Pub Date : 2026-03-01Epub Date: 2026-01-08DOI: 10.1016/j.eml.2026.102443
Chih-Jung Lin , Heng-Kwong Tsao , Yu-Jane Sheng
Hydrogel elastomers display stress relaxation, hysteresis, and the Mullins effect even in highly crosslinked networks where chain mobility is strongly suppressed, yet their microscopic origin remains elusive. Although bond rupture has been recognized as a possible contributor, its temporal and spatial occurrence under applied force has not been clearly elucidated. Dissipative particle dynamics simulations with bond-rupture capability reproduce the macroscopic responses, attributed to rare rupture events in tensile strands. Rupture does not result from direct mechanical fracture but from thermal fluctuations that surpass a stress-lowered energy barrier, initiating network reconfiguration that relaxes stress and produces hysteresis. Microscopic variations in mean bond length quantitatively mirror macroscopic stress evolution, ruling out viscoelastic dissipation as the primary mechanism. Our results establish thermally activated bond rupture as the unifying microscopic origin of stress relaxation and hysteresis in hydrogel elastomers, linking microscopic bond dynamics to macroscopic stress responses under cyclic deformations.
{"title":"Force-facilitated rare thermally activated bond rupture enables stress relaxation and hysteresis in hydrogel elastomers","authors":"Chih-Jung Lin , Heng-Kwong Tsao , Yu-Jane Sheng","doi":"10.1016/j.eml.2026.102443","DOIUrl":"10.1016/j.eml.2026.102443","url":null,"abstract":"<div><div>Hydrogel elastomers display stress relaxation, hysteresis, and the Mullins effect even in highly crosslinked networks where chain mobility is strongly suppressed, yet their microscopic origin remains elusive. Although bond rupture has been recognized as a possible contributor, its temporal and spatial occurrence under applied force has not been clearly elucidated. Dissipative particle dynamics simulations with bond-rupture capability reproduce the macroscopic responses, attributed to rare rupture events in tensile strands. Rupture does not result from direct mechanical fracture but from thermal fluctuations that surpass a stress-lowered energy barrier, initiating network reconfiguration that relaxes stress and produces hysteresis. Microscopic variations in mean bond length quantitatively mirror macroscopic stress evolution, ruling out viscoelastic dissipation as the primary mechanism. Our results establish thermally activated bond rupture as the unifying microscopic origin of stress relaxation and hysteresis in hydrogel elastomers, linking microscopic bond dynamics to macroscopic stress responses under cyclic deformations.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"83 ","pages":"Article 102443"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979436","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: 2025-12-30DOI: 10.1016/j.eml.2025.102439
Yijian Zheng, Yang Gao, Tongqing Lu
The fatigue threshold of covalent hydrogels follows the Lake-Thomas model, equating to the energy needed to break covalent bonds between crosslinks at the crack tip. Dynamic bonds are widely introduced as secondary crosslinks to toughen hydrogels. Previous studies have reported that dynamic bonds contribute to the fatigue threshold in some tough hydrogels but not in others, making their contribution unclear. In this work, we prepare dual-crosslinking hydrogels (PAV-M2+) by introducing ligands along covalent polymer chains, enabling dynamic coordination with various M2+ ions to tune the relaxation time. In such hydrogels, we propose that covalent bonds contribute to the fatigue threshold via the Lake-Thomas model, while dynamic bonds contribute based on the competition between relaxation time and the crack-tip strain rate. When the strain rate greatly exceeds the inverse of the relaxation time, dynamic bonds cannot re-associate and contribute little to fatigue threshold. Conversely, when the strain rate is much lower than the inverse of relaxation time, they re-associate reversibly and enhance the threshold. The fatigue threshold of PAV-Ni hydrogels (relaxation time ∼ 300 ms) is 10.5 J/m2 at a strain rate of 1 s−1 (consistent with the Lake-Thomas prediction, 9.4 J/m2), and increases to 17.7 J/m2 at 0.1 s−1. The fatigue threshold of PAV-Zn hydrogels (relaxation time ∼ 0.3 ms) is 39.8 J/m2 at 1 s−1 and 41.4 J/m2 at 0.1 s−1, due to the recovery of dynamic bonds during loading cycles. Based on these results, we propose a modified Lake-Thomas model that incorporates the contribution of dynamic bonds to fatigue threshold, capturing the competition between relaxation time and strain rate.
{"title":"Fatigue threshold of dual-crosslinking hydrogels","authors":"Yijian Zheng, Yang Gao, Tongqing Lu","doi":"10.1016/j.eml.2025.102439","DOIUrl":"10.1016/j.eml.2025.102439","url":null,"abstract":"<div><div>The fatigue threshold of covalent hydrogels follows the Lake-Thomas model, equating to the energy needed to break covalent bonds between crosslinks at the crack tip. Dynamic bonds are widely introduced as secondary crosslinks to toughen hydrogels. Previous studies have reported that dynamic bonds contribute to the fatigue threshold in some tough hydrogels but not in others, making their contribution unclear. In this work, we prepare dual-crosslinking hydrogels (PAV-M<sup>2</sup><sup>+</sup>) by introducing ligands along covalent polymer chains, enabling dynamic coordination with various M<sup>2+</sup> ions to tune the relaxation time. In such hydrogels, we propose that covalent bonds contribute to the fatigue threshold via the Lake-Thomas model, while dynamic bonds contribute based on the competition between relaxation time and the crack-tip strain rate. When the strain rate greatly exceeds the inverse of the relaxation time, dynamic bonds cannot re-associate and contribute little to fatigue threshold. Conversely, when the strain rate is much lower than the inverse of relaxation time, they re-associate reversibly and enhance the threshold. The fatigue threshold of PAV-Ni hydrogels (relaxation time ∼ 300 ms) is 10.5 J/m<sup>2</sup> at a strain rate of 1 s<sup>−1</sup> (consistent with the Lake-Thomas prediction, 9.4 J/m<sup>2</sup>), and increases to 17.7 J/m<sup>2</sup> at 0.1 s<sup>−1</sup>. The fatigue threshold of PAV-Zn hydrogels (relaxation time ∼ 0.3 ms) is 39.8 J/m<sup>2</sup> at 1 s<sup>−1</sup> and 41.4 J/m<sup>2</sup> at 0.1 s<sup>−1</sup>, due to the recovery of dynamic bonds during loading cycles. Based on these results, we propose a modified Lake-Thomas model that incorporates the contribution of dynamic bonds to fatigue threshold, capturing the competition between relaxation time and strain rate.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"83 ","pages":"Article 102439"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886073","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: 2026-01-10DOI: 10.1016/j.eml.2026.102444
Graeme W. Milton
We bring attention to the fact that the claim of Brambilla et.al. [1] of discovering a novel design for pentamode materials is incorrect. Back in 2016 Briane Harutyunyan and myself [2] designed a class of stiff pentamodes, that include the high bulk modulus pentamodes of Brambilla et.al. Our design generalized to three-dimensions, and to full anisotropy, the main aspects of a two-dimensional construction of Sigmund [3]. It is emphasized that the in depth analysis of Brambilla et.al. goes well beyond our brief treatment.
{"title":"A rediscovery of stiff pentmodes. A comment on “High bulk modulus pentamodes: the three-dimensional metal water''","authors":"Graeme W. Milton","doi":"10.1016/j.eml.2026.102444","DOIUrl":"10.1016/j.eml.2026.102444","url":null,"abstract":"<div><div>We bring attention to the fact that the claim of Brambilla et.al. <span><span>[1]</span></span> of discovering a novel design for pentamode materials is incorrect. Back in 2016 Briane Harutyunyan and myself <span><span>[2]</span></span> designed a class of stiff pentamodes, that include the high bulk modulus pentamodes of Brambilla et.al. Our design generalized to three-dimensions, and to full anisotropy, the main aspects of a two-dimensional construction of Sigmund <span><span>[3]</span></span>. It is emphasized that the in depth analysis of Brambilla et.al. goes well beyond our brief treatment.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"83 ","pages":"Article 102444"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147397468","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: 2026-01-02DOI: 10.1016/j.eml.2025.102437
Wenjie Li , Yu Herng Tan , Zhong Wang , Xuguang Dong , Huichan Zhao
Soft cylindrical shell grippers consist of a rigid outer shell and a soft inner layer that inflates inward under internal pressure. This inflatable ring actuator mechanism enables the gripper to conform to and stably grasp objects, offering unique advantages in handling irregular shapes and compliant materials, and making these grippers promising candidates for soft robotic manipulation. However, upon inflation, their soft inner walls often undergo a sequence of buckling instabilities—from wrinkling to creasing and more complex post-buckling behaviors. Due to the stochastic nature of these buckling instabilities, the resulting deformation patterns—such as the number, positions, and deflections of creases—vary unpredictably, leading to inconsistencies in gripper performance. This study investigates the factors governing the buckling instabilities of soft cylindrical shell grippers and proposes strategies for their stabilization. Through theoretical analysis and finite element (FE) simulations, we establish the relationship between geometric parameters and the predicted buckling instabilities. To control the instability morphology, we introduce evenly distributed geometric imperfections and implement a material training process to mitigate non-uniform deformation by leveraging the Mullins effect. We demonstrate that these combined strategies significantly improve grasping performance, including increased contact area, enhanced self-centering, and improved repeatability. Finally, we validate the gripper’s effectiveness in real-world scenarios through on-arm pick-and-place experiments. This work provides a framework for designing soft cylindrical shell grippers with greater reliability, while maintaining simplicity in fabrication.
{"title":"Stabilizing the buckling instabilities of soft cylindrical shell grippers","authors":"Wenjie Li , Yu Herng Tan , Zhong Wang , Xuguang Dong , Huichan Zhao","doi":"10.1016/j.eml.2025.102437","DOIUrl":"10.1016/j.eml.2025.102437","url":null,"abstract":"<div><div>Soft cylindrical shell grippers consist of a rigid outer shell and a soft inner layer that inflates inward under internal pressure. This inflatable ring actuator mechanism enables the gripper to conform to and stably grasp objects, offering unique advantages in handling irregular shapes and compliant materials, and making these grippers promising candidates for soft robotic manipulation. However, upon inflation, their soft inner walls often undergo a sequence of buckling instabilities—from wrinkling to creasing and more complex post-buckling behaviors. Due to the stochastic nature of these buckling instabilities, the resulting deformation patterns—such as the number, positions, and deflections of creases—vary unpredictably, leading to inconsistencies in gripper performance. This study investigates the factors governing the buckling instabilities of soft cylindrical shell grippers and proposes strategies for their stabilization. Through theoretical analysis and finite element (FE) simulations, we establish the relationship between geometric parameters and the predicted buckling instabilities. To control the instability morphology, we introduce evenly distributed geometric imperfections and implement a material <em>training</em> process to mitigate non-uniform deformation by leveraging the Mullins effect. We demonstrate that these combined strategies significantly improve grasping performance, including increased contact area, enhanced self-centering, and improved repeatability. Finally, we validate the gripper’s effectiveness in real-world scenarios through on-arm pick-and-place experiments. This work provides a framework for designing soft cylindrical shell grippers with greater reliability, while maintaining simplicity in fabrication.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"83 ","pages":"Article 102437"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928519","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: 2026-01-14DOI: 10.1016/j.eml.2026.102448
Zumrat Usmanova, Ruobing Bai
Elastomeric balloons are widely studied in various soft actuation systems owing to their simplicity and versatility. Recently, balloons made of liquid crystal elastomers (LCEs) stand out with their unconventional, thermal-responsive inflation behaviors due to the intrinsic coupling between directionally ordered liquid crystal mesogens and stretchable polymer networks, offering an attractive way for fast, large, reversible, and stimuli-responsive actuation. However, this thermomechanical coupling, together with their resultant actuation and instability in LCE balloons, remains poorly understood. Here we show the anomalous thermomechanical actuation of a spherical LCE balloon by solving a boundary-value problem based on the well-established quasi-convex elastic energy for polydomain LCE. We modify the elastic energy to ensure its consistency with the classical model by Bladon, Warner, and Terentjev based on freely jointed chains. We predict the thermally modulated pressure-volume response of the LCE balloon, where the peak pressure for snap-through instability depends non-monotonically on temperature. This nonmonotonic dependence originates from the competing temperature-dependent effects of the mesogen order and the network elasticity, which also govern the modulus of the LCE in the nematic phase. Finally, by extending the free energy to a Gent-like model, we quantify the detailed temperature-dependent snap-through behavior, compare multiple performance metrics of spherical and cylindrical balloons, and analyze an envisioned thermally modulated fluid pump across a wide range of operating temperatures.
{"title":"Anomalous thermomechanical actuation of liquid crystal elastomer balloons","authors":"Zumrat Usmanova, Ruobing Bai","doi":"10.1016/j.eml.2026.102448","DOIUrl":"10.1016/j.eml.2026.102448","url":null,"abstract":"<div><div>Elastomeric balloons are widely studied in various soft actuation systems owing to their simplicity and versatility. Recently, balloons made of liquid crystal elastomers (LCEs) stand out with their unconventional, thermal-responsive inflation behaviors due to the intrinsic coupling between directionally ordered liquid crystal mesogens and stretchable polymer networks, offering an attractive way for fast, large, reversible, and stimuli-responsive actuation. However, this thermomechanical coupling, together with their resultant actuation and instability in LCE balloons, remains poorly understood. Here we show the anomalous thermomechanical actuation of a spherical LCE balloon by solving a boundary-value problem based on the well-established quasi-convex elastic energy for polydomain LCE. We modify the elastic energy to ensure its consistency with the classical model by Bladon, Warner, and Terentjev based on freely jointed chains. We predict the thermally modulated pressure-volume response of the LCE balloon, where the peak pressure for snap-through instability depends non-monotonically on temperature. This nonmonotonic dependence originates from the competing temperature-dependent effects of the mesogen order and the network elasticity, which also govern the modulus of the LCE in the nematic phase. Finally, by extending the free energy to a Gent-like model, we quantify the detailed temperature-dependent snap-through behavior, compare multiple performance metrics of spherical and cylindrical balloons, and analyze an envisioned thermally modulated fluid pump across a wide range of operating temperatures.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"83 ","pages":"Article 102448"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038424","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: 2026-01-21DOI: 10.1016/j.eml.2026.102452
Yisen Peng , Feng Hao
The cracking of electrode active materials causes capacity fade that is one of the bottlenecks in high-performance battery design. Electrolyte infiltrates surface cracks, increasing electrochemically active area and offering fast pathways for lithium-ion insertion/extraction, while interior cracks hinder lithium-ion diffusion within active materials. However, the theoretical model is still lacking to differentiate electrolyte infiltration into surface crack and interior crack. Herein, a chemo-mechanical phase field model coupling the modified smoothed boundary method (SBM) is established to investigate the effect of electrolyte infiltration on chemo-mechanical responses. Within a unified framework, the proposed model captures the coupled processes of electrolyte infiltration and crack growth by distinguishing between interior and surface cracks and tracking the electrolyte-active material interface. It is found that surface cracks infiltrated by electrolyte enhance the accumulation of lithium ions and stress concentration at the crack tip, which further accelerates fracture propagation. The freshly exposed crack surfaces in turn enable more electrochemical reaction sites and improve rate capability, although the cracks destroy the mechanical integrity of active materials. The voltage jump could be induced by coalescence of surface and interior cracks, accompanying by electrolyte penetration. The proposed model provides insights into the complex interaction of electrolyte infiltration, lithium-ion diffusion, stress evolution, and fracture propagation.
{"title":"Effects of electrolyte infiltration on the cracking of active materials in lithium-ion batteries","authors":"Yisen Peng , Feng Hao","doi":"10.1016/j.eml.2026.102452","DOIUrl":"10.1016/j.eml.2026.102452","url":null,"abstract":"<div><div>The cracking of electrode active materials causes capacity fade that is one of the bottlenecks in high-performance battery design. Electrolyte infiltrates surface cracks, increasing electrochemically active area and offering fast pathways for lithium-ion insertion/extraction, while interior cracks hinder lithium-ion diffusion within active materials. However, the theoretical model is still lacking to differentiate electrolyte infiltration into surface crack and interior crack. Herein, a chemo-mechanical phase field model coupling the modified smoothed boundary method (SBM) is established to investigate the effect of electrolyte infiltration on chemo-mechanical responses. Within a unified framework, the proposed model captures the coupled processes of electrolyte infiltration and crack growth by distinguishing between interior and surface cracks and tracking the electrolyte-active material interface. It is found that surface cracks infiltrated by electrolyte enhance the accumulation of lithium ions and stress concentration at the crack tip, which further accelerates fracture propagation. The freshly exposed crack surfaces in turn enable more electrochemical reaction sites and improve rate capability, although the cracks destroy the mechanical integrity of active materials. The voltage jump could be induced by coalescence of surface and interior cracks, accompanying by electrolyte penetration. The proposed model provides insights into the complex interaction of electrolyte infiltration, lithium-ion diffusion, stress evolution, and fracture propagation.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"83 ","pages":"Article 102452"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038427","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: 2026-02-04DOI: 10.1016/j.eml.2026.102455
Wanying Zheng , Zhida Gao , Chuanli Yu , Jun Yin , Zhaohe Dai
When an elastic membrane is deformed, the external work is stored not only as volume-related elastic strain energy but also as area-related surface energies, since the total membrane area changes. The latter contribution is challenging to quantify experimentally, especially for ultrathin membranes. Here, we demonstrate that such surface effects can be revealed through indentation by comparing tests performed at gas and liquid interfaces. Specifically, using monolayer graphene indented across –graphene and water–graphene interfaces, we show that graphene indented against water appears significantly softer—a signature of interfacial energetics favoring the water–graphene configuration. A membrane theory incorporating both elasticity and surface forces quantitatively reproduces the measured force–displacement curves, enabling the extraction of the interfacial tension difference and, in turn, membrane’s wettability. These results establish indentation as a probe of solid–liquid surface tension at the membrane limit and highlight that surface effects – often regarded as negligible in 2D materials – must be carefully accounted for in applications ranging from straintronics to nanofluidics.
{"title":"Revealing surface tension in elastic membranes via indentation","authors":"Wanying Zheng , Zhida Gao , Chuanli Yu , Jun Yin , Zhaohe Dai","doi":"10.1016/j.eml.2026.102455","DOIUrl":"10.1016/j.eml.2026.102455","url":null,"abstract":"<div><div>When an elastic membrane is deformed, the external work is stored not only as volume-related elastic strain energy but also as area-related surface energies, since the total membrane area changes. The latter contribution is challenging to quantify experimentally, especially for ultrathin membranes. Here, we demonstrate that such surface effects can be revealed through indentation by comparing tests performed at gas and liquid interfaces. Specifically, using monolayer graphene indented across <span><math><msub><mrow><mi>N</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>–graphene and water–graphene interfaces, we show that graphene indented against water appears significantly softer—a signature of interfacial energetics favoring the water–graphene configuration. A membrane theory incorporating both elasticity and surface forces quantitatively reproduces the measured force–displacement curves, enabling the extraction of the interfacial tension difference and, in turn, membrane’s wettability. These results establish indentation as a probe of solid–liquid surface tension at the membrane limit and highlight that surface effects – often regarded as negligible in 2D materials – must be carefully accounted for in applications ranging from straintronics to nanofluidics.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"83 ","pages":"Article 102455"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146188738","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: 2026-01-15DOI: 10.1016/j.eml.2026.102450
Xiangyu Guo , Yuanming Xu , Nan Zhu , Hang Xu
Multistable mechanical metamaterials (MMMs) program shape reconfigurations through snap-through transitions between multiple stable states in response to environmental stimuli, such as changes in mechanical load, temperature, or magnetic field. One major unresolved challenge is the trade-off resulting from the inherent coupling between the critical actuation load and the multistability. MMMs that require high actuation loads to snap through exhibit strong mechanical stability but are difficult to trigger and cannot respond to small-amplitude environmental stimuli. In contrast, those that can snap through under low loads become highly susceptible to disturbances and may fail to maintain multistability. This study introduces a tri-beam bistable building block to decouple critical actuation load and structural multistability. The constructed MMMs are capable of programming strain energy barriers into their layouts to achieve multistability under arbitrary actuation loads, even low to near-zero. The mechanical properties and deformation mechanisms of MMMs are investigated via a combination of numerical simulation, analytical modeling, and experimental validation. The proposed heterogeneous discrete assembly strategy integrates rigid and flexible components into MMM unit cells, enabling support-free additive manufacturing of reconfigurable one-directional, planar, and spatial MMMs with near-isotropic mechanical behavior. The developed MMMs exhibit post-manufacturing re-programmable deformation, high compactability, and multi-directional stability.
{"title":"Multistable mechanical metamaterials with compatible sensitive actuation and high stability","authors":"Xiangyu Guo , Yuanming Xu , Nan Zhu , Hang Xu","doi":"10.1016/j.eml.2026.102450","DOIUrl":"10.1016/j.eml.2026.102450","url":null,"abstract":"<div><div>Multistable mechanical metamaterials (MMMs) program shape reconfigurations through snap-through transitions between multiple stable states in response to environmental stimuli, such as changes in mechanical load, temperature, or magnetic field. One major unresolved challenge is the trade-off resulting from the inherent coupling between the critical actuation load and the multistability. MMMs that require high actuation loads to snap through exhibit strong mechanical stability but are difficult to trigger and cannot respond to small-amplitude environmental stimuli. In contrast, those that can snap through under low loads become highly susceptible to disturbances and may fail to maintain multistability. This study introduces a tri-beam bistable building block to decouple critical actuation load and structural multistability. The constructed MMMs are capable of programming strain energy barriers into their layouts to achieve multistability under arbitrary actuation loads, even low to near-zero. The mechanical properties and deformation mechanisms of MMMs are investigated via a combination of numerical simulation, analytical modeling, and experimental validation. The proposed heterogeneous discrete assembly strategy integrates rigid and flexible components into MMM unit cells, enabling support-free additive manufacturing of reconfigurable one-directional, planar, and spatial MMMs with near-isotropic mechanical behavior. The developed MMMs exhibit post-manufacturing re-programmable deformation, high compactability, and multi-directional stability.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"83 ","pages":"Article 102450"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979435","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: 2026-01-10DOI: 10.1016/j.eml.2026.102446
Hao Wu , Chen Yu , Chuang Liu , HengAn Wu
Designing multiscale metamaterial systems necessitates the creation of microstructures with compatible boundaries to achieve desired elastic properties induced by topological optimization. However, fulfilling these multiple target requirements remains a significant challenge when designing microstructures with compatible boundaries. To address these issues, we propose a data-driven framework leveraging a conditional diffusion model for the inverse design of microstructures with specific elastic properties and geometrical boundary constraints. Utilizing a large dataset of microstructures generated via topological optimization, our generative model accurately produces diverse geometrical designs for target elastic properties, providing a broad design space for boundary compatibility. The model's accuracy in designing microstructures surpasses that of previous studies. We comprehensively study the relationships between elastic properties and varying ranges of geometrical boundary shapes. Moreover, by incorporating boundary constraints during generation, the proposed BoundaryDiff method ensures mechanical consistency from microscale units to macroscale assemblies. Numerical experiments show that stitched structures generated by our model maintain homogenized elastic properties in close agreement with theoretical predictions, effectively addressing incompatibilities between adjacent microstructures. A numerical case demonstrates the feasibility of our approach in designing multiscale metamaterial systems. This study bridges the gap between microstructure design and topological optimization, holding significant promise for designing functional multiscale metamaterial systems.
{"title":"Conditional diffusion modeling for constructing geometrical connectivity in multiscale metamaterial system","authors":"Hao Wu , Chen Yu , Chuang Liu , HengAn Wu","doi":"10.1016/j.eml.2026.102446","DOIUrl":"10.1016/j.eml.2026.102446","url":null,"abstract":"<div><div>Designing multiscale metamaterial systems necessitates the creation of microstructures with compatible boundaries to achieve desired elastic properties induced by topological optimization. However, fulfilling these multiple target requirements remains a significant challenge when designing microstructures with compatible boundaries. To address these issues, we propose a data-driven framework leveraging a conditional diffusion model for the inverse design of microstructures with specific elastic properties and geometrical boundary constraints. Utilizing a large dataset of microstructures generated via topological optimization, our generative model accurately produces diverse geometrical designs for target elastic properties, providing a broad design space for boundary compatibility. The model's accuracy in designing microstructures surpasses that of previous studies. We comprehensively study the relationships between elastic properties and varying ranges of geometrical boundary shapes. Moreover, by incorporating boundary constraints during generation, the proposed BoundaryDiff method ensures mechanical consistency from microscale units to macroscale assemblies. Numerical experiments show that stitched structures generated by our model maintain homogenized elastic properties in close agreement with theoretical predictions, effectively addressing incompatibilities between adjacent microstructures. A numerical case demonstrates the feasibility of our approach in designing multiscale metamaterial systems. This study bridges the gap between microstructure design and topological optimization, holding significant promise for designing functional multiscale metamaterial systems.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"83 ","pages":"Article 102446"},"PeriodicalIF":4.5,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979437","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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