Pub Date : 2025-02-19DOI: 10.1016/j.ijsolstr.2025.113286
Zhongtong Wang , Robert J. Wagner , Tianke Chen , Sagar P. Shah , Marianna Maiaru , Meredith N. Silberstein
Polymer matrix fiber composites often suffer from residual stresses due to differences in coefficients of thermal expansion between the fibers and resins, as well as contractile strain of the resins during curing. To address residual stress driven composite failure, we propose the use of vitrimers as composite resins, which can undergo thermally activated, stress alleviating, bond exchange reactions (BERs). We conduct fiber Bragg grating measurements for a single glass fiber within bulk vitrimer. These show that the fiber strain in vitrimers with 5% catalyst is significantly lower than in those with 0% catalyst (minimal BER expected) during both curing and post-curing phases. We developed a finite deformation, micromechanically-inspired model that incorporates curing, thermal processes, and BERs, and then implemented this model it into finite element software to simulate stress evolution within single fiber composite systems. The combination of experimental and computational results reveals that BERs can effectively mitigate, but not eliminate, the residual stress in polymer matrix fiber composites.
{"title":"Bond exchange reactions as a paradigm for mitigating residual stress in polymer matrix fiber composites","authors":"Zhongtong Wang , Robert J. Wagner , Tianke Chen , Sagar P. Shah , Marianna Maiaru , Meredith N. Silberstein","doi":"10.1016/j.ijsolstr.2025.113286","DOIUrl":"10.1016/j.ijsolstr.2025.113286","url":null,"abstract":"<div><div>Polymer matrix fiber composites often suffer from residual stresses due to differences in coefficients of thermal expansion between the fibers and resins, as well as contractile strain of the resins during curing. To address residual stress driven composite failure, we propose the use of vitrimers as composite resins, which can undergo thermally activated, stress alleviating, bond exchange reactions (BERs). We conduct fiber Bragg grating measurements for a single glass fiber within bulk vitrimer. These show that the fiber strain in vitrimers with 5% catalyst is significantly lower than in those with 0% catalyst (minimal BER expected) during both curing and post-curing phases. We developed a finite deformation, micromechanically-inspired model that incorporates curing, thermal processes, and BERs, and then implemented this model it into finite element software to simulate stress evolution within single fiber composite systems. The combination of experimental and computational results reveals that BERs can effectively mitigate, but not eliminate, the residual stress in polymer matrix fiber composites.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"313 ","pages":"Article 113286"},"PeriodicalIF":3.4,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143508042","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 : 2025-02-18DOI: 10.1016/j.ijsolstr.2025.113283
Farshid Masoumi, Jia Lu
This article presents an inverse method for extracting constitutive parameters in hyperelastic materials from partial field displacement data. The work is motivated by applications in which some displacement data are unavailable or too noisy to use. The method is developed on the basis of finite element force balance, and can be readily interfaced with finite element program. The method is evaluated using simulated displacement data with added noise. Two-dimensional and three-dimensional test problems are introduced to collectively assess the sensitivity to noise level, tolerance to missing data, the feasibility identifying heterogeneous properties using surface data only, and the influence of using local force distribution versus using the force resultant. In addition, a cross-model analysis is conducted in some test problems to evaluate influence of material model. A novel scheme involving deep learning network is introduced to smooth the noised displacement and generate the input displacements for different meshes. The forward displacement computation is carried out only at the finest mesh level. The simulated displacements with added white noised is smoothed, and the ensuing displacement field is evaluated at coarse meshes to generate the input data for the coarse models. The tests showed that, up to 10% noise, method performed satisfactorily and robustly in all cases.
{"title":"Identifying hyperelastic material parameters using force balance and partial displacement data","authors":"Farshid Masoumi, Jia Lu","doi":"10.1016/j.ijsolstr.2025.113283","DOIUrl":"10.1016/j.ijsolstr.2025.113283","url":null,"abstract":"<div><div>This article presents an inverse method for extracting constitutive parameters in hyperelastic materials from partial field displacement data. The work is motivated by applications in which some displacement data are unavailable or too noisy to use. The method is developed on the basis of finite element force balance, and can be readily interfaced with finite element program. The method is evaluated using simulated displacement data with added noise. Two-dimensional and three-dimensional test problems are introduced to collectively assess the sensitivity to noise level, tolerance to missing data, the feasibility identifying heterogeneous properties using surface data only, and the influence of using local force distribution versus using the force resultant. In addition, a cross-model analysis is conducted in some test problems to evaluate influence of material model. A novel scheme involving deep learning network is introduced to smooth the noised displacement and generate the input displacements for different meshes. The forward displacement computation is carried out only at the finest mesh level. The simulated displacements with added white noised is smoothed, and the ensuing displacement field is evaluated at coarse meshes to generate the input data for the coarse models. The tests showed that, up to 10% noise, method performed satisfactorily and robustly in all cases.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"313 ","pages":"Article 113283"},"PeriodicalIF":3.4,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143453919","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 : 2025-02-17DOI: 10.1016/j.ijsolstr.2025.113291
Kai Zhang , Tian Tian , Yong Li , Bailin Zheng , Fuqian Yang
The J-integral, which is commonly used to analyze the crack propagation under mechanical loading, loses path-independence in chemo-mechanical coupling problems. Research has been focused on the development of two-dimensional coupled chemo-mechanical integrals to address this issue. However, directly calculating the two-dimensional coupled chemo-mechanical integrals in axisymmetric plane does not provide the energy release rate. There is a need to develop path-independent integrals for axisymmetric chemo-mechanical coupling problems. This work introduces a path-independent axisymmetric J-integral for chemo-mechanical fracture problems, which is established by extending the three-dimensional surface integrals under chemo-mechanical loading to axisymmetric structure and loading. The path-independence of the proposed integral is demonstrated both theoretically and numerically. Using an axisymmetric elastoplastic incremental model, the fracture behavior of a silicon anode particle with pre-existing conical cracks is examined as a practical example. The impacts of crack size, crack inclination angle, and surface flux on the crack propagation are studied. Numerical results are presented in phase diagrams to illustrate the changes in the maximum value of the integral during lithiation.
{"title":"Path-independent axisymmetric J-integral for the chemo-mechanical fracture analysis of elastoplastic electrodes in lithium-ion batteries","authors":"Kai Zhang , Tian Tian , Yong Li , Bailin Zheng , Fuqian Yang","doi":"10.1016/j.ijsolstr.2025.113291","DOIUrl":"10.1016/j.ijsolstr.2025.113291","url":null,"abstract":"<div><div>The <em>J</em>-integral, which is commonly used to analyze the crack propagation under mechanical loading, loses path-independence in chemo-mechanical coupling problems. Research has been focused on the development of two-dimensional coupled chemo-mechanical integrals to address this issue. However, directly calculating the two-dimensional coupled chemo-mechanical integrals in axisymmetric plane does not provide the energy release rate. There is a need to develop path-independent integrals for axisymmetric chemo-mechanical coupling problems. This work introduces a path-independent axisymmetric <em>J</em>-integral for chemo-mechanical fracture problems, which is established by extending the three-dimensional surface integrals under chemo-mechanical loading to axisymmetric structure and loading. The path-independence of the proposed integral is demonstrated both theoretically and numerically. Using an axisymmetric elastoplastic incremental model, the fracture behavior of a silicon anode particle with pre-existing conical cracks is examined as a practical example. The impacts of crack size, crack inclination angle, and surface flux on the crack propagation are studied. Numerical results are presented in phase diagrams to illustrate the changes in the maximum value of the integral during lithiation.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"313 ","pages":"Article 113291"},"PeriodicalIF":3.4,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143445195","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}
Uncertainties and errors caused in the experimental procedure and finite element modeling (FEM) of the shot peening can impact the residual stress (RS) magnitude and distribution significantly. In the present work, a machine learning-based model is used to predict the RS distribution in an Al 2024 shell formed by the shot peening process. The experimental test is performed to measure the induced RS at three points around the center of the shell. FEM is performed to capture the RS diagram considering single-shot and multi-shot scenarios. FEM validation with experimental results is also carried out. In the next step, K-nearest neighbors (KNN), random forest (RF), and XGBoost algorithms predicted the RS profile considering data with 0%, 5%, 10%, and 15% noise. The results show that the KNN algorithm indicates the highest accuracy in estimating the location and value of the maximum negative residual stress (MNRS), which is about 97.6%. However, this model is influenced by the applied random noise and cannot estimate the RS profile correctly. On the other hand, although the RF model has a 5% higher mean error in predicting the value and location of the MNRS, it has accurately forecasted the RS diagram.
{"title":"A Machine learning-based model to predict residual stress in aluminum shell formed by shot peening","authors":"Amirhossein Golmohammadi, Hossein Soroush, Saeed Khodaygan","doi":"10.1016/j.ijsolstr.2025.113250","DOIUrl":"10.1016/j.ijsolstr.2025.113250","url":null,"abstract":"<div><div>Uncertainties and errors caused in the experimental procedure and finite element modeling (FEM) of the shot peening can impact the residual stress (RS) magnitude and distribution significantly. In the present work, a machine learning-based model is used to predict the RS distribution in an Al 2024 shell formed by the shot peening process. The experimental test is performed to measure the induced RS at three points around the center of the shell. FEM is performed to capture the RS diagram considering single-shot and multi-shot scenarios. FEM validation with experimental results is also carried out. In the next step, K-nearest neighbors (KNN), random forest (RF), and XGBoost algorithms predicted the RS profile considering data with 0%, 5%, 10%, and 15% noise. The results show that the KNN algorithm indicates the highest accuracy in estimating the location and value of the maximum negative residual stress (MNRS), which is about 97.6%. However, this model is influenced by the applied random noise and cannot estimate the RS profile correctly. On the other hand, although the RF model has a 5% higher mean error in predicting the value and location of the MNRS, it has accurately forecasted the RS diagram.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"313 ","pages":"Article 113250"},"PeriodicalIF":3.4,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143479505","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 : 2025-02-16DOI: 10.1016/j.ijsolstr.2025.113280
Sunil Kumar Dutta, Gaurav Singh
Fracture in polycrystalline silicon solar cell is affected by the distance (DCG) between the crack tip and grain boundary (GB). The mechanics of crack propagation processes can be understood by studying the bicrystal silicon as a primer. In the present work, the role of distance between the crack tip and GB on the mechanics of crack propagation has been studied using molecular dynamics (MD) simulations. Four hypothetical bicrystals of different DCG have been considered for the present study. A side edge crack has been made and an uniaxial extension has been applied perpendicular to the initial crack plane.
The analysis of fracture processes like crack propagation initiation, crack/GB interaction, crack arrest and re-initiation requires the determination of stress intensity factor (SIF), crack tip opening displacement (CTOD) and energy release rate (ERR) through near-tip mechanics. SIFs calculated using the near-tip stress field are quite useful for this analysis. However, SIF cannot be calculated when crack tip is close to the GB (DCG 50 Å). To overcome this limitation, ERR, evaluated using CTOD, has been used for all the analysis when crack tip is close to the GB. The CTOD determination is not an established method at atomistic scale. Hence, in the present work, ERR determined through CTOD will be verified for atomistic scale through atomistic and continuum scale integral. integral at atomistic scale is determined using volume integral method and verified by its path independence.
From the present analysis, it has been found that when the crack tip is close to GB (DCG 50 Å), the crack propagation initiation occurs at lower ERR and remote strain. With the increase in DCG, the crack propagation initiation happens at a higher ERR and strain. The effect of DCG becomes less relevant after a certain value, beyond which the crack propagation initiation resembles that of Single Crystal (SC). Further, the crack GB interaction and crack propagation in these bicrystals happened differently due to the different DCGs.
{"title":"Role of the distance between crack tip and grain boundary in mechanics of crack propagation in bicrystal silicon","authors":"Sunil Kumar Dutta, Gaurav Singh","doi":"10.1016/j.ijsolstr.2025.113280","DOIUrl":"10.1016/j.ijsolstr.2025.113280","url":null,"abstract":"<div><div>Fracture in polycrystalline silicon solar cell is affected by the distance (DCG) between the crack tip and grain boundary (GB). The mechanics of crack propagation processes can be understood by studying the bicrystal silicon as a primer. In the present work, the role of distance between the crack tip and GB on the mechanics of crack propagation has been studied using molecular dynamics (MD) simulations. Four hypothetical bicrystals of different DCG have been considered for the present study. A side edge crack has been made and an uniaxial extension has been applied perpendicular to the initial crack plane.</div><div>The analysis of fracture processes like crack propagation initiation, crack/GB interaction, crack arrest and re-initiation requires the determination of stress intensity factor (SIF), crack tip opening displacement (CTOD) and energy release rate (ERR) through near-tip mechanics. SIFs calculated using the near-tip stress field are quite useful for this analysis. However, SIF cannot be calculated when crack tip is close to the GB (DCG <span><math><mo>≤</mo></math></span> 50 Å). To overcome this limitation, ERR, evaluated using CTOD, has been used for all the analysis when crack tip is close to the GB. The CTOD determination is not an established method at atomistic scale. Hence, in the present work, ERR determined through CTOD will be verified for atomistic scale through atomistic and continuum scale <span><math><mi>J</mi></math></span> integral. <span><math><mi>J</mi></math></span> integral at atomistic scale is determined using volume integral method and verified by its path independence.</div><div>From the present analysis, it has been found that when the crack tip is close to GB (DCG <span><math><mo>≤</mo></math></span> 50 Å), the crack propagation initiation occurs at lower ERR and remote strain. With the increase in DCG, the crack propagation initiation happens at a higher ERR and strain. The effect of DCG becomes less relevant after a certain value, beyond which the crack propagation initiation resembles that of Single Crystal (SC). Further, the crack GB interaction and crack propagation in these bicrystals happened differently due to the different DCGs.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"313 ","pages":"Article 113280"},"PeriodicalIF":3.4,"publicationDate":"2025-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143512483","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 : 2025-02-13DOI: 10.1016/j.ijsolstr.2025.113285
Xu Long , Ruipeng Dong , Jiao Li , Yutai Su , Chao Chang , Fengrui Jia , Xin Wan
Delamination remains a critical challenge in achieving robust cohesion between thin films and elastic substrates, particularly in electronic applications subjected to harsh operating conditions. Accurate assessment of the constitutive properties governing film/substrate cohesion is essential for addressing this delamination issue, yet in-situ measurement poses significant challenges. In this study, a numerical model is presented aimed at determining the mechanical properties of elastoplastic film materials adhered to an elastic substrate, leveraging the indentation response generated by a Berkovich indenter. To capture the interfacial damage effectively, cohesive elements are integrated into the finite element model to simulate the cohesive behavior between the elastoplastic film and the elastic substrate. The elastoplastic behavior of the film is characterized using a power-law constitutive model, while the tension-separation model is employed to describe interfacial cohesion. The constitutive parameters of thin film materials are deduced by treating the parameters of the substrate material, film material, and cohesion as dominant factors influencing the load–penetration depth curve. These parameters are combined dimensionlessly, offering an elegant method for solving the constitutive parameters of elastoplastic thin film materials. Evaluation of Young’s modulus, yield strength, and hardening exponent across different indentation depths reveals a highly consistent response in the applied load–penetration depth curve under varying parameter influences. Furthermore, the theoretical consideration of dislocation effects on the indentation process provides insight into the underlying failure mechanisms beneath the indenter. To refine the macroscale finite element model, the evolution of mesoscale dislocations during the indentation process is discussed based on plasticity gradient theory and reverse analysis. Finally, leveraging both macroscale finite element simulation and mesoscale theoretical models, a dimensionless equation is proposed for determining elastoplastic material parameters using the applied load–penetration depth curve. The proposed dimensionless equation demonstrates a fitting degree of up to 0.90, offering compelling evidence for its efficacy in employing indentation as a promising method for efficiently estimating constitutive properties of cohesion between the elastoplastic film and the elastic substrate by accounting for dislocations.
{"title":"Reverse analysis of film/substrate cohesion by indentation: A mesoscopic perspective","authors":"Xu Long , Ruipeng Dong , Jiao Li , Yutai Su , Chao Chang , Fengrui Jia , Xin Wan","doi":"10.1016/j.ijsolstr.2025.113285","DOIUrl":"10.1016/j.ijsolstr.2025.113285","url":null,"abstract":"<div><div>Delamination remains a critical challenge in achieving robust cohesion between thin films and elastic substrates, particularly in electronic applications subjected to harsh operating conditions. Accurate assessment of the constitutive properties governing film/substrate cohesion is essential for addressing this delamination issue, yet in-situ measurement poses significant challenges. In this study, a numerical model is presented aimed at determining the mechanical properties of elastoplastic film materials adhered to an elastic substrate, leveraging the indentation response generated by a Berkovich indenter. To capture the interfacial damage effectively, cohesive elements are integrated into the finite element model to simulate the cohesive behavior between the elastoplastic film and the elastic substrate. The elastoplastic behavior of the film is characterized using a power-law constitutive model, while the tension-separation model is employed to describe interfacial cohesion. The constitutive parameters of thin film materials are deduced by treating the parameters of the substrate material, film material, and cohesion as dominant factors influencing the load–penetration depth curve. These parameters are combined dimensionlessly, offering an elegant method for solving the constitutive parameters of elastoplastic thin film materials. Evaluation of Young’s modulus, yield strength, and hardening exponent across different indentation depths reveals a highly consistent response in the applied load–penetration depth curve under varying parameter influences. Furthermore, the theoretical consideration of dislocation effects on the indentation process provides insight into the underlying failure mechanisms beneath the indenter. To refine the macroscale finite element model, the evolution of mesoscale dislocations during the indentation process is discussed based on plasticity gradient theory and reverse analysis. Finally, leveraging both macroscale finite element simulation and mesoscale theoretical models, a dimensionless equation is proposed for determining elastoplastic material parameters using the applied load–penetration depth curve. The proposed dimensionless equation demonstrates a fitting degree of up to 0.90, offering compelling evidence for its efficacy in employing indentation as a promising method for efficiently estimating constitutive properties of cohesion between the elastoplastic film and the elastic substrate by accounting for dislocations.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"312 ","pages":"Article 113285"},"PeriodicalIF":3.4,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143419853","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}
We consider the classical problem of the buckling of a planar elastica inside a rectangular cavity. We compute the equilibrium solutions analytically in the (von Kármán) small deflection approximation. We list the different equilibrium states and their domain of validity in terms of the imposed horizontal and vertical displacements. We compute the horizontal and the vertical applied forces and show how they increase and scale when the compaction ratio is increased. Finally, we introduce an approximate response state, where the system adopts a periodic configuration with a noninteger number of repeated folds. This solution represents an average response of the structure and brings information on its global behavior.
{"title":"Constrained Euler buckling: The von Kármán approximation","authors":"Jiayu Wang, Stéphanie Deboeuf, Arnaud Antkowiak, Sébastien Neukirch","doi":"10.1016/j.ijsolstr.2025.113279","DOIUrl":"10.1016/j.ijsolstr.2025.113279","url":null,"abstract":"<div><div>We consider the classical problem of the buckling of a planar elastica inside a rectangular cavity. We compute the equilibrium solutions analytically in the (von Kármán) small deflection approximation. We list the different equilibrium states and their domain of validity in terms of the imposed horizontal <span><math><mi>Δ</mi></math></span> and vertical <span><math><mi>H</mi></math></span> displacements. We compute the horizontal <span><math><mi>P</mi></math></span> and the vertical <span><math><mi>F</mi></math></span> applied forces and show how they increase and scale when the compaction ratio <span><math><mrow><msqrt><mrow><mi>Δ</mi></mrow></msqrt><mo>/</mo><mi>H</mi></mrow></math></span> is increased. Finally, we introduce an approximate response state, where the system adopts a periodic configuration with a noninteger number of repeated folds. This solution represents an average response of the structure and brings information on its global behavior.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"313 ","pages":"Article 113279"},"PeriodicalIF":3.4,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143445194","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2025-02-13DOI: 10.1016/j.ijsolstr.2025.113272
Ryan C. McAvoy
This paper discusses the three-dimensional finite element implementation of a nonlinear constrained Cosserat model for fibrous materials that accounts for extensional, flexural, and torsional fiber stiffness. Fiber bending and twisting effects are recorded by a rotation field introduced as an additional kinematic variable, the gradient of which is included in the pointwise constitutive response. A fiber-materiality constraint, enforced implicitly through Lagrange multipliers, convects the fibers as material curves. Two independent length scales corresponding to the fiber embedding, in the present case fiber cross sectional radius and fiber spacing, are explicitly included in the model. The open-source finite element code FEniCS is utilized for the numerical implementation, with which we study compression-induced flexural buckling of an elastic rectangular cantilever. Simulations reveal that fiber flexural stiffness affects out-of-plane buckling modes, and that by modifying the fiber size, modulus, and embedding pattern, unusual deformation patterns and global force–displacement responses can be achieved. These results are expected to facilitate more effective analysis of these materials and ultimately guide their design in the spirit of the metamaterial paradigm.
{"title":"Exotic buckling patterns in fiber-reinforced materials: Numerical simulations of Cosserat elasticity","authors":"Ryan C. McAvoy","doi":"10.1016/j.ijsolstr.2025.113272","DOIUrl":"10.1016/j.ijsolstr.2025.113272","url":null,"abstract":"<div><div>This paper discusses the three-dimensional finite element implementation of a nonlinear constrained Cosserat model for fibrous materials that accounts for extensional, flexural, and torsional fiber stiffness. Fiber bending and twisting effects are recorded by a rotation field introduced as an additional kinematic variable, the gradient of which is included in the pointwise constitutive response. A fiber-materiality constraint, enforced implicitly through Lagrange multipliers, convects the fibers as material curves. Two independent length scales corresponding to the fiber embedding, in the present case fiber cross sectional radius and fiber spacing, are explicitly included in the model. The open-source finite element code FEniCS is utilized for the numerical implementation, with which we study compression-induced flexural buckling of an elastic rectangular cantilever. Simulations reveal that fiber flexural stiffness affects out-of-plane buckling modes, and that by modifying the fiber size, modulus, and embedding pattern, unusual deformation patterns and global force–displacement responses can be achieved. These results are expected to facilitate more effective analysis of these materials and ultimately guide their design in the spirit of the metamaterial paradigm.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"312 ","pages":"Article 113272"},"PeriodicalIF":3.4,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429984","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 : 2025-02-13DOI: 10.1016/j.ijsolstr.2025.113276
Yihang Chen , Tingjun Wang , Yuanyuan Cui, Yingzhuo Lun, Jiawang Hong
Buckle-delamination, a typical instability mode, can spontaneously introduce large, sizable-area and tunable strain gradients in nanofilms adhered to compliant substrates, which helps to exploit the flexoelectric effect. However, the role of flexoelectricity in the buckle-delamination behavior of dielectric nanofilms remains unclear. Here, an electromechanical coupling model is developed to capture the flexoelectric effect in buckle-delaminated films on compliant substrates. The energy analysis indicates that the interplay between flexoelectricity and buckling promotes the delamination process by increasing the width of buckle-delaminated blisters. Moreover, the coupling of flexoelectricity and piezoelectricity breaks the anti-symmetric distribution of in-plane stress, thereby affecting the position and magnitude of the maximum tensile stress. We also investigate the size-dependent effect of flexoelectricity in buckle-delamination behavior and demonstrate its crucial role in films of nanoscale thickness. This work can advance the understanding of the flexoelectric effect in buckle-delamination behavior and pave the way for its practical applications.
{"title":"Effect of flexoelectricity on buckle-delamination of nanofilms adhered to compliant substrates","authors":"Yihang Chen , Tingjun Wang , Yuanyuan Cui, Yingzhuo Lun, Jiawang Hong","doi":"10.1016/j.ijsolstr.2025.113276","DOIUrl":"10.1016/j.ijsolstr.2025.113276","url":null,"abstract":"<div><div>Buckle-delamination, a typical instability mode, can spontaneously introduce large, sizable-area and tunable strain gradients in nanofilms adhered to compliant substrates, which helps to exploit the flexoelectric effect. However, the role of flexoelectricity in the buckle-delamination behavior of dielectric nanofilms remains unclear. Here, an electromechanical coupling model is developed to capture the flexoelectric effect in buckle-delaminated films on compliant substrates. The energy analysis indicates that the interplay between flexoelectricity and buckling promotes the delamination process by increasing the width of buckle-delaminated blisters. Moreover, the coupling of flexoelectricity and piezoelectricity breaks the anti-symmetric distribution of in-plane stress, thereby affecting the position and magnitude of the maximum tensile stress. We also investigate the size-dependent effect of flexoelectricity in buckle-delamination behavior and demonstrate its crucial role in films of nanoscale thickness. This work can advance the understanding of the flexoelectric effect in buckle-delamination behavior and pave the way for its practical applications.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"312 ","pages":"Article 113276"},"PeriodicalIF":3.4,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143444617","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 : 2025-02-12DOI: 10.1016/j.ijsolstr.2025.113282
Yun-Long Chen, Li Ma
Reusable mechanical metamaterials with both high energy-dissipating and load-bearing features are ideal candidates for widespread dynamic applications, ranging from impact mitigation to vibration suppression. Despite great demands, the existing designs either exhibit limited damping or stiffness, and perhaps work well only for one-time use. To reconcile these contradictions, a synchronous enhancements strategy of damping and stiffness is proposed to create novel mechanical metamaterial by replacing the viscous damping in the viscoelastic material Kelvin-Voigt constitutive to frictional damping, exemplified by auxetic self-tensioning friction damping metamaterials (FDM). They trigger an embedded sliding friction behavior through auxetic effect to achieve energy dissipation, which especially shows high stiffness while achieving extreme damping ability synergistically under large compressive strain. This synchronous enhancement mechanism is analysed by combining finite element modelling, theoretical analysis, and experimental validation. These innovative mechanical metamaterials with repeatability and self-recoverability have broad applications in engineering materials-structures-systems for energy-dissipation and load-carrying.
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