Pub Date : 2026-03-01Epub Date: 2026-01-25DOI: 10.1016/j.eml.2026.102453
Yi Zhang , Wei Zhong Jiang , Xue Gang Zhang , Hui Chen Luo , Xiang Jie Wei , Han Yan , Jun Dong , Xin Ren
Conventional materials exhibit uniformly positive coefficients of thermal expansion (CTE). While anomalous CTE values have been documented, including negative or zero coefficients, the achievable deformation modes remain constrained to the orthogonal direction. Realizing thermally driven rotational or torsional deformation continues to present fundamental challenges. Here, we introduce a design strategy integrating thermostat metal strips into 3D chiral metamaterials. The critical geometrical parameters are analyzed numerically, including tessellating cellular numbers and strips’ relative lengths. An oil bath heating test is conducted to examine the thermal rotating effect of the assembled specimen. Results indicate that the increase in cellular number diminishes the rotating behavior. Enhancing the relevant length of metal strips will enhance intrinsic bending-driven rotating mechanisms, thereby amplifying the angle. A maximum rotating angle of 13.8° is achieved over a temperature range of 25 ℃ to 300 ℃. These findings expand the scope of thermally responsive metamaterials and show the potential application for temperature-sensitive devices in structural engineering.
{"title":"Thermal rotation behavior of 3D bimaterial bending-dominated chiral metamaterials","authors":"Yi Zhang , Wei Zhong Jiang , Xue Gang Zhang , Hui Chen Luo , Xiang Jie Wei , Han Yan , Jun Dong , Xin Ren","doi":"10.1016/j.eml.2026.102453","DOIUrl":"10.1016/j.eml.2026.102453","url":null,"abstract":"<div><div>Conventional materials exhibit uniformly positive coefficients of thermal expansion (CTE). While anomalous CTE values have been documented, including negative or zero coefficients, the achievable deformation modes remain constrained to the orthogonal direction. Realizing thermally driven rotational or torsional deformation continues to present fundamental challenges. Here, we introduce a design strategy integrating thermostat metal strips into 3D chiral metamaterials. The critical geometrical parameters are analyzed numerically, including tessellating cellular numbers and strips’ relative lengths. An oil bath heating test is conducted to examine the thermal rotating effect of the assembled specimen. Results indicate that the increase in cellular number diminishes the rotating behavior. Enhancing the relevant length of metal strips will enhance intrinsic bending-driven rotating mechanisms, thereby amplifying the angle. A maximum rotating angle of 13.8° is achieved over a temperature range of 25 ℃ to 300 ℃. These findings expand the scope of thermally responsive metamaterials and show the potential application for temperature-sensitive devices in structural engineering.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"83 ","pages":"Article 102453"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146078334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-01Epub Date: 2026-01-09DOI: 10.1016/j.eml.2026.102445
Giacomo Brambilla , Sebastiano Cominelli , Marco Verbicaro , Gabriele Cazzulani , Francesco Braghin
This letter responds to Milton’s commentary [1], which questions the originality of the microstructure proposed by Brambilla et al.[2]. We trace the origins of this class of designs to Sigmund’s 2000 work in 2D [3] and to the 3D extension introduced by Milton et al. in 2017 [4]. Finally, we highlight that our study makes several important contributions. One of these is the design of a material whose properties closely resemble those of water, making it ideal for acoustic applications.
{"title":"Reply to “A rediscovery of stiff pentamodes. A comment on high bulk modulus pentamodes: The three-dimensional metal water''","authors":"Giacomo Brambilla , Sebastiano Cominelli , Marco Verbicaro , Gabriele Cazzulani , Francesco Braghin","doi":"10.1016/j.eml.2026.102445","DOIUrl":"10.1016/j.eml.2026.102445","url":null,"abstract":"<div><div>This letter responds to Milton’s commentary <span><span>[1]</span></span>, which questions the originality of the microstructure proposed by Brambilla <em>et al.</em> <span><span>[2]</span></span>. We trace the origins of this class of designs to Sigmund’s 2000 work in 2D <span><span>[3]</span></span> and to the 3D extension introduced by Milton <em>et al.</em> in 2017 <span><span>[4]</span></span>. Finally, we highlight that our study makes several important contributions. One of these is the design of a material whose properties closely resemble those of water, making it ideal for acoustic applications.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"83 ","pages":"Article 102445"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147397472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-01Epub Date: 2025-12-02DOI: 10.1016/j.eml.2025.102431
Christine Heera Ahn, Zheqi Chen, Xianyang Bao, Zhigang Suo
In a brittle polymer glass, a fracture property increases with the length of polymer chains and then plateaus. Here, we use poly(methyl methacrylate) to study such transitions in several fracture properties. We measure strength using samples without precut crack, and measure toughness and fatigue threshold using samples with precut crack. The three properties plateau at different chain lengths. These transitions arise from a change in fracture mechanism—from chain pullout to chain scission. The chain length for a fracture property to plateau is understood using a shear-lag model. The plateau length is set by the balance of the strengths of bonds of two types: the covalent bonds along the chains, which resists scission, and the noncovalent bonds between the chains, which resist pullout. For each of the three fracture properties, we discuss the chain length for the property to plateau, as well as the value of the plateau.
{"title":"How does chain length affect fracture of a brittle polymer glass?","authors":"Christine Heera Ahn, Zheqi Chen, Xianyang Bao, Zhigang Suo","doi":"10.1016/j.eml.2025.102431","DOIUrl":"10.1016/j.eml.2025.102431","url":null,"abstract":"<div><div>In a brittle polymer glass, a fracture property increases with the length of polymer chains and then plateaus. Here, we use poly(methyl methacrylate) to study such transitions in several fracture properties. We measure strength using samples without precut crack, and measure toughness and fatigue threshold using samples with precut crack. The three properties plateau at different chain lengths. These transitions arise from a change in fracture mechanism—from chain pullout to chain scission. The chain length for a fracture property to plateau is understood using a shear-lag model. The plateau length is set by the balance of the strengths of bonds of two types: the covalent bonds along the chains, which resists scission, and the noncovalent bonds between the chains, which resist pullout. For each of the three fracture properties, we discuss the chain length for the property to plateau, as well as the value of the plateau.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"82 ","pages":"Article 102431"},"PeriodicalIF":4.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-01Epub Date: 2025-12-13DOI: 10.1016/j.eml.2025.102436
Zheyu Dong , Jiabao Bai , Daochen Yin , Kunqing Yu , Siqi Yan , Zhi Sheng , Zheng Jia
Recent advances in soft material adhesion have attracted considerable interest due to their potential implications for various scientific disciplines. Solving the 1D Diffusion-Convection-Reaction Equation (DCR Equation) remains a critical challenge in adhesion systems of soft materials, often hindered by computational complexities. Specifically, solving the 1D DCR Equation is particularly challenging owing to its intrinsic complexity as a nonlinear dynamical system, which is governed by an equation combining temporal evolution with zeroth, first, and second-order spatial differential terms. While substantial progress has been made through both experimental and theoretical approaches, the application of neural network-based methods in this area remains relatively underdeveloped. In this study, we address this gap by introducing, for the first time, Chebyshev physics-informed Kolmogorov-Arnold networks (c-PIKANs) specifically for modeling 1D DCR Equation of soft-material adhesion, a framework that systematically optimizes architecture parameters (learning rate, polynomial order, layer size) to maximize predictive performance. The c-PIKAN architecture outperforms conventional multilayer perceptron (MLP)-based physics-informed neural networks (PINNs) in accuracy and efficiency while requiring a smaller network size. This work paves the way for future applications of Kolmogorov-Arnold Networks (KANs) in soft material mechanics and provides crucial guidance for the adjustment of network hyperparameters, potentially opening new avenues for innovation in the field.
{"title":"Chebyshev physics-informed Kolmogorov-Arnold networks for diffusion-convection-reaction equation in soft material adhesion system","authors":"Zheyu Dong , Jiabao Bai , Daochen Yin , Kunqing Yu , Siqi Yan , Zhi Sheng , Zheng Jia","doi":"10.1016/j.eml.2025.102436","DOIUrl":"10.1016/j.eml.2025.102436","url":null,"abstract":"<div><div>Recent advances in soft material adhesion have attracted considerable interest due to their potential implications for various scientific disciplines. Solving the 1D Diffusion-Convection-Reaction Equation (DCR Equation) remains a critical challenge in adhesion systems of soft materials, often hindered by computational complexities. Specifically, solving the 1D DCR Equation is particularly challenging owing to its intrinsic complexity as a nonlinear dynamical system, which is governed by an equation combining temporal evolution with zeroth, first, and second-order spatial differential terms. While substantial progress has been made through both experimental and theoretical approaches, the application of neural network-based methods in this area remains relatively underdeveloped. In this study, we address this gap by introducing, for the first time, Chebyshev physics-informed Kolmogorov-Arnold networks (c-PIKANs) specifically for modeling 1D DCR Equation of soft-material adhesion, a framework that systematically optimizes architecture parameters (learning rate, polynomial order, layer size) to maximize predictive performance. The c-PIKAN architecture outperforms conventional multilayer perceptron (MLP)-based physics-informed neural networks (PINNs) in accuracy and efficiency while requiring a smaller network size. This work paves the way for future applications of Kolmogorov-Arnold Networks (KANs) in soft material mechanics and provides crucial guidance for the adjustment of network hyperparameters, potentially opening new avenues for innovation in the field.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"82 ","pages":"Article 102436"},"PeriodicalIF":4.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-01Epub Date: 2025-11-29DOI: 10.1016/j.eml.2025.102429
Dichao Ning, Zihan Zhang, Chenyu Jin, Qian Shi
Rubber is widely applied due to its high elasticity and durability, but traditional crosslinked networks are non-recyclable. The incorporation of dynamic covalent bonds endows vitrimers with recyclability and self-healing ability. However, the regulatory effect of curing kinetics and chemical ratio on dynamic covalent bonds has not been systematically studied, and such regulation is crucial for designing high-performance rubber vitrimers. In this work, rubber vitrimers with hybrid network were synthesized by using epoxy monomers and curing agent containing disulfide bonds. By varying the chemical ratio of soft segments (PEG) and hard segments (BPDG or DGEBA), and tuning curing time, we characterized their dynamic performance, tensile properties and fracture toughness. Furthermore, kinetic equation was incorporated into and used to extend the Lake–Thomas model, enabling quantitative description and prediction of fracture energy. The results demonstrate that increased curing degree and disulfide bond proportion enhance the fracture toughness and fracture strain of the rubber polymer, but slightly reduce its strength and modulus. Moreover, the introduction of dynamic covalent bonds favors both fracture toughness and dynamic performance. This work provides theoretical guidance and processing strategies for the design of high-performance rubbers.
{"title":"The role of dynamic covalent bonds on mechanical properties of rubber vitrimer with hybrid networks","authors":"Dichao Ning, Zihan Zhang, Chenyu Jin, Qian Shi","doi":"10.1016/j.eml.2025.102429","DOIUrl":"10.1016/j.eml.2025.102429","url":null,"abstract":"<div><div>Rubber is widely applied due to its high elasticity and durability, but traditional crosslinked networks are non-recyclable. The incorporation of dynamic covalent bonds endows vitrimers with recyclability and self-healing ability. However, the regulatory effect of curing kinetics and chemical ratio on dynamic covalent bonds has not been systematically studied, and such regulation is crucial for designing high-performance rubber vitrimers. In this work, rubber vitrimers with hybrid network were synthesized by using epoxy monomers and curing agent containing disulfide bonds. By varying the chemical ratio of soft segments (PEG) and hard segments (BPDG or DGEBA), and tuning curing time, we characterized their dynamic performance, tensile properties and fracture toughness. Furthermore, kinetic equation was incorporated into and used to extend the Lake–Thomas model, enabling quantitative description and prediction of fracture energy. The results demonstrate that increased curing degree and disulfide bond proportion enhance the fracture toughness and fracture strain of the rubber polymer, but slightly reduce its strength and modulus. Moreover, the introduction of dynamic covalent bonds favors both fracture toughness and dynamic performance. This work provides theoretical guidance and processing strategies for the design of high-performance rubbers.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"82 ","pages":"Article 102429"},"PeriodicalIF":4.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-01Epub Date: 2025-12-03DOI: 10.1016/j.eml.2025.102428
Sourav Kumar Panja , Kunnath Ranjith
We investigate the control of frictional instabilities at bi-material interfaces using mechanical metamaterials with unconventional dynamic properties. Specifically, we examine two configurations: (i) an anti-plane shear problem involving a metaelastic layer with negative effective density and shear modulus slipping on a classical elastic half-space, and (ii) an in-plane problem where a metaelastic half-space exhibiting triple-negative properties (negative density, bulk modulus, and shear modulus) overlies a conventional elastic half-space. Guided by a linear stability analysis of quasi-static steady sliding, we carry out numerical simulations of spontaneous rupture propagation at the interface with a slip-weakening friction law. This work shows the possibility of rupture arrest or propagation control at bi-material interfaces by negative effective properties of mechanical metamaterial with implications for seismic fault engineering, tribology, and advanced material design.
{"title":"Control of dynamic frictional instability using mechanical metamaterials","authors":"Sourav Kumar Panja , Kunnath Ranjith","doi":"10.1016/j.eml.2025.102428","DOIUrl":"10.1016/j.eml.2025.102428","url":null,"abstract":"<div><div>We investigate the control of frictional instabilities at bi-material interfaces using mechanical metamaterials with unconventional dynamic properties. Specifically, we examine two configurations: (i) an anti-plane shear problem involving a metaelastic layer with negative effective density and shear modulus slipping on a classical elastic half-space, and (ii) an in-plane problem where a metaelastic half-space exhibiting triple-negative properties (negative density, bulk modulus, and shear modulus) overlies a conventional elastic half-space. Guided by a linear stability analysis of quasi-static steady sliding, we carry out numerical simulations of spontaneous rupture propagation at the interface with a slip-weakening friction law. This work shows the possibility of rupture arrest or propagation control at bi-material interfaces by negative effective properties of mechanical metamaterial with implications for seismic fault engineering, tribology, and advanced material design.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"82 ","pages":"Article 102428"},"PeriodicalIF":4.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685368","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-01Epub Date: 2025-11-29DOI: 10.1016/j.eml.2025.102426
Yucheng Huo , Kexin Guo , Massimo Paradiso , K. Jimmy Hsia
Collective behaviors in cellular systems are regulated not only by biochemical signaling pathways but also by intercellular mechanical forces, whose quantification in contractile monolayers remains poorly understood. Here, by integrating traction force microscopy and numerical simulations, we reconstruct the stress distribution in C2C12 myoblast monolayers to reveal the roles of local mechanical forces in determining the collective cellular structures. We find that contractile monolayers exhibit positive maximum and negative minimum principal stresses, reflecting the intrinsic anisotropy of active tension. Distinct stress patterns emerge around topological defects, coinciding with singularities in cell alignment, density, and morphology, indicating a strong coupling between mechanical forces and structural organization. Moreover, tensile stresses are preferentially transmitted along the cell elongation axis and compressive stresses transversely, demonstrating that local stress guides cell arrangement. This mechanical guidance appears to be universal among contractile systems, as observed also in bone marrow–derived mesenchymal stem cells. Together, our work establishes a quantitative framework for characterizing mechanical anisotropy in active cellular monolayers and reveals a general principle of force–structure coupling, providing a physical basis for understanding how mechanics governs myogenesis, morphogenesis, and collective organization in contractile cellular systems.
{"title":"Stress distribution in contractile cell monolayers","authors":"Yucheng Huo , Kexin Guo , Massimo Paradiso , K. Jimmy Hsia","doi":"10.1016/j.eml.2025.102426","DOIUrl":"10.1016/j.eml.2025.102426","url":null,"abstract":"<div><div>Collective behaviors in cellular systems are regulated not only by biochemical signaling pathways but also by intercellular mechanical forces, whose quantification in contractile monolayers remains poorly understood. Here, by integrating traction force microscopy and numerical simulations, we reconstruct the stress distribution in C2C12 myoblast monolayers to reveal the roles of local mechanical forces in determining the collective cellular structures. We find that contractile monolayers exhibit positive maximum and negative minimum principal stresses, reflecting the intrinsic anisotropy of active tension. Distinct stress patterns emerge around topological defects, coinciding with singularities in cell alignment, density, and morphology, indicating a strong coupling between mechanical forces and structural organization. Moreover, tensile stresses are preferentially transmitted along the cell elongation axis and compressive stresses transversely, demonstrating that local stress guides cell arrangement. This mechanical guidance appears to be universal among contractile systems, as observed also in bone marrow–derived mesenchymal stem cells. Together, our work establishes a quantitative framework for characterizing mechanical anisotropy in active cellular monolayers and reveals a general principle of force–structure coupling, providing a physical basis for understanding how mechanics governs myogenesis, morphogenesis, and collective organization in contractile cellular systems.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"82 ","pages":"Article 102426"},"PeriodicalIF":4.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685314","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-01Epub Date: 2025-12-01DOI: 10.1016/j.eml.2025.102430
Dezhong Tong , Andrew Choi , Jiaqi Wang , Weicheng Huang , Zexiong Chen , Jiahao Li , Xiaonan Huang , Mingchao Liu , Huajian Gao , K. Jimmy Hsia
Flexible slender structures such as rods, ribbons, plates, and shells exhibit extreme nonlinear responses – bending, twisting, buckling, wrinkling, and self-contact – that defy conventional simulation frameworks. Discrete Differential Geometry (DDG) has emerged as a geometry-first, structure-preserving paradigm for modeling such behaviors. Unlike finite element or mass–spring methods, DDG discretizes geometry rather than governing equations, allowing curvature, twist, and strain to be defined directly on meshes. This approach yields robust large-deformation dynamics, accurate handling of contact, and differentiability essential for inverse design and learning-based control. This review consolidates the rapidly expanding landscape of DDG models across 1D and 2D systems, including discrete elastic rods, ribbons, plates, and shells, as well as multiphysics extensions to contact, magnetic actuation, and fluid–structure interaction. We synthesize applications spanning mechanics of nonlinear instabilities, biological morphogenesis, functional structures and devices, and robotics from manipulation to soft machines. Compared with established approaches, DDG offers a unique balance of geometric fidelity, computational efficiency, and algorithmic differentiability, bridging continuum rigor with real-time, contact-rich performance. We conclude by outlining opportunities for multiphysics coupling, hybrid physics–data pipelines, and scalable GPU-accelerated solvers, and by emphasizing DDG’s role in enabling digital twins, sim-to-real transfer, and intelligent design of next-generation flexible systems.
{"title":"Discrete differential geometry for simulating nonlinear behaviors of flexible systems: A survey","authors":"Dezhong Tong , Andrew Choi , Jiaqi Wang , Weicheng Huang , Zexiong Chen , Jiahao Li , Xiaonan Huang , Mingchao Liu , Huajian Gao , K. Jimmy Hsia","doi":"10.1016/j.eml.2025.102430","DOIUrl":"10.1016/j.eml.2025.102430","url":null,"abstract":"<div><div>Flexible slender structures such as rods, ribbons, plates, and shells exhibit extreme nonlinear responses – bending, twisting, buckling, wrinkling, and self-contact – that defy conventional simulation frameworks. Discrete Differential Geometry (DDG) has emerged as a geometry-first, structure-preserving paradigm for modeling such behaviors. Unlike finite element or mass–spring methods, DDG discretizes geometry rather than governing equations, allowing curvature, twist, and strain to be defined directly on meshes. This approach yields robust large-deformation dynamics, accurate handling of contact, and differentiability essential for inverse design and learning-based control. This review consolidates the rapidly expanding landscape of DDG models across 1D and 2D systems, including discrete elastic rods, ribbons, plates, and shells, as well as multiphysics extensions to contact, magnetic actuation, and fluid–structure interaction. We synthesize applications spanning mechanics of nonlinear instabilities, biological morphogenesis, functional structures and devices, and robotics from manipulation to soft machines. Compared with established approaches, DDG offers a unique balance of geometric fidelity, computational efficiency, and algorithmic differentiability, bridging continuum rigor with real-time, contact-rich performance. We conclude by outlining opportunities for multiphysics coupling, hybrid physics–data pipelines, and scalable GPU-accelerated solvers, and by emphasizing DDG’s role in enabling digital twins, sim-to-real transfer, and intelligent design of next-generation flexible systems.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"82 ","pages":"Article 102430"},"PeriodicalIF":4.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-01Epub Date: 2025-12-07DOI: 10.1016/j.eml.2025.102435
Baihong Chen , Huxiao Yang , Rui Xiao
The exchangeable liquid crystal elastomers (LCEs) with dynamic disulfide bonds possess excellent processability, recyclability and room-temperature programmability, making them highly promising for applications in soft robotics and shape-morphing structures. In this work, we combine experimental and theoretical approaches to systematically investigate the effect of programming stretches on the anisotropic mechanical response of LCEs with exchangeable disulfide bonds. We first fabricated a series of monodomain LCEs by applying varying programming stretches using disulfide exchange reactions. The thermal actuation response of these specimens was then characterized. Uniaxial tensile tests were further conducted to elucidate the effects of the programming stretches on the anisotropic mechanical responses at different strain rates. A viscoelastic model is then applied to simulate the anisotropic and rate-dependent mechanical response of monodomain LCEs. The results reveal the existence of a saturation programming stretch. Below this threshold, increasing programming stretches extends the length of the stress plateau, while the plateau stress remains unchanged. Notably, the Young’s moduli along orthogonal directions are identical prior to director rotation, contrasting with conventional two-step polymerized monodomain LCEs. This suggests that the anisotropic modulus of conventional LCEs may originate from the prestretched network. The experimental results also reveal that hysteresis loops under uniaxial loading along the director are larger than those under perpendicular loading. This indicates that the viscosity associated with director rotation is significantly lower than that of network deformation. For the theoretical part, the viscoelastic model with multiple relaxation processes successfully captures the anisotropic and rate-dependent mechanical response of monodomain LCEs, while the model with a single relaxation process fails to predict the area of the hysteresis loop over a wide rate region.
{"title":"Experimental characterization and modeling anisotropic mechanical responses of liquid crystal elastomers with exchangeable disulfide bonds","authors":"Baihong Chen , Huxiao Yang , Rui Xiao","doi":"10.1016/j.eml.2025.102435","DOIUrl":"10.1016/j.eml.2025.102435","url":null,"abstract":"<div><div>The exchangeable liquid crystal elastomers (LCEs) with dynamic disulfide bonds possess excellent processability, recyclability and room-temperature programmability, making them highly promising for applications in soft robotics and shape-morphing structures. In this work, we combine experimental and theoretical approaches to systematically investigate the effect of programming stretches on the anisotropic mechanical response of LCEs with exchangeable disulfide bonds. We first fabricated a series of monodomain LCEs by applying varying programming stretches using disulfide exchange reactions. The thermal actuation response of these specimens was then characterized. Uniaxial tensile tests were further conducted to elucidate the effects of the programming stretches on the anisotropic mechanical responses at different strain rates. A viscoelastic model is then applied to simulate the anisotropic and rate-dependent mechanical response of monodomain LCEs. The results reveal the existence of a saturation programming stretch. Below this threshold, increasing programming stretches extends the length of the stress plateau, while the plateau stress remains unchanged. Notably, the Young’s moduli along orthogonal directions are identical prior to director rotation, contrasting with conventional two-step polymerized monodomain LCEs. This suggests that the anisotropic modulus of conventional LCEs may originate from the prestretched network. The experimental results also reveal that hysteresis loops under uniaxial loading along the director are larger than those under perpendicular loading. This indicates that the viscosity associated with director rotation is significantly lower than that of network deformation. For the theoretical part, the viscoelastic model with multiple relaxation processes successfully captures the anisotropic and rate-dependent mechanical response of monodomain LCEs, while the model with a single relaxation process fails to predict the area of the hysteresis loop over a wide rate region.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"82 ","pages":"Article 102435"},"PeriodicalIF":4.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-01Epub Date: 2025-11-27DOI: 10.1016/j.eml.2025.102423
Cosima du Pasquier , Sehui Jeong , Pan Liu , Susan Williams , Nour Mnejja , Allison M. Okamura , Skylar Tibbits , Tian Chen
This work presents a multi-level modeling and design framework for weft knitted fabrics, beginning with a volumetric finite element analysis capturing their mechanical behavior from fundamental principles. Incorporating yarn-level data, it accurately predicts stress–strain responses, reducing the need for extensive physical testing. A simplified strain energy approach homogenizes the results into three key variables, enabling rapid, accurate predictions in minutes. After validation against experiments, our framework can simulate new knit fabrics without additional tests. In real-world scenarios, fabrics often feature variations in yarn materials or patterns. The framework extends to heterogeneous fabrics, showing that transitions between distinct regions can be captured using simple mechanical analogies: springs in series and parallel. This allows heterogeneous textiles to be treated as idealized patchworks of homogeneous pieces, preserving predictive accuracy. The method is demonstrated by designing and producing a compression sleeve with uniform pressure, illustrating how the framework supports development of knits tailored to specific assistance levels and anatomical features. By combining volumetric finite element analysis, simplified model through homogenization, and controlled material transitions, this approach provides a scalable, high-fidelity path toward next-generation weft knitted fabric design.
{"title":"Multi-level mechanical modeling and computational design framework for weft knitted fabrics","authors":"Cosima du Pasquier , Sehui Jeong , Pan Liu , Susan Williams , Nour Mnejja , Allison M. Okamura , Skylar Tibbits , Tian Chen","doi":"10.1016/j.eml.2025.102423","DOIUrl":"10.1016/j.eml.2025.102423","url":null,"abstract":"<div><div>This work presents a multi-level modeling and design framework for weft knitted fabrics, beginning with a volumetric finite element analysis capturing their mechanical behavior from fundamental principles. Incorporating yarn-level data, it accurately predicts stress–strain responses, reducing the need for extensive physical testing. A simplified strain energy approach homogenizes the results into three key variables, enabling rapid, accurate predictions in minutes. After validation against experiments, our framework can simulate new knit fabrics without additional tests. In real-world scenarios, fabrics often feature variations in yarn materials or patterns. The framework extends to heterogeneous fabrics, showing that transitions between distinct regions can be captured using simple mechanical analogies: springs in series and parallel. This allows heterogeneous textiles to be treated as idealized patchworks of homogeneous pieces, preserving predictive accuracy. The method is demonstrated by designing and producing a compression sleeve with uniform pressure, illustrating how the framework supports development of knits tailored to specific assistance levels and anatomical features. By combining volumetric finite element analysis, simplified model through homogenization, and controlled material transitions, this approach provides a scalable, high-fidelity path toward next-generation weft knitted fabric design.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"82 ","pages":"Article 102423"},"PeriodicalIF":4.5,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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