Natural defects such as nano inclusions and nanocracks are inevitable in dielectric materials. When materials are subjected to mechanical loading, the strain gradient around crack tips and inclusions would become large and induce significant flexoelectric fields. In contrast to classical crack-inclusion problems, the interactions between these flexoelectric fields may locally change the electromechanical behaviors of materials, and result in some interesting phenomena. To better understand the crack-inclusion interactions in flexoelectric solids, in this work, we use a collocation mixed finite element method to model and analyze the flexoelectric fields around the crack tip and inclusion. Based on the J-integral, we analyze how the flexoelectric effect affect the interactions energy between nanocracks and nearby nano inclusions. This work proposes a new coupling mechanism in crack-inclusion problems and may inspire future experiments in flexoelectric solids.
{"title":"Modeling the interaction between inclusions and nanocracks in flexoelectric solid","authors":"Mengkang Xu, Xinpeng Tian, Q. Deng, Qun Li","doi":"10.1115/1.4062659","DOIUrl":"https://doi.org/10.1115/1.4062659","url":null,"abstract":"\u0000 Natural defects such as nano inclusions and nanocracks are inevitable in dielectric materials. When materials are subjected to mechanical loading, the strain gradient around crack tips and inclusions would become large and induce significant flexoelectric fields. In contrast to classical crack-inclusion problems, the interactions between these flexoelectric fields may locally change the electromechanical behaviors of materials, and result in some interesting phenomena. To better understand the crack-inclusion interactions in flexoelectric solids, in this work, we use a collocation mixed finite element method to model and analyze the flexoelectric fields around the crack tip and inclusion. Based on the J-integral, we analyze how the flexoelectric effect affect the interactions energy between nanocracks and nearby nano inclusions. This work proposes a new coupling mechanism in crack-inclusion problems and may inspire future experiments in flexoelectric solids.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63503969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Multistable structures can maintain multiple steady states without additional loads. However, the presence of geometric and material nonlinearities in multistable structures adds complexity and difficulty to their optimal design. In this paper, a novel method is proposed to achieve multistability in conical structures by local cross-section modification. A conical multistable structure with varying cross-section is designed based on this method. The finite element model considering the nonlinear large deformation mechanics and rubber material's hyperelasticity was established for analyzing the multistable properties and meanwhile verified by experiments. The influence of geometric parameters of the cross-section (thickness, width, position) on the multistabilities (number, distribution, and snapping threshold) was analyzed. The steady-state number can be effectively used to redesign the multistable properties by local reinforcement. It is also observed that the quasi-zero stiffness region of the force-displacement curve can be extended by 61.7% compared to the original conical structure. Moreover, the optimized QZS structure allows for an actively-designable stepped dynamic response under forced vibration.
{"title":"Reshape of the bistable and multistable properties of conical structures through integrated modification of local cross-section","authors":"Jian Zhao, Qifeng Fang, Jian Zhang, Yu Huang, Hongyuan Wang, Pengbo Liu","doi":"10.1115/1.4062655","DOIUrl":"https://doi.org/10.1115/1.4062655","url":null,"abstract":"\u0000 Multistable structures can maintain multiple steady states without additional loads. However, the presence of geometric and material nonlinearities in multistable structures adds complexity and difficulty to their optimal design. In this paper, a novel method is proposed to achieve multistability in conical structures by local cross-section modification. A conical multistable structure with varying cross-section is designed based on this method. The finite element model considering the nonlinear large deformation mechanics and rubber material's hyperelasticity was established for analyzing the multistable properties and meanwhile verified by experiments. The influence of geometric parameters of the cross-section (thickness, width, position) on the multistabilities (number, distribution, and snapping threshold) was analyzed. The steady-state number can be effectively used to redesign the multistable properties by local reinforcement. It is also observed that the quasi-zero stiffness region of the force-displacement curve can be extended by 61.7% compared to the original conical structure. Moreover, the optimized QZS structure allows for an actively-designable stepped dynamic response under forced vibration.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48511708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, a new original justification of an homogenized model for ionic diffusion in porous media is proposed. The approach used enables to specify clearly the domain of validity of this homogenized model, involving a source term characterizing the electrical double layer effect at the macroscale. This homogenized model is obtained from the formal periodic homogenization of Nernst-Planck-Poisson system at the pore scale accounting for conductivity of the solid phase which is generally neglected. The Poisson equation is defined in both fluid and solid phases and the discontinuity of fluxes at the solid-fluid interface is modeled by a jump of the electrical field, linked to the surface electrical charge of the solid interface. Numerical simulations are carried out at the scale of the unit cell to underscore the influence of the contrast on the electrical permittivity between fluid and solid phases. The comparison of the concentrations and the electrical potential given at the macro-scale by the homogenized model and by a direct pore scale model reveals the accuracy of the homogenized model which is very simple to use.
{"title":"Justification of a new original homogenized model for ionic diffusion in porous media.","authors":"M. K. Bourbatache, O. Millet, G. Gagneux","doi":"10.1115/1.4062657","DOIUrl":"https://doi.org/10.1115/1.4062657","url":null,"abstract":"\u0000 In this work, a new original justification of an homogenized model for ionic diffusion in porous media is proposed. The approach used enables to specify clearly the domain of validity of this homogenized model, involving a source term characterizing the electrical double layer effect at the macroscale. This homogenized model is obtained from the formal periodic homogenization of Nernst-Planck-Poisson system at the pore scale accounting for conductivity of the solid phase which is generally neglected. The Poisson equation is defined in both fluid and solid phases and the discontinuity of fluxes at the solid-fluid interface is modeled by a jump of the electrical field, linked to the surface electrical charge of the solid interface. Numerical simulations are carried out at the scale of the unit cell to underscore the influence of the contrast on the electrical permittivity between fluid and solid phases. The comparison of the concentrations and the electrical potential given at the macro-scale by the homogenized model and by a direct pore scale model reveals the accuracy of the homogenized model which is very simple to use.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45046350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Understanding the contact characteristics of rough surfaces is essential to explain engineering phenomenon in interface. In order to improve accuracy of contact model, a novel simplified fully plastic contact model of sphere asperity was proposed considering material properties based on fractal theory. Firstly based on Von Mises yield criteria maximum contact pressure factor was derived. Secondly relationships taking into consideration strain hardening were proposed to describe contact area based on definition of the fully plastic contact area index and contact pressure. Then the critical interference at inception of fully plastic deformation was derived. Lastly validations were conducted for different materials. The results show that present work is remarkably consistent with experiment results and has higher accuracy than other models.
{"title":"A New Contact Model of Sphere Asperity in the Fully Plastic Regime Considering Strain Hardening","authors":"Jinli Xu, Jiwei Zhu","doi":"10.1115/1.4062656","DOIUrl":"https://doi.org/10.1115/1.4062656","url":null,"abstract":"\u0000 Understanding the contact characteristics of rough surfaces is essential to explain engineering phenomenon in interface. In order to improve accuracy of contact model, a novel simplified fully plastic contact model of sphere asperity was proposed considering material properties based on fractal theory. Firstly based on Von Mises yield criteria maximum contact pressure factor was derived. Secondly relationships taking into consideration strain hardening were proposed to describe contact area based on definition of the fully plastic contact area index and contact pressure. Then the critical interference at inception of fully plastic deformation was derived. Lastly validations were conducted for different materials. The results show that present work is remarkably consistent with experiment results and has higher accuracy than other models.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42635292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We perform finite element simulations to study the impact of defect-defect interactions on the pressure-induced buckling of thin, elastic, spherical shells containing two dimpled imperfections. Throughout, we quantify the critical buckling pressure of these shells using their knockdown factor. We examine cases featuring either identical or different geometric defects and systematically explore the parameter space, including the angular separation between the defects, their widths and amplitudes, and the radius-to-thickness ratio of the shell. As the angular separation between the defects is increased, the buckling strength initially decreases, then increases before reaching a plateau. Our primary finding is that the onset of defect-defect interactions, as quantified by a characteristic length scale associated with the onset of the plateau, is set by the critical buckling wavelength reported in the classic shell-buckling literature. Beyond this threshold, within the plateau regime, the buckling behavior of the shell is dictated by the largest defect.
{"title":"Defect-Defect Interactions in the Buckling of Imperfect Spherical Shells","authors":"F. Derveni, A. Abbasi, P. Reis","doi":"10.1115/1.4062774","DOIUrl":"https://doi.org/10.1115/1.4062774","url":null,"abstract":"\u0000 We perform finite element simulations to study the impact of defect-defect interactions on the pressure-induced buckling of thin, elastic, spherical shells containing two dimpled imperfections. Throughout, we quantify the critical buckling pressure of these shells using their knockdown factor. We examine cases featuring either identical or different geometric defects and systematically explore the parameter space, including the angular separation between the defects, their widths and amplitudes, and the radius-to-thickness ratio of the shell. As the angular separation between the defects is increased, the buckling strength initially decreases, then increases before reaching a plateau. Our primary finding is that the onset of defect-defect interactions, as quantified by a characteristic length scale associated with the onset of the plateau, is set by the critical buckling wavelength reported in the classic shell-buckling literature. Beyond this threshold, within the plateau regime, the buckling behavior of the shell is dictated by the largest defect.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46284348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study aims to improve the impact protection performance of composite structures by combining a honeycomb core with negative Poisson's ratio and graphene platelets reinforced (GPR) face sheets. The paper investigates the nonlinear repeated low-velocity impact responses of auxetic honeycomb composite plates, taking into account loading-unloading-reloading processes. Effective material properties of the auxetic honeycomb core and GPR face sheets are obtained by using the proposed modified Gibson function and Halpin-Tsai model. Then, taking into account geometric nonlinearity, the nonlinear equations of motion for the system were derived by the Hamilton's principle. Afterward, the time-varying contact force between the composite plate and a spherical impactor is defined by the modified nonlinear Hertz contact theory. The Galerkin method and variable-step Runge-Kutta algorithm are selected to obtain nonlinear impact responses. The proposed methods are verified by finite element simulation and experiment. Finally, the study evaluates the effects of key parameters on the nonlinear repeated low-velocity impact responses.
{"title":"A nonlinear repeated impact model of auxetic honeycomb structures considering geometric nonlinearity and tensile/compressive deformation","authors":"Yunfei Liu, Zhao-ye Qin, F. Chu","doi":"10.1115/1.4062592","DOIUrl":"https://doi.org/10.1115/1.4062592","url":null,"abstract":"\u0000 This study aims to improve the impact protection performance of composite structures by combining a honeycomb core with negative Poisson's ratio and graphene platelets reinforced (GPR) face sheets. The paper investigates the nonlinear repeated low-velocity impact responses of auxetic honeycomb composite plates, taking into account loading-unloading-reloading processes. Effective material properties of the auxetic honeycomb core and GPR face sheets are obtained by using the proposed modified Gibson function and Halpin-Tsai model. Then, taking into account geometric nonlinearity, the nonlinear equations of motion for the system were derived by the Hamilton's principle. Afterward, the time-varying contact force between the composite plate and a spherical impactor is defined by the modified nonlinear Hertz contact theory. The Galerkin method and variable-step Runge-Kutta algorithm are selected to obtain nonlinear impact responses. The proposed methods are verified by finite element simulation and experiment. Finally, the study evaluates the effects of key parameters on the nonlinear repeated low-velocity impact responses.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49406751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Metal tube is a traditional energy-absorbing structure, and metal foam is a lightweight material with advantages, i.e. high energy absorption and high specific strength. The foam-filled square tube can improve the crashworthiness and has better energy absorption, which is higher than the sum of the energy absorption of the tube and foam. Axial crushing behaviors of metal density gradient foam (DGF) filled square taper tubes are studied analytically and numerically in this paper. An analytical model is presented to study the crushing behavior of DGF filled square taper metal tube under axial loading, in which the interaction between square taper tube and DGF is considered. The numerical calculation is conducted, and the deformation mode is obtained. The analytical predictions are well consistent with the experimental and numerical results. The influences of taper angle, foam strength, maximum relative density and minimum relative density of gradient foam on the compressive behavior of metal DGF filled square taper tube under axial loading are considered. It is demonstrated that when the taper angle is less than 85°, the average crushing force increases as the minimum density of the DGF increases. However, when the taper angle is greater than 85°, the average crushing force decreases with the increase of the minimum density of gradient. This proposed analytical model can effectively predict the axial crushing behaviors of metal DGF filled square taper tube.
{"title":"Axial crushing behaviors of metal density gradient foam-filled square taper tubes: Analytical model and numerical calculation","authors":"Xiwei Wu, Jianxun Zhang","doi":"10.1115/1.4062577","DOIUrl":"https://doi.org/10.1115/1.4062577","url":null,"abstract":"\u0000 Metal tube is a traditional energy-absorbing structure, and metal foam is a lightweight material with advantages, i.e. high energy absorption and high specific strength. The foam-filled square tube can improve the crashworthiness and has better energy absorption, which is higher than the sum of the energy absorption of the tube and foam. Axial crushing behaviors of metal density gradient foam (DGF) filled square taper tubes are studied analytically and numerically in this paper. An analytical model is presented to study the crushing behavior of DGF filled square taper metal tube under axial loading, in which the interaction between square taper tube and DGF is considered. The numerical calculation is conducted, and the deformation mode is obtained. The analytical predictions are well consistent with the experimental and numerical results. The influences of taper angle, foam strength, maximum relative density and minimum relative density of gradient foam on the compressive behavior of metal DGF filled square taper tube under axial loading are considered. It is demonstrated that when the taper angle is less than 85°, the average crushing force increases as the minimum density of the DGF increases. However, when the taper angle is greater than 85°, the average crushing force decreases with the increase of the minimum density of gradient. This proposed analytical model can effectively predict the axial crushing behaviors of metal DGF filled square taper tube.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48752824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Due to the forming or curing process, the materials of three-dimensional (3D) printing have periodic mesodefects, which result in complex constitutive relations and anisotropy. Fused deposition modeling (FDM), which is a typical 3D printing process, inevitably introduces stacking pore defects due to the three-dimensional stacking of materials along the printing direction. At present, research focuses on the mechanical properties of materials printed along only one single direction. To consider the possibility of changing the mechanical properties of materials by adjusting the printing direction, the change in the properties of printing materials along the multiple printing direction combinations was analyzed in this paper. First, based on a continuous medium model, the constitutive model proposed by Garzon-Hernandez et al. was considered, and then to improve the prediction accuracy of the model in the plastic stage, a model describing the porosity change rate of porous materials was introduced to obtain better prediction results. Then, the finite element method (FEM) was developed using the new constitutive relation model implemented by the User Defined Material subroutine (USERMAT) into ANSYS software. Second, through the finite element subroutine, the mechanical response of the FDM 3D printing plate with two different printing direction combinations was simulated. The results show that by adjusting the print direction combination of the double-layer FDM 3D printing materials, the materials show a different anisotropy, maximum bearing capacity of tension and shear and buckling resistance
{"title":"Constitutive relation development for FDM 3D printing materials and simulation of printing direction combination","authors":"Meng Li, B. Sun","doi":"10.1115/1.4062535","DOIUrl":"https://doi.org/10.1115/1.4062535","url":null,"abstract":"\u0000 Due to the forming or curing process, the materials of three-dimensional (3D) printing have periodic mesodefects, which result in complex constitutive relations and anisotropy. Fused deposition modeling (FDM), which is a typical 3D printing process, inevitably introduces stacking pore defects due to the three-dimensional stacking of materials along the printing direction. At present, research focuses on the mechanical properties of materials printed along only one single direction. To consider the possibility of changing the mechanical properties of materials by adjusting the printing direction, the change in the properties of printing materials along the multiple printing direction combinations was analyzed in this paper. First, based on a continuous medium model, the constitutive model proposed by Garzon-Hernandez et al. was considered, and then to improve the prediction accuracy of the model in the plastic stage, a model describing the porosity change rate of porous materials was introduced to obtain better prediction results. Then, the finite element method (FEM) was developed using the new constitutive relation model implemented by the User Defined Material subroutine (USERMAT) into ANSYS software. Second, through the finite element subroutine, the mechanical response of the FDM 3D printing plate with two different printing direction combinations was simulated. The results show that by adjusting the print direction combination of the double-layer FDM 3D printing materials, the materials show a different anisotropy, maximum bearing capacity of tension and shear and buckling resistance","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43184000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The misfit stress in a thin layer embedded in a semi-infinite matrix has been first determined near the free-surface of the structure, using the virtual dislocation formalism. From a Peach-Koehler force analysis, the different equilibrium positions (unstable and stable) of an edge dislocation gliding in a plane of the layer inclined with respect to the upper interface and emerging at the point of intersection of the upper interface and this free-surface have been then characterized with respect to the lattice mismatch and the inclination angle of the gliding plane. It has been found that the dislocation may exhibit stable equilibrium position near the interface and/or near the free-surface. A diagram of the position stability has been then determined versus the misfit parameter and the inclination angle. The energy variation due to the introduction of an edge dislocation from the free-surface until the matrix-layer interface has been finally determined, when the dislocation is gliding in the plane inclined with respect to the interface horizontal axis. A critical thickness of the layer beyond which the formation of the dislocation in the interfaces is energetically favorable has been finally determined as well as its position with respect to the free-surface in the lower interface.
{"title":"Dislocation in a strained layer embedded in a semi-infinite matrix","authors":"J. Colin","doi":"10.1115/1.4062537","DOIUrl":"https://doi.org/10.1115/1.4062537","url":null,"abstract":"\u0000 The misfit stress in a thin layer embedded in a semi-infinite matrix has been first determined near the free-surface of the structure, using the virtual dislocation formalism. From a Peach-Koehler force analysis, the different equilibrium positions (unstable and stable) of an edge dislocation gliding in a plane of the layer inclined with respect to the upper interface and emerging at the point of intersection of the upper interface and this free-surface have been then characterized with respect to the lattice mismatch and the inclination angle of the gliding plane. It has been found that the dislocation may exhibit stable equilibrium position near the interface and/or near the free-surface. A diagram of the position stability has been then determined versus the misfit parameter and the inclination angle. The energy variation due to the introduction of an edge dislocation from the free-surface until the matrix-layer interface has been finally determined, when the dislocation is gliding in the plane inclined with respect to the interface horizontal axis. A critical thickness of the layer beyond which the formation of the dislocation in the interfaces is energetically favorable has been finally determined as well as its position with respect to the free-surface in the lower interface.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41295622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Weicheng Huang, Yingchao Zhang, T. Yu, Mingchao Liu
Discrete Elastic Rods (DER) method provides a computationally efficient means of simulating the nonlinear dynamics of one-dimensional slender structures. However, this dynamic-based framework can only provide first-order stable equilibrium configuration when combined with the dynamic relaxation method, while the unstable equilibria and potential critical points (i.e. bifurcation and fold point) cannot be obtained, which are important for understanding the bifurcation and stability landscape of slender bodies. Our approach modifies the existing DER technique from dynamic simulation to a static framework and computes eigenvalues and eigenvectors of the tangential stiffness matrix after each load incremental step for bifurcation and stability analysis. This treatment can capture both stable and unstable equilibrium modes, critical points, and trace solution curves. Three representative types of structures -- beams, strips, and gridshells -- are used as demonstrations to show the effectiveness of the modified numerical framework, which provides a robust tool for unveiling the bifurcation and multistable behaviors of slender structures.
{"title":"Bifurcations and stability analysis of elastic slender structures using static discrete elastic rods method","authors":"Weicheng Huang, Yingchao Zhang, T. Yu, Mingchao Liu","doi":"10.1115/1.4062533","DOIUrl":"https://doi.org/10.1115/1.4062533","url":null,"abstract":"\u0000 Discrete Elastic Rods (DER) method provides a computationally efficient means of simulating the nonlinear dynamics of one-dimensional slender structures. However, this dynamic-based framework can only provide first-order stable equilibrium configuration when combined with the dynamic relaxation method, while the unstable equilibria and potential critical points (i.e. bifurcation and fold point) cannot be obtained, which are important for understanding the bifurcation and stability landscape of slender bodies. Our approach modifies the existing DER technique from dynamic simulation to a static framework and computes eigenvalues and eigenvectors of the tangential stiffness matrix after each load incremental step for bifurcation and stability analysis. This treatment can capture both stable and unstable equilibrium modes, critical points, and trace solution curves. Three representative types of structures -- beams, strips, and gridshells -- are used as demonstrations to show the effectiveness of the modified numerical framework, which provides a robust tool for unveiling the bifurcation and multistable behaviors of slender structures.","PeriodicalId":54880,"journal":{"name":"Journal of Applied Mechanics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47886537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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