlinear mechanical behaviors of soft networks with fractal-inspired horseshoe microstructures (Figure 2c)[19], anisotropic 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].

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 (Figure 3f i)[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 (Figure 3f ii). 


Mechanics modeling of 3D soft network materials

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 Figure 3g i.  The constitutive relation of the loading force (F) and the elongation (p/p_0) of the helix along the helical axis could be obtained based on this assumption.  Then, every unit segment (dS) of the helical microstructure (including two joint parts) undergoes a similar deformation to that of an ideal helical structure, as schematically shown in Figure 3g ii.  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 (σ) 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 (σɛapplied) 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 Figure 3g iii.  The stress-strain curves obtained from theoretical model show good agreements with FEA and experimental results, as shown in Figure 3g iv.

Figure 3 Mechanical properties of soft network materials. a)  Representative uniaxial tensile characterization of electrospun PI membrane, and the SEM images showing the microstructural network at the initial and deformed states[22]. b) Tensile and compressive stress-strain curves of 3D network materials with straight beams[23]. c) optical images of soft network materials with horseshoe microstructures at different tensile strain (i), a representative J-shaped stress-strain curve of soft network material with horseshoe microstructures with three distinct phases (ii). d) Schematic illustration of a mechanics model for the horseshoe microstructure (i), schematic illustration of the theoretical model of the hierarchical triangular lattice subject to a uniform tensile stress along horizontal stretching (ii)[17]. e) 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 (iii)[17]. f) Flow chart for acquiring nonlinear stress-strain curves of soft network materials with randomly curved microstructures based on the phenomenological framework (i), uniaxial tensile responses of two types of random soft networks predicted by the phenomenological framework, and their corresponding validation via FEA and experiments (ii)[26]. g) Schematic illustration of mechanics model for helical microstructure under uniaxial stretching, initial and deformed configurations of an ideal helical structure (i), deformation of a unit element for a helical microstructure with nonuniform curvature (ii), deformation analyses of soft cubic network materials with helical microstructure under horizontal stretching (iii), the representative stress-strain curves of 3D cubic network material obtained from theoretical model, FEA, and experiments (iv)[27].


4. Summaries and perspectives

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. 


Perspectives on mechanics

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. 

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.

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). 


Perspective on synthesis and fabrication

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 in vitro and in vivo 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.

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, in situ study of organisms regeneration, smart patch for regenerative medicine, and continuously shaping of organoids among others.



1.      H. Zhang, X. Guo, J. Wu, D. Fang, Y. Zhang, Soft mechanical metamaterials with unusual swelling behavior and tunable stress-strain curves. Science Advances 4, eaar8535 (2018).

2.      J. Liu, D. Yan, W. Pang, Y. Zhang, Design, fabrication and applications of soft network materials. Materials Today 49, 324-350 (2021).

3.      Y. Yin, M. Li, Z. Yang, Y. Li, Stretch-induced shear deformation in periodic soft networks. Extreme Mechanics Letters 47, 101370 (2021).

4.      W. Yang, Q. Liu, Z. Gao, Z. Yue, B. Xu, Theoretical search for heterogeneously architected 2D structures. Proceedings of the National Academy of Sciences 115, E7245-E7254 (2018).

5.      Z. Yang et al., Conductive and elastic 3D helical fibers for use in washable and wearable electronics. Advanced Materials 32, 1907495 (2020).

6.      Z.-P. Wang, Y. Wang, L. H. Poh, Z. Liu, Integrated shape and size optimization of curved tetra-chiral and anti-tetra-chiral auxetics using isogeometric analysis. Composite Structures, 116094 (2022).

7.      A. Rafsanjani, A. Akbarzadeh, D. Pasini, Snapping mechanical metamaterials under tension. Advanced Materials 27, 5931-5935 (2015).

8.      Y. Chen, T. Li, F. Scarpa, L. Wang, Lattice metamaterials with mechanically tunable Poisson’s ratio for vibration control. Physical Review Applied 7, 024012 (2017).

9.      Q. Wang et al., Lightweight mechanical metamaterials with tunable negative thermal expansion. Physical review letters 117, 175901 (2016).

10.    H. Song et al., Highly-integrated, miniaturized, stretchable electronic systems based on stacked multilayer network materials. Science Advances 8, eabm3785 (2022).

11.    Z. Ma et al., Permeable superelastic liquid-metal fibre mat enables biocompatible and monolithic stretchable electronics. Nature Materials 20, 859-868 (2021).

12.    D. Li et al., Scalable and hierarchically designed polymer film as a selective thermal emitter for high-performance all-day radiative cooling. Nature Nanotechnology 16, 153-158 (2021).

13.    J. Wu et al., Liquid crystal elastomer metamaterials with giant biaxial thermal shrinkage for enhancing skin regeneration. Advanced Materials 33, 2106175 (2021).

14.    X. Xin, L. Liu, Y. Liu, J. Leng, 4D pixel mechanical metamaterials with programmable and reconfigurable properties. Advanced Functional Materials 32, 2107795 (2022).

15.    Y. Gao, B. Li, J. Wang, X.-Q. Feng, Fracture toughness analysis of helical fiber-reinforced biocomposites. Journal of the Mechanics and Physics of Solids 146, 104206 (2021).

16.    D. J. Yan et al., Soft three-dimensional network materials with rational bio-mimetic designs. Nature Communications 11,  (2020).

17.    Q. Ma et al., A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures. Journal of the Mechanics and Physics of Solids 90, 179-202 (2016).

18.    K. I. Jang et al., Soft network composite materials with deterministic and bio-inspired designs. Nature Communications 6,  (2015).

19.    Q. Ma, Y. H. Zhang, Mechanics of Fractal-Inspired Horseshoe Microstructures for Applications in Stretchable Electronics. Journal of Applied Mechanics, Transactions ASME 83,  (2016).

20.    J. X. Liu, D. J. Yan, Y. H. Zhang, Mechanics of unusual soft network materials with rotatable structural nodes. Journal of the Mechanics and Physics of Solids 146,  (2021).

21.    J. X. Liu, Y. H. Zhang, Soft network materials with isotropic negative Poisson's ratios over large strains. Soft Matter 14, 693-703 (2018).

22.    M. N. Silberstein, C.-L. Pai, G. C. Rutledge, M. C. Boyce, Elastic–plastic behavior of non-woven fibrous mats. Journal of the Mechanics and Physics of Solids 60, 295-318 (2012).

23.    B. B. Babamiri, H. Askari, K. Hazeli, Deformation mechanisms and post-yielding behavior of additively manufactured lattice structures. Materials & Design 188, 108443 (2020).

24.    Y. F. Yin, Z. Zhao, Y. H. Li, Theoretical and experimental research on anisotropic and nonlinear mechanics of periodic network materials. Journal of the Mechanics and Physics of Solids 152,  (2021).

25.    L. Dong et al., Modeling and Design of Periodic Polygonal Lattices Constructed from Microstructures with Varying Curvatures. Physical Review Applied 17, 044032 (2022).

26.    S. Cao et al., A phenomenological framework for modeling of nonlinear mechanical responses in soft network materials with arbitrarily curved microstructures. Extreme Mechanics Letters, 101795 (2022).

27.    J. H. Chang, D. J. Yan, J. X. Liu, F. Zhang, Y. H. Zhang, Mechanics of Three-Dimensional Soft Network Materials With a Class of Bio-Inspired Designs. Journal of Applied Mechanics, Transactions ASME 89,  (2022).

28.    Y. Kim, H. Yuk, R. Zhao, S. A. Chester, X. Zhao, Printing ferromagnetic domains for untethered fast-transforming soft materials. Nature 558, 274-279 (2018).

29.    K. M. Herbert et al., Synthesis and alignment of liquid crystalline elastomers. Nature Reviews Materials 7, 23-38 (2022).

30.    Z. Huang et al., Highly compressible glass-like supramolecular polymer networks. Nature materials 21, 103-109 (2022).

31.    J. Liu et al., Tough supramolecular polymer networks with extreme stretchability and fast roomtemperature self-healing. Advanced Materials 29, 1605325 (2017).

32.    S. Li et al., Liquid-induced topological transformations of cellular microstructures. Nature 592, 386-391 (2021).

Image icon Figure 1.jpg5.66 MB
Image icon Figure 2.jpg489.67 KB
Image icon Figure 3.jpg524.83 KB


Teng zhang's picture

Hi Yihui,

Thanks a lot for your excellent summary of this very exciting field! The engineered nonlinear stress-strain curve is very impressive. I have a few questions related to newtwork imperfections:

(1) As you mentioned that some of the studies are inspired by biological networks, those structures are also less regular and may have some random distribution of the network. How will this affect the modulus of your designed structures?

(2) If the network imperfections are too large, they become flaws/cracks. Did you study the fracture toughness and crack propagation in the soft network structures? 

(3) Many biological structures are designed to be flaw insensitive, which is determined by the mechanical properties and sample sizes. Will you be able to engineer flaw insensitive soft newtwork structures?



Yihui Zhang's picture

Hi Teng,

Many thanks for your insightful questions! Please see my replies below:

1. Yes, the soft tissues in biology are typically composed of randomly distributed networks.  The 'J-shaped' nonlinear stress-strain curves of randomly distributed networks are usually not as sharp as that of periodically distributed networks - the tangential modulus of periodically distributed networks increases more rapidly than the network with randomness, as the strain increases.  This is because the transition of bending-dominated deformation to stretching-dominated one is more abrupt in periodically distributed networks.

2. My group has not studied the fracture toughness or crack propagation in soft network materials.  But we did analyze the stress concentration in soft network materials with circular-hole imperfections (i.e., with a certain number of missing horseshoe microstructures, depending on the hole size in relative to the microstructure size) (see ACS Applied Materials & Interface, 2019, 11: 36100-3610; Acta Mechanica Sinica, 2021, 37: 1050-1062).  Both the size and location of the circular-hole imperfections are shown to have profound influences on the stretchability of the network.  But the factor of stress-concentration is usually much smaller than the case in 2D solid materials. 

3. Missing microstructures, manufacturing imperfections (unequal sizes or material defects), notchs and cracks can be regarded as different types of flaws.  In addition to the aforementioned hole-type imperfections, Prof. Norman A. Fleck's group has studied the influence of manufacturing imperfections and notch sensitivities on the mechanical responses of lattice materials consisting of wavy microstructures in comparison to those with straight microstructures (see International Journal of Mechanical Sciences, 2019, 192: 106137; JAM, 2021, 88: 031011).  The soft networks with wavy microstructures are found to be more imperfection insensitive than corresponding lattice materials with straight microstructures in most cases.  Along this direction, it might be interesting to introduce the tools of topology optimization or machine learning to design soft network materials with further enhanced flaw insensitivity.

Warm regards!

Yihui's picture

Dear Yihui,

Really appreciate for sharing your profound and original insights into this emerging field of soft materials. Soft network materials can be designed to reproduce the J-shaped stress-strain curves of soft tissues, as well as to offer unusual mechanical properties that differ from natural materials. I have two questions

1. Is that possible to design a type of soft network materials with combining attributes of biomimetic materials and metamaterials?

2. Since I have been working on fatigue of soft materials, I wonder if the fatigue performance of such soft network materials is good or not.

Thank you.



Yihui Zhang's picture

Dear Tongqing,

Many thanks for your kind words and inspiring questions! Please see my replies below:

1. It would be very interesting to explore soft network designs that can combine the physical attributes of both biomimetic materials and metamaterials.  Some progress has been made by introducing soft active materials (e.g., SMP, LCE and hydrogels) into network designs for development of mechanical metamaterials that offer, simultaneously, biomimetic mechanical properties (e.g., J-shaped stress-strain curves and flaw-insensitive behavior) and exotic mechanical behavior (e.g., negative Poisson’s ratios, unusual swelling responses, negative thermal expansion, and abnormal acoustic properties).  For example, my group developed a class of soft network metamaterials by exploiting horseshoe-shaped composite microstructures of hydrogel and passive materials as building blocks, which showed both large negative swelling responses and J-shaped stress-strain curves (see Science Advances, 2018, 4: eaar8535).  The mechanics-guided designs consisting of zigzag microstructures could also endow network materials with both J-shaped stress-strain curves and isotropic negative Poisson’s ratios at large strains (see Soft Matter, 2018, 14:693).

2. The fatigue performance of soft network materials should be important to consider, especially in practical applications.  Intuitively, their fatigue performances mainly depend on the mechanical properties of the constituent materials.  As such, if fatigue-resistant materials are exploited to fabricate the network structures, then the fatigue performance of the entire soft network should be good as well.  The fatigue behavior of the soft network materials embedded in anti-fatigue hydrogels is also worthy of further exploration. 

Warm regards!


Dear Prof. Zhang,

Very stimulating post! Really outstanding work! I have a few questions.

(1) Work on 3D lattice metamaterials is still rare. What are the main difficulties in fabrication and design?

(2) The materials used in lattice metamaterials generally have a low fracture strain. Lattice metamaterials constructed using softer materials with larger stretchabilities are promising. But it poses challenges to fabrications and modeling. What are the potential approaches?

Thank you. 

Best regards, Dong Wang

Yihui Zhang's picture

Dear Dong,

Many thanks for your kind words and questions!  Please see my replies below:

1. In comparison to 2D couterparts, the 3D lattice metamaterials involve much more complex geometries and complicated deformation modes, which makes the development of quantitative mechanics model and design method more challenging.  Despite these difficulties, several important achievements have been made regarding the design of 3D lattice metamaterials, aside from the aforementioned work.  For instance, Prof. Qiming Wang’s group developed a mechanics model of elastomer lattices in the finite deformation regime (see Journal of the Mechanics and Physics of Solids, 2022, 159: 104782), and Prof. Mohsen Asle Zaeem’s group developed a constitutive thermo-visco-hyperelastic model to analyze the shape-memory behavior of several SMP octet-truss lattices (see International Journal of Mechanical Sciences, 2022, 232: 107593).  The main difficulty in their fabrication is elaborated in the reply to your second comment.

2. Indeed, the lack of general, high-resolution 3D fabrication techniques applicable to a very broad range of material types represents a key challenge.  Two/multi-photon lithography, stereolithography technique, digital light processing (DLP) technique and nozzle-based 3D printing techniques correspond to a few promising fabrication techniques of 3D lattice metmaterials.  Excluding the two/multi-photon lithography, the other techniques can all be used in the fabrication of soft lattice metamaterials.  For instance, Prof. Jinsong Leng’s group, Prof. Qi Ge's group (in collaboration with Prof. Yakacki) and Prof. Qiming Wang’s group already employed the laser cladding deposition (LCD), digital light processing (DLP) technique, and stereolithography technique to fabricate SMP lattice metamaterials (see Advanced Functional Materials, 2020, 30: 2004226), LCE lattice metamaterials (see Advanced Materials, 2020, 32: 2000797), and elastomer-based lattice metamaterials (see Journal of the Mechanics and Physics of Solids, 2022, 159: 104782), respectively.  For the modeling approaches, both micromechanics and phenomenological models show promising potentials to guide the design of soft lattice metamaterials.

Warm regards!


Zheng Jia's picture

Dear Yihui,

Thank you very much for putting together this nice and timely topic of soft network materials. This is a very informative and fascinating summary! I have one question: Most soft network materials, especially 3D soft network materials, are homogeneous; That is, the lattice structure or pattern is the same throughout the material. Is it possible to design and fabricate heterogeneous soft network materials that impart different material properties (e.g. Young's modulus) to different regions of the soft network material? Will that enable new functions of soft network materials?

Thank you in advance.






Yihui Zhang's picture

Dear Zheng,

Thank you so much for your comments and insightful questions!  Engineering heteogeneous soft network materials is a very important direction in this area.  While I did not mention the heteogeneous designs in this summary, there are already some explorations reported in the literature.  Regarding the biomimetic soft network materials, the heteogeneous designs can be exploited to better reproduce the spatially non-uniform mechanical properties of skins (Nature Communications, 2015, 6: 6566), noting that the human skin actually has gradient mechanical responses (e.g., nearby waist).  Regarding the soft mechanical metamaterials, introducing heteogenous bi-material horseshoe microstructure design can enable unusual modes of thermal expansion, such as thermally-induced shearing and bending (Advanced Materials, 2019, 31, 1905405).  Regarding the practical applications related to stretchable inorganic electronics, the heteogeneous designs can be exploited to achieve a better integration with the complexly patterned electrical interconnects and hard chips (Science Advances, 2022, 8, eabm3785). 

In terms of the fabrication of heteogeneous soft network materials, the photolithographic processes for creating the 2D networks can easily afford access to gradient forms of the microstructure with spatially varying values of the widths of the ribbon microstructures.  I totally agree it is more challenging to fabricate 3D heteogeneous networks.  You may refer to my reply to Prof. Dong Wang's 2nd comment.

Warm regards!


Lifeng Wang's picture

Dear Yihui,

Thanks for this excellent and timely discussion. I am involved in some studies in 2D soft network materials and believe that these materials have remarkable futures. I have some thoughts in this topic.

1) To be active - soft network materials in response to various external stimuli. There are many active materials available in bulk material state, and are there any convenient methods to structure them in to a network state at different length scale? 

2) Randomly distributed vs highly ordered - To have well controlled macroscopic material properties, clearly highly-ordered network materials are desired. Electrospinning provides a convenient way to fabricate randomly distributed network materials in mesoscale. Is it possible to convert them into highly ordered nano-/micro-structures?  


Best wishes,



Yihui Zhang's picture

Dear Lifeng,

Many thanks for your kind words and comments!  Please see my replies below:

1. The booming of the light-based 3D techniques has attracted lots of attention in the precise fabrication of active-soft network materials at different length scales.  For instance, Prof. Qi Ge's group has used the digital light processing (DLP) based 3D-printing technique to fabricate shape-memory polymers (SMPs), liquid crystal elastomer (LCE), and hydrogel-based active soft network materials at microscale, where the width of microstructure ranges from 100 μm to 1 mm (see Advanced Materials, 2021, 33: 2101298; Advanced Materials, 2020, 32: 2000797; Science Advances, 2021, 7: eaba4261).  Prof. Rayne Zeng’s group used the projection stereolithography systems to fabricate the polymer-based soft network piezoelectric materials, where the width of microstructure is around 100 μm (see Natural Materials, 2019, 18: 234).  Buckling-guided 3D assembly could also be exploited to transform 2D active network materials into well-ordered 3D structures (see Nature Communications, 2022, 13: 524).

2. Existing studies showed the possibility of forming soft network materials with ordered microstructure in nano/micro-scale through electrospinning technique.  For example, the fixed metallic receiver always resulted in randomly distributed microstructures, due to the irregular spraying, but if the fixed receiver turns to the rotated metallic receiver, the aligned nano/micro-scale fibers can be obtained (see Advanced Materials Interfaces, 2022, 9: 2101808; ACS Applied Materials Interfaces, 2021, 13: 26339).  To obtain ordered nano/microstructures with more complex geometries, it might still remain challenging. 

Warm regards!


Subscribe to Comments for "Journal Club for September 2022: Mechanics of soft network materials"

Recent comments

More comments


Subscribe to Syndicate