Pub Date : 2025-01-11DOI: 10.1016/j.jmps.2025.106037
Ao Li , Zhuo-Ming Bai , Xu Yin , Tao Zhu , Zi-Yan Sun , Jiang Yang , Li-Yuan Zhang
Inertial amplification metastructure, known for its negative effective stiffness, exhibits excellent low-frequency vibration isolation, rendering it widely applicable in mechanical filters and elastic waveguides. However, research into their tunable dynamic characteristics, such as bandgaps, remains scarce. In this paper, we propose an inertial amplification metastructure with tunable dynamic characteristics, leveraging the adjustability of tensegrity. The cell of the metastructure comprises two tensegrity-based units with opposite chirality and an additional resonator, enabling it to selectively transmit axial vibrations. Using theoretical and simulated models, we investigate the static and dynamic characteristics of the metastructure. The results demonstrate that both the magnitude and the sign (positive or negative) of the effective mass and stiffness of the metastructure can be remarkably altered by externally applied forces. Notably, the separation and merging of bandgaps can be achieved with this design. Finally, static and dynamic experiments are conducted to validate our theoretical predictions. The present metastructure holds considerable potential for applications in elastic wave control and wide low-frequency vibration isolation.
{"title":"A tensegrity-inspired inertial amplification metastructure with tunable dynamic characteristics","authors":"Ao Li , Zhuo-Ming Bai , Xu Yin , Tao Zhu , Zi-Yan Sun , Jiang Yang , Li-Yuan Zhang","doi":"10.1016/j.jmps.2025.106037","DOIUrl":"10.1016/j.jmps.2025.106037","url":null,"abstract":"<div><div>Inertial amplification metastructure, known for its negative effective stiffness, exhibits excellent low-frequency vibration isolation, rendering it widely applicable in mechanical filters and elastic waveguides. However, research into their tunable dynamic characteristics, such as bandgaps, remains scarce. In this paper, we propose an inertial amplification metastructure with tunable dynamic characteristics, leveraging the adjustability of tensegrity. The cell of the metastructure comprises two tensegrity-based units with opposite chirality and an additional resonator, enabling it to selectively transmit axial vibrations. Using theoretical and simulated models, we investigate the static and dynamic characteristics of the metastructure. The results demonstrate that both the magnitude and the sign (positive or negative) of the effective mass and stiffness of the metastructure can be remarkably altered by externally applied forces. Notably, the separation and merging of bandgaps can be achieved with this design. Finally, static and dynamic experiments are conducted to validate our theoretical predictions. The present metastructure holds considerable potential for applications in elastic wave control and wide low-frequency vibration isolation.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"196 ","pages":"Article 106037"},"PeriodicalIF":5.0,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-01-11DOI: 10.1016/j.jmps.2025.106042
Yang Liu , Zhiqiang Meng , Yifan Wang , Chang Qing Chen
Structures capable of multiple stable configurations are increasingly attractive for applications in shape-morphing and adaptive systems. Among these, corrugated sheets are promising due to their ability to achieve different loading-position-dependent stable morphologies. In this work, the bistability of corrugated sheets is systematically investigated, where point loads at different positions can lead to distinct stability responses. To quantify the mechanical behavior, a theoretical model of the sheet is developed, combined with finite element analysis (FEA) and experimental validation. The analysis begins with a single-cell model, from which a phase diagram is derived for the transition between monostable and bistable regimes as a function of nondimensional geometric parameters. The model is then extended to multi-cell corrugated sheets to reveal the effects of intercellular interactions on the overall stability landscape of the structure. Finally, the theoretical model enables customization of bistable regions in the corrugated sheets—such as butterfly-like and diamond-like bistability regions—achieving programmable bistability through the geometric design of unit cells and their spatial arrangement. This work provides insights into how loading position influences the mechanical stability of corrugated sheets, presenting significant potential for advanced applications in shape-morphing structures, soft robotics, and sensor technologies, where tailored mechanical responses are crucial.
{"title":"Corrugated sheets with loading-position-dependent bistability","authors":"Yang Liu , Zhiqiang Meng , Yifan Wang , Chang Qing Chen","doi":"10.1016/j.jmps.2025.106042","DOIUrl":"10.1016/j.jmps.2025.106042","url":null,"abstract":"<div><div>Structures capable of multiple stable configurations are increasingly attractive for applications in shape-morphing and adaptive systems. Among these, corrugated sheets are promising due to their ability to achieve different loading-position-dependent stable morphologies. In this work, the bistability of corrugated sheets is systematically investigated, where point loads at different positions can lead to distinct stability responses. To quantify the mechanical behavior, a theoretical model of the sheet is developed, combined with finite element analysis (FEA) and experimental validation. The analysis begins with a single-cell model, from which a phase diagram is derived for the transition between monostable and bistable regimes as a function of nondimensional geometric parameters. The model is then extended to multi-cell corrugated sheets to reveal the effects of intercellular interactions on the overall stability landscape of the structure. Finally, the theoretical model enables customization of bistable regions in the corrugated sheets—such as butterfly-like and diamond-like bistability regions—achieving programmable bistability through the geometric design of unit cells and their spatial arrangement. This work provides insights into how loading position influences the mechanical stability of corrugated sheets, presenting significant potential for advanced applications in shape-morphing structures, soft robotics, and sensor technologies, where tailored mechanical responses are crucial.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"196 ","pages":"Article 106042"},"PeriodicalIF":5.0,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-01-11DOI: 10.1016/j.jmps.2025.106034
Rui Shi, Hongbin Fang, Jian Xu
In this study, we present a continuous dynamics model for peristaltic rectilinear locomotion that accounts for three-dimensional deformation, inertia, friction, nonlinear constitutive profile, and strain waves. Using tensile tests and contact force measurements from earthworms, we derived the constitutive and anisotropic Coulomb's dry friction models. The developed dynamic model uniquely incorporates inertial effects and strain waves, the latter of which is a mathematical abstraction of the retrograde peristaltic wave mechanism and earthworm-like robotic gaits. We analyze locomotion dynamics under both force field and strain field, which reveal qualitatively similar peristaltic locomotion but different average velocities due to varying backward slippage. We further investigate the impact of inertia and strain wave parameters, finding that larger inertia under force fields increases backward sliding and reduces average velocity, while higher strain wave amplitudes under strain fields enhance velocity but also backward sliding. Anchoring and extension/contraction intervals in the strain wave also significantly affect the non-smooth stick-slip dynamics and the average velocity, and the results are consistent with previous studies on earthworm-like robot gaits. Overall, this research highlights the significance of the continuum dynamic model in analyzing the peristaltic locomotion of living earthworms. This model also holds promise for extending its use to the realm of robotics, providing valuable insights into the control and performance optimization of earthworm-like robots.
{"title":"Continuum modeling and dynamics of earthworm-like peristaltic locomotion","authors":"Rui Shi, Hongbin Fang, Jian Xu","doi":"10.1016/j.jmps.2025.106034","DOIUrl":"10.1016/j.jmps.2025.106034","url":null,"abstract":"<div><div>In this study, we present a continuous dynamics model for peristaltic rectilinear locomotion that accounts for three-dimensional deformation, inertia, friction, nonlinear constitutive profile, and strain waves. Using tensile tests and contact force measurements from earthworms, we derived the constitutive and anisotropic Coulomb's dry friction models. The developed dynamic model uniquely incorporates inertial effects and strain waves, the latter of which is a mathematical abstraction of the retrograde peristaltic wave mechanism and earthworm-like robotic gaits. We analyze locomotion dynamics under both force field and strain field, which reveal qualitatively similar peristaltic locomotion but different average velocities due to varying backward slippage. We further investigate the impact of inertia and strain wave parameters, finding that larger inertia under force fields increases backward sliding and reduces average velocity, while higher strain wave amplitudes under strain fields enhance velocity but also backward sliding. Anchoring and extension/contraction intervals in the strain wave also significantly affect the non-smooth stick-slip dynamics and the average velocity, and the results are consistent with previous studies on earthworm-like robot gaits. Overall, this research highlights the significance of the continuum dynamic model in analyzing the peristaltic locomotion of living earthworms. This model also holds promise for extending its use to the realm of robotics, providing valuable insights into the control and performance optimization of earthworm-like robots.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"196 ","pages":"Article 106034"},"PeriodicalIF":5.0,"publicationDate":"2025-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-01-10DOI: 10.1016/j.jmps.2024.106019
Wenfeng Liu , Bernard Ennis , Corentin Coulais
Material nonlinearities such as hyperelasticity, viscoelasticity, and plasticity have recently emerged as design paradigms for metamaterials based on buckling. These metamaterials exhibit properties such as shape morphing, transition waves, and sequential deformation. In particular, plasticity has been used in the design of sequential metamaterials which combine high stiffness, strength, and dissipation at low density and produce superior shock absorbing performances. However, the use of plasticity for tuning buckling sequences in metamaterials remains largely unexplored. In this work, we introduce yield area, yield criterion, and loading history as new design tools of plasticity in tuning the buckling load and sequence in metamaterials. We numerically and experimentally demonstrate a controllable buckling sequence in different metamaterial architectures with the above three strategies. Our findings enrich the toolbox of plasticity in the design of metamaterials with more controllable sequential deformations and leverage plasticity to broader applications in multifunctional metamaterials, high-performance soft robotics, and mechanical self-assembly.
{"title":"Tuning the buckling sequences of metamaterials using plasticity","authors":"Wenfeng Liu , Bernard Ennis , Corentin Coulais","doi":"10.1016/j.jmps.2024.106019","DOIUrl":"10.1016/j.jmps.2024.106019","url":null,"abstract":"<div><div>Material nonlinearities such as hyperelasticity, viscoelasticity, and plasticity have recently emerged as design paradigms for metamaterials based on buckling. These metamaterials exhibit properties such as shape morphing, transition waves, and sequential deformation. In particular, plasticity has been used in the design of sequential metamaterials which combine high stiffness, strength, and dissipation at low density and produce superior shock absorbing performances. However, the use of plasticity for tuning buckling sequences in metamaterials remains largely unexplored. In this work, we introduce yield area, yield criterion, and loading history as new design tools of plasticity in tuning the buckling load and sequence in metamaterials. We numerically and experimentally demonstrate a controllable buckling sequence in different metamaterial architectures with the above three strategies. Our findings enrich the toolbox of plasticity in the design of metamaterials with more controllable sequential deformations and leverage plasticity to broader applications in multifunctional metamaterials, high-performance soft robotics, and mechanical self-assembly.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"196 ","pages":"Article 106019"},"PeriodicalIF":5.0,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-09DOI: 10.1016/j.jmps.2025.106027
Yu Zhou, Chen Wei, Lihua Jin
Liquid crystal elastomers (LCEs) are emerging actuating materials composed of polymer networks and liquid crystal mesogens. A plateau in the stress-strain curve of LCEs, typical of the semi-soft characteristics, is commonly observed. Although the classical semi-soft model based on compositional fluctuations intends to capture this feature, it does not accurately predict the stress plateau. Moreover, the extended viscoelastic models often lack quantitative comparisons between their theoretical predictions and experimental results. To address these limitations, we phenomenologically modify the semi-soft model, applying it to capture both of the elastic and viscoelastic responses of LCEs. The modified model is further implemented into finite element simulations and used to study intriguing inhomogeneous deformation of LCEs. We demonstrated robust predictions of our model by quantitatively comparing with experimental results.
{"title":"A modified semi-soft model of liquid crystal elastomers: Application to elastic and viscoelastic responses","authors":"Yu Zhou, Chen Wei, Lihua Jin","doi":"10.1016/j.jmps.2025.106027","DOIUrl":"10.1016/j.jmps.2025.106027","url":null,"abstract":"<div><div>Liquid crystal elastomers (LCEs) are emerging actuating materials composed of polymer networks and liquid crystal mesogens. A plateau in the stress-strain curve of LCEs, typical of the semi-soft characteristics, is commonly observed. Although the classical semi-soft model based on compositional fluctuations intends to capture this feature, it does not accurately predict the stress plateau. Moreover, the extended viscoelastic models often lack quantitative comparisons between their theoretical predictions and experimental results. To address these limitations, we phenomenologically modify the semi-soft model, applying it to capture both of the elastic and viscoelastic responses of LCEs. The modified model is further implemented into finite element simulations and used to study intriguing inhomogeneous deformation of LCEs. We demonstrated robust predictions of our model by quantitatively comparing with experimental results.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"196 ","pages":"Article 106027"},"PeriodicalIF":5.0,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-08DOI: 10.1016/j.jmps.2025.106030
Shaoxiong Huang , Yafeng Wang , Xian Xu , Yaozhi Luo
Fiber networks are essential functional materials, yet existing mechanical models only capture specific aspects of their mechanical properties. This paper proposes a general mechanical model for fiber networks based on pin-jointed bar assemblies. The topology and stress modes of the networks are generated through topology optimization. The model decouples and quantifies the contributions of entropy fluctuation, rearrangement, and fiber stress to the overall stiffness, explaining stiffness variations in actin networks and the differences in stiffness between thermal and athermal networks. It also replicates the experimental strengthening effects of prestressed fiber networks, theoretically justifying the power-law relationship between applied stress/strain and stiffness. A macroscopic 3D-printed experiment validates the model's ability to replicate stiffness variations and the rearrangement phenomena observed in collagen networks under compression and shear. This model enables a comprehensive investigation of the mechanical properties of fiber networks and contributes to the design of novel biomimetic metamaterials.
{"title":"Topology generation and quantitative stiffness analysis for fiber networks based on disordered spatial truss","authors":"Shaoxiong Huang , Yafeng Wang , Xian Xu , Yaozhi Luo","doi":"10.1016/j.jmps.2025.106030","DOIUrl":"10.1016/j.jmps.2025.106030","url":null,"abstract":"<div><div>Fiber networks are essential functional materials, yet existing mechanical models only capture specific aspects of their mechanical properties. This paper proposes a general mechanical model for fiber networks based on pin-jointed bar assemblies. The topology and stress modes of the networks are generated through topology optimization. The model decouples and quantifies the contributions of entropy fluctuation, rearrangement, and fiber stress to the overall stiffness, explaining stiffness variations in actin networks and the differences in stiffness between thermal and athermal networks. It also replicates the experimental strengthening effects of prestressed fiber networks, theoretically justifying the power-law relationship between applied stress/strain and stiffness. A macroscopic 3D-printed experiment validates the model's ability to replicate stiffness variations and the rearrangement phenomena observed in collagen networks under compression and shear. This model enables a comprehensive investigation of the mechanical properties of fiber networks and contributes to the design of novel biomimetic metamaterials.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"196 ","pages":"Article 106030"},"PeriodicalIF":5.0,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 : 2025-01-08DOI: 10.1016/j.jmps.2025.106025
Tianwen Tan, Ikumu Watanabe
In the field of damage modeling for ductile materials, numerous models have successfully addressed various fracture responses, as well as the need for robust algorithms and solutions to computational challenges. This study developed a damage model based on continuum damage mechanics. It addresses mesh regularization, a primary computational issue in macroscopic structural fracture analysis through a gradient-enhanced damage model using micromorphic theory and incorporating damage hardening variables. To provide a physical explanation for the characteristic lengths associated with the gradient-enhanced term, an extended “two-scale” computational homogenization approach was employed to define the length scale between the macro- and microscale. This microvariable within a micromorphic extension can be utilized to model the damage hardening mechanism, which cannot be fully captured via high-resolution localized characterization. In duplex microstructures, the length scale can be defined by the microstructure size relative to the width of the micro-shear band. This explains the damage overlapping phenomenon between the two-scales.
{"title":"Gradient-enhanced ductile fracture constitutive modeling in implicit two-scale finite element analysis","authors":"Tianwen Tan, Ikumu Watanabe","doi":"10.1016/j.jmps.2025.106025","DOIUrl":"10.1016/j.jmps.2025.106025","url":null,"abstract":"<div><div>In the field of damage modeling for ductile materials, numerous models have successfully addressed various fracture responses, as well as the need for robust algorithms and solutions to computational challenges. This study developed a damage model based on continuum damage mechanics. It addresses mesh regularization, a primary computational issue in macroscopic structural fracture analysis through a gradient-enhanced damage model using micromorphic theory and incorporating damage hardening variables. To provide a physical explanation for the characteristic lengths associated with the gradient-enhanced term, an extended “two-scale” computational homogenization approach was employed to define the length scale between the macro- and microscale. This microvariable within a micromorphic extension can be utilized to model the damage hardening mechanism, which cannot be fully captured via high-resolution localized characterization. In duplex microstructures, the length scale can be defined by the microstructure size relative to the width of the micro-shear band. This explains the damage overlapping phenomenon between the two-scales.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"196 ","pages":"Article 106025"},"PeriodicalIF":5.0,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142989357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-07DOI: 10.1016/j.jmps.2024.106020
Michele Tricarico , Michele Ciavarella , Antonio Papangelo
High-frequency micrometrical vibrations have been shown to greatly influence the adhesive performance of soft interfaces, however a detailed comparison between theoretical predictions and experimental results is still missing. Here, the problem of a rigid spherical indenter, hung on a soft spring, that is unloaded from an adhesive viscoelastic vibrating substrate is considered. The experimental tests were performed by unloading a borosilicate glass lens from a soft PDMS substrate excited by high-frequency micrometrical vibrations. We show that as soon as the vibration starts, the contact area increases abruptly and during unloading it decreases following approximately the JKR classical model, but with a much increased work of adhesion with respect to its thermodynamic value. We find that the pull-off force increases with the amplitude of vibration up to a certain saturation level, which appeared to be frequency dependent. Under the hypothesis of short range adhesion, a lumped mechanical model was derived, which, starting from an independent characterization of the rate-dependent interfacial adhesion, predicted qualitatively and quantitatively the experimental results, without the need of any adjustable parameters.
{"title":"Enhancement of adhesion strength through microvibrations: Modeling and experiments","authors":"Michele Tricarico , Michele Ciavarella , Antonio Papangelo","doi":"10.1016/j.jmps.2024.106020","DOIUrl":"10.1016/j.jmps.2024.106020","url":null,"abstract":"<div><div>High-frequency micrometrical vibrations have been shown to greatly influence the adhesive performance of soft interfaces, however a detailed comparison between theoretical predictions and experimental results is still missing. Here, the problem of a rigid spherical indenter, hung on a soft spring, that is unloaded from an adhesive viscoelastic vibrating substrate is considered. The experimental tests were performed by unloading a borosilicate glass lens from a soft PDMS substrate excited by high-frequency micrometrical vibrations. We show that as soon as the vibration starts, the contact area increases abruptly and during unloading it decreases following approximately the JKR classical model, but with a much increased work of adhesion with respect to its thermodynamic value. We find that the pull-off force increases with the amplitude of vibration up to a certain saturation level, which appeared to be frequency dependent. Under the hypothesis of short range adhesion, a lumped mechanical model was derived, which, starting from an independent characterization of the rate-dependent interfacial adhesion, predicted qualitatively and quantitatively the experimental results, without the need of any adjustable parameters.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"196 ","pages":"Article 106020"},"PeriodicalIF":5.0,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142967827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-01-06DOI: 10.1016/j.jmps.2025.106028
Qingao Wang , Antonio Papangelo , Michele Ciavarella , Huajian Gao , Qunyang Li
For a typical adhesive contact problem, a rigid sphere initially adhered to a relaxed viscoelastic substrate is pulled away from the substrate at finite speeds, and the pull-off force is often found to depend on the rate of pulling. Despite significant theoretical advancements in this area, how the apparent adhesion enhancement is affected by the Maugis parameter and preload remains unclear, and existing models are sometimes contentious. In this work, we revisit this adhesive contact problem and propose a theoretical model to predict the upper bound detachment behavior when the pulling speed approaches infinity. Our analysis reveals that the apparent work of adhesion can always be enhanced, regardless of the Maugis parameter, when the initial contact radius exceeds a critical threshold. Conversely, when the initial contact radius is below this critical value, the adhesion enhancement becomes limited and depends on both the Maugis parameter and the preload condition. Further model calculations suggest that the critical initial contact radius is dependent on the Maugis parameter. In the JKR-like regime, this critical radius converges to a constant value, whereas in the DMT-like regime, it diverges rapidly following an inverse power law with respect to the Maugis parameter. As a result, observing adhesion enhancement is generally more challenging in DMT-like contacts compared to JKR-like contacts. In the meantime, our model also suggests that the adhesion enhancement arises from the expansion of the cohesive zone area due to the viscoelastic properties of the material not only within the cohesive zone but also in the intimate contact zone. Overall, our findings offer a more comprehensive understanding of viscoelastic effects in adhesive contacts, which can be used to rationally predict or optimize adhesion strength in viscoelastic interfaces.
{"title":"Rapid detachment of a rigid sphere adhered to a viscoelastic substrate: An upper bound model incorporating Maugis parameter and preload effects","authors":"Qingao Wang , Antonio Papangelo , Michele Ciavarella , Huajian Gao , Qunyang Li","doi":"10.1016/j.jmps.2025.106028","DOIUrl":"10.1016/j.jmps.2025.106028","url":null,"abstract":"<div><div>For a typical adhesive contact problem, a rigid sphere initially adhered to a relaxed viscoelastic substrate is pulled away from the substrate at finite speeds, and the pull-off force is often found to depend on the rate of pulling. Despite significant theoretical advancements in this area, how the apparent adhesion enhancement is affected by the Maugis parameter and preload remains unclear, and existing models are sometimes contentious. In this work, we revisit this adhesive contact problem and propose a theoretical model to predict the upper bound detachment behavior when the pulling speed approaches infinity. Our analysis reveals that the apparent work of adhesion can always be enhanced, regardless of the Maugis parameter, when the initial contact radius exceeds a critical threshold. Conversely, when the initial contact radius is below this critical value, the adhesion enhancement becomes limited and depends on both the Maugis parameter and the preload condition. Further model calculations suggest that the critical initial contact radius is dependent on the Maugis parameter. In the JKR-like regime, this critical radius converges to a constant value, whereas in the DMT-like regime, it diverges rapidly following an inverse power law with respect to the Maugis parameter. As a result, observing adhesion enhancement is generally more challenging in DMT-like contacts compared to JKR-like contacts. In the meantime, our model also suggests that the adhesion enhancement arises from the expansion of the cohesive zone area due to the viscoelastic properties of the material not only within the cohesive zone but also in the intimate contact zone. Overall, our findings offer a more comprehensive understanding of viscoelastic effects in adhesive contacts, which can be used to rationally predict or optimize adhesion strength in viscoelastic interfaces.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"196 ","pages":"Article 106028"},"PeriodicalIF":5.0,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142967829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we introduce a comprehensive 3D finite-deformation constitutive model for shape memory polymers focused on addressing the Mullins effect when subjected to substantial elongation, reaching up to 200 % strain. Considering only four Maxwell branches with nonlinear viscous components integrated with the WLF equation, our modeling framework inherently ensures thermodynamic consistency without imposing excessive constraints, linear (Boltzmann) or phenomenological modeling. This approach allows the study of time- and temperature-dependent behaviors, including stress relaxation, cyclic loadings related to the shape memory effect, shape and force recovery, and damage phenomena in SMPs under large elongations. The model integrates hyperelasticity and stress-softening effects while employing the concept of rational thermodynamics and internal state variables in the realm of the thermo-visco-green-elastic continuum approach. Additionally, we delve into the influence of strain levels on stretch-induced softening effects and their subsequent impact on free-shape recovery behavior. To streamline characterization and calibration, we conducted extensive experimental uniaxial cyclic loading tests across various strain rates and temperatures on a shape memory polymer. The model is compatible with both COMSOL and Abaqus software, enabling robust simulations of complex material responses. Through rigorous comparison against experimental data and extensive finite element multi-physics analysis simulations, we evaluate the model's performance via several multi-physics case studies and validate our proposed algorithm while minimizing both the number of parameters and computational costs.
{"title":"A Nonlinear Thermo-Visco-Green-Elastic Constitutive Model for Mullins Damage of Shape Memory Polymers under Giant Elongations","authors":"Alireza Ostadrahimi , Alireza Enferadi , Mostafa Baghani , Siavash Sarrafan , Guoqiang Li","doi":"10.1016/j.jmps.2025.106029","DOIUrl":"10.1016/j.jmps.2025.106029","url":null,"abstract":"<div><div>In this paper, we introduce a comprehensive 3D finite-deformation constitutive model for shape memory polymers focused on addressing the Mullins effect when subjected to substantial elongation, reaching up to 200 % strain. Considering only four Maxwell branches with nonlinear viscous components integrated with the WLF equation, our modeling framework inherently ensures thermodynamic consistency without imposing excessive constraints, linear (Boltzmann) or phenomenological modeling. This approach allows the study of time- and temperature-dependent behaviors, including stress relaxation, cyclic loadings related to the shape memory effect, shape and force recovery, and damage phenomena in SMPs under large elongations. The model integrates hyperelasticity and stress-softening effects while employing the concept of rational thermodynamics and internal state variables in the realm of the thermo-visco-green-elastic continuum approach. Additionally, we delve into the influence of strain levels on stretch-induced softening effects and their subsequent impact on free-shape recovery behavior. To streamline characterization and calibration, we conducted extensive experimental uniaxial cyclic loading tests across various strain rates and temperatures on a shape memory polymer. The model is compatible with both COMSOL and Abaqus software, enabling robust simulations of complex material responses. Through rigorous comparison against experimental data and extensive finite element multi-physics analysis simulations, we evaluate the model's performance via several multi-physics case studies and validate our proposed algorithm while minimizing both the number of parameters and computational costs.</div></div>","PeriodicalId":17331,"journal":{"name":"Journal of The Mechanics and Physics of Solids","volume":"196 ","pages":"Article 106029"},"PeriodicalIF":5.0,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142967828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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