Pub Date : 2024-05-30DOI: 10.1177/10812865241256800
Roberto Fedele, Gabriele Milani, Francesco dell’Isola
{"title":"Special issue: “Integrated approaches for the mechanics of masonry structures: Novel strategies for experimental characterization, mathematical modelling and computer simulations”","authors":"Roberto Fedele, Gabriele Milani, Francesco dell’Isola","doi":"10.1177/10812865241256800","DOIUrl":"https://doi.org/10.1177/10812865241256800","url":null,"abstract":"","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"18 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141194030","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}
Pub Date : 2024-05-27DOI: 10.1177/10812865241251470
Xiang Zhou, Guoshuang Shui
Considering the importance of understanding the propagation of transient waves in the piezomagnetic solids, the thermal effect on the transient behavior of a piezomagnetic half-space subjected to dynamic anti-plane load is investigated analytically in this paper. Using one-sided, two-sided Laplace transformation and Cagniard–de Hoop (CH) technique, an efficient and accurate analytical derivation for the solution of the anti-plane displacement, shear stress, magnetic potential, and induction in Laplace domain is presented. The study shows that the thermal stresses developed in x-axis and y-axis directions have significant influence on the transient response of the half-space. The magnetic induction [Formula: see text] increases obviously when the thermal stress is applied in x-axis direction, while it decreases when the thermal stress is applied in y-axis direction. Approaching time of magnetic induction [Formula: see text] and [Formula: see text] will become longer with higher thermal stress in x-axis direction. With the growth of the thermal stress in x-direction, contribution from the electromagnetic–elastic head (EH) wave increases, while the contribution from the shear elastic (SE) wave and the static value of shear stress decrease.
考虑到理解瞬态波在压磁固体中传播的重要性，本文分析研究了热效应对承受动态反面载荷的压磁半空间瞬态行为的影响。利用单面、双面拉普拉斯变换和 Cagniard-de Hoop（CH）技术，给出了拉普拉斯域中反平面位移、剪应力、磁势和感应的高效、精确的分析推导。研究表明，在 x 轴和 y 轴方向产生的热应力对半空间的瞬态响应有显著影响。当在 x 轴方向施加热应力时，磁感应强度[计算公式：见正文]明显增加，而当在 y 轴方向施加热应力时，磁感应强度降低。随着 x 轴方向热应力的增加，磁感应强度[计算公式：见正文]和[计算公式：见正文]的接近时间会变长。随着 x 轴方向热应力的增加，电磁弹性头（EH）波的贡献增大，而剪切弹性（SE）波的贡献和剪应力的静态值减小。
{"title":"Thermal effect on the transient behavior of a piezomagnetic half-space subjected to dynamic anti-plane load","authors":"Xiang Zhou, Guoshuang Shui","doi":"10.1177/10812865241251470","DOIUrl":"https://doi.org/10.1177/10812865241251470","url":null,"abstract":"Considering the importance of understanding the propagation of transient waves in the piezomagnetic solids, the thermal effect on the transient behavior of a piezomagnetic half-space subjected to dynamic anti-plane load is investigated analytically in this paper. Using one-sided, two-sided Laplace transformation and Cagniard–de Hoop (CH) technique, an efficient and accurate analytical derivation for the solution of the anti-plane displacement, shear stress, magnetic potential, and induction in Laplace domain is presented. The study shows that the thermal stresses developed in x-axis and y-axis directions have significant influence on the transient response of the half-space. The magnetic induction [Formula: see text] increases obviously when the thermal stress is applied in x-axis direction, while it decreases when the thermal stress is applied in y-axis direction. Approaching time of magnetic induction [Formula: see text] and [Formula: see text] will become longer with higher thermal stress in x-axis direction. With the growth of the thermal stress in x-direction, contribution from the electromagnetic–elastic head (EH) wave increases, while the contribution from the shear elastic (SE) wave and the static value of shear stress decrease.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"48 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168571","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}
Pub Date : 2024-05-13DOI: 10.1177/10812865241243086
Erick Pruchnicki
In this work, we present a new two-scale finite-strain plate theory for highly heterogeneous plates described by a repetitive periodic microstructure. Two scales exist, the macroscopic scale is linked to the entire plate and the microscopic one is linked to the size of the heterogeneity. This work aims to propose such a theory for thick plates in a nonlinear setting when the thickness and the size of heterogeneities are of the same order of magnitude. The homogenization theory for large deformation with growth is suitable for the modelization of nearly incompressible plant tissue. This model is suitable for wavy leaves. For thick plates, the transverse normal stress and transverse shearing are modelized at both microscopic and macroscopic levels. At the macroscopic level, we consider a nonlinear Cosserat plate model. At the microscopic level, we impose that the average of contribution of the microscopic displacement to rotation angles is equal to zero. We also deal with the problem of boundary layer problem near the lateral boundary. The model recently proposed by Pruchnicki is valid for thin heterogeneous plates; we present an extension for thick plates that takes into account both transverse normal stress and shearing. This model is equivalent to the first model presented but it involves a second-order derivative of the macroscopic displacement field.
{"title":"Homogenization of nonlinear Cosserat plate including growth theory when the thickness of the plate and the size of the in-plane heterogeneities are of the same order of magnitude","authors":"Erick Pruchnicki","doi":"10.1177/10812865241243086","DOIUrl":"https://doi.org/10.1177/10812865241243086","url":null,"abstract":"In this work, we present a new two-scale finite-strain plate theory for highly heterogeneous plates described by a repetitive periodic microstructure. Two scales exist, the macroscopic scale is linked to the entire plate and the microscopic one is linked to the size of the heterogeneity. This work aims to propose such a theory for thick plates in a nonlinear setting when the thickness and the size of heterogeneities are of the same order of magnitude. The homogenization theory for large deformation with growth is suitable for the modelization of nearly incompressible plant tissue. This model is suitable for wavy leaves. For thick plates, the transverse normal stress and transverse shearing are modelized at both microscopic and macroscopic levels. At the macroscopic level, we consider a nonlinear Cosserat plate model. At the microscopic level, we impose that the average of contribution of the microscopic displacement to rotation angles is equal to zero. We also deal with the problem of boundary layer problem near the lateral boundary. The model recently proposed by Pruchnicki is valid for thin heterogeneous plates; we present an extension for thick plates that takes into account both transverse normal stress and shearing. This model is equivalent to the first model presented but it involves a second-order derivative of the macroscopic displacement field.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"68 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940646","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}
Pub Date : 2024-05-10DOI: 10.1177/10812865241239647
Ciprian D Coman, Andrew P Bassom
The classical lateral–torsional instability of a cantilever beam with continuous elastic lateral restraint and a transverse point-load applied at the free end is discussed here through the lens of asymptotic simplifications. One of our main goals is to provide analytical approximations for the critical buckling load, as well as its dependence on various key non-dimensional groups. The first part of this study is concerned with a scenario in which a doubly symmetric beam is constrained to rotate about a fixed axis situated at an arbitrary height above the shear centroidal axis. The second part examines a beam that features a continuous elastic lateral restraint spanning its entire length. Assuming that the stiffness of the constraint, [Formula: see text] (say), is finite, the buckling equations in the second case are described by a system of two coupled fourth-order differential equations in the lateral displacement and the angle of twist. We show that as [Formula: see text], the problem discussed in the first part provides an outer solution for the aforementioned system; the relevant boundary conditions for the next-to-leading-order outer approximation are also derived using matched asymptotics. Our theoretical findings are confirmed by comparisons with direct numerical simulations of the full buckling problem.
{"title":"Flexural–torsional buckling with enforced axis of twist and related problems","authors":"Ciprian D Coman, Andrew P Bassom","doi":"10.1177/10812865241239647","DOIUrl":"https://doi.org/10.1177/10812865241239647","url":null,"abstract":"The classical lateral–torsional instability of a cantilever beam with continuous elastic lateral restraint and a transverse point-load applied at the free end is discussed here through the lens of asymptotic simplifications. One of our main goals is to provide analytical approximations for the critical buckling load, as well as its dependence on various key non-dimensional groups. The first part of this study is concerned with a scenario in which a doubly symmetric beam is constrained to rotate about a fixed axis situated at an arbitrary height above the shear centroidal axis. The second part examines a beam that features a continuous elastic lateral restraint spanning its entire length. Assuming that the stiffness of the constraint, [Formula: see text] (say), is finite, the buckling equations in the second case are described by a system of two coupled fourth-order differential equations in the lateral displacement and the angle of twist. We show that as [Formula: see text], the problem discussed in the first part provides an outer solution for the aforementioned system; the relevant boundary conditions for the next-to-leading-order outer approximation are also derived using matched asymptotics. Our theoretical findings are confirmed by comparisons with direct numerical simulations of the full buckling problem.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"48 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940555","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}
Pub Date : 2024-05-07DOI: 10.1177/10812865241240484
Ivan I Argatov, Gennady S Mishuris, Valentin L Popov
Non-axisymmetric frictionless JKR-type adhesive contact between a rigid body and a thin incompressible elastic layer bonded to a rigid base is considered in the framework of the leading-order asymptotic model, which has the form of an overdetermined boundary value problem. Based on the first-order perturbation of the Neumann operator in the Dirichlet problem for Poisson’s equation, the decohesion initiation problem is formulated in the form of a variational inequality. The asymptotic model assumes that the contact zone and its boundary contour during the detachment process are unknown. The absence of the solvability theorem is illustrated by an example of the instability of an axisymmetric flat circular contact.
{"title":"Initiation of decohesion between a flat punch and a thin bonded incompressible layer","authors":"Ivan I Argatov, Gennady S Mishuris, Valentin L Popov","doi":"10.1177/10812865241240484","DOIUrl":"https://doi.org/10.1177/10812865241240484","url":null,"abstract":"Non-axisymmetric frictionless JKR-type adhesive contact between a rigid body and a thin incompressible elastic layer bonded to a rigid base is considered in the framework of the leading-order asymptotic model, which has the form of an overdetermined boundary value problem. Based on the first-order perturbation of the Neumann operator in the Dirichlet problem for Poisson’s equation, the decohesion initiation problem is formulated in the form of a variational inequality. The asymptotic model assumes that the contact zone and its boundary contour during the detachment process are unknown. The absence of the solvability theorem is illustrated by an example of the instability of an axisymmetric flat circular contact.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"6 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940481","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}
Pub Date : 2024-05-06DOI: 10.1177/10812865241245338
László Péter Kiss
The in-plane stability of internally hinged, end-fixed shallow arches is in the spotlight. The non-linear model accounts for the coupled effect of the bending moment and axial force on the membrane strain. The model itself can handle homogeneous or non-homogeneous material distributions along the thickness of the uniform arch. Analytical findings reveal how the typical geometrical data, like arch length, radius of gyration, and arch angle, affect the lowest buckling loads. The typical non-linear behaviour of arches is also assessed including the equilibrium path and the internal force system.
{"title":"Stability of arches with internal hinge","authors":"László Péter Kiss","doi":"10.1177/10812865241245338","DOIUrl":"https://doi.org/10.1177/10812865241245338","url":null,"abstract":"The in-plane stability of internally hinged, end-fixed shallow arches is in the spotlight. The non-linear model accounts for the coupled effect of the bending moment and axial force on the membrane strain. The model itself can handle homogeneous or non-homogeneous material distributions along the thickness of the uniform arch. Analytical findings reveal how the typical geometrical data, like arch length, radius of gyration, and arch angle, affect the lowest buckling loads. The typical non-linear behaviour of arches is also assessed including the equilibrium path and the internal force system.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"18 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140887542","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}
Pub Date : 2024-05-04DOI: 10.1177/10812865241233675
Salvatore Federico
This brief contribution provides an overview of the Hill–Ogden generalised strain tensors, and some considerations on their representation in generalised (curvilinear) coordinates, in a fully covariant formalism that is adaptable to a more general theory on Riemannian manifolds. These strains may be naturally defined with covariant components or naturally defined with contravariant components. Each of these two macro-families is best suited to a specific geometrical context.
{"title":"A note on the Hill–Ogden generalised strains","authors":"Salvatore Federico","doi":"10.1177/10812865241233675","DOIUrl":"https://doi.org/10.1177/10812865241233675","url":null,"abstract":"This brief contribution provides an overview of the Hill–Ogden generalised strain tensors, and some considerations on their representation in generalised (curvilinear) coordinates, in a fully covariant formalism that is adaptable to a more general theory on Riemannian manifolds. These strains may be naturally defined with covariant components or naturally defined with contravariant components. Each of these two macro-families is best suited to a specific geometrical context.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"9 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140838481","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}
Pub Date : 2024-05-02DOI: 10.1177/10812865241242998
Xin Zhuan, Debao Guan, Hao Gao, Peter Theobald, Xiaoyu Luo
Soft tissue growth is crucial across various physiological applications, with mathematical modelling playing a pivotal role in understanding the underlying processes. The volumetric growth theory serves as a commonly used mathematical framework in this context. Our previous research on volumetric growth theory primarily concentrated on defining the incremental growth tensor in loaded and stressed configurations, revealing that this approach closely aligns with experimental observations of residual hoop stress distribution. However, given the assumptions employed, the approach has limitations in accurately predicting the growth timeline. In this work, we address these issues by incorporating the effect of initial residual strain and introducing a new mixed trigger growth evolution law. In this growth law, we do not use growth saturation as an upper limit, as this assumption cannot represent many physiological conditions. Instead, we propose that growth in soft tissues leads to a new equilibrium state. To illustrate this idea, we introduce a growth incompatibility function, denoted as [Formula: see text]. We establish the analytical relationship between [Formula: see text] and the opening angle in a simplified cylindrical geometry resembling the structure of the heart or arteries. We put forth a revised growth law that is both stress and incompatibility driven/Our results show that by using this mixed trigger growth law, tissues will not grow indefinitely. Instead, a stress-driven homeostasis incompatibility state will be reached. In addition, by accounting for the initial opening angle in the model, we can accurately trace the growth history of the heart, aligning with experimental data obtained from measuring the opening angle in young pigs from birth to maturity.
{"title":"A mixed trigger volumetric growth law for cylindrical deformation in stressed configurations","authors":"Xin Zhuan, Debao Guan, Hao Gao, Peter Theobald, Xiaoyu Luo","doi":"10.1177/10812865241242998","DOIUrl":"https://doi.org/10.1177/10812865241242998","url":null,"abstract":"Soft tissue growth is crucial across various physiological applications, with mathematical modelling playing a pivotal role in understanding the underlying processes. The volumetric growth theory serves as a commonly used mathematical framework in this context. Our previous research on volumetric growth theory primarily concentrated on defining the incremental growth tensor in loaded and stressed configurations, revealing that this approach closely aligns with experimental observations of residual hoop stress distribution. However, given the assumptions employed, the approach has limitations in accurately predicting the growth timeline. In this work, we address these issues by incorporating the effect of initial residual strain and introducing a new mixed trigger growth evolution law. In this growth law, we do not use growth saturation as an upper limit, as this assumption cannot represent many physiological conditions. Instead, we propose that growth in soft tissues leads to a new equilibrium state. To illustrate this idea, we introduce a growth incompatibility function, denoted as [Formula: see text]. We establish the analytical relationship between [Formula: see text] and the opening angle in a simplified cylindrical geometry resembling the structure of the heart or arteries. We put forth a revised growth law that is both stress and incompatibility driven/Our results show that by using this mixed trigger growth law, tissues will not grow indefinitely. Instead, a stress-driven homeostasis incompatibility state will be reached. In addition, by accounting for the initial opening angle in the model, we can accurately trace the growth history of the heart, aligning with experimental data obtained from measuring the opening angle in young pigs from birth to maturity.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"64 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140838531","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}
Pub Date : 2024-04-27DOI: 10.1177/10812865241238985
Yangkun Du, Nicholas A Hill, Xiaoyu Luo
Soft materials exhibit significant nonlinear geometric deformations and stress–strain relationships under external forces. This paper explores weakly nonlinear elasticity theories, including Landau’s and Murnaghan’s formulations, advancing understanding beyond linear elasticity. We establish connections between these methods and extend strain-energy functions to the third and fourth orders in power of [Formula: see text], where [Formula: see text] and [Formula: see text], and [Formula: see text] is the perturbation to the deformation gradient tensor [Formula: see text]. Furthermore, we address simplified strain-energy functions applicable to incompressible materials. Through this work, we contribute to a comprehensive understanding of nonlinear elasticity and its relationship to weakly nonlinear elasticity, facilitating the study of moderate deformations in soft material behavior and its practical applications.
{"title":"Connecting weakly nonlinear elasticity theories of isotropic hyperelastic materials","authors":"Yangkun Du, Nicholas A Hill, Xiaoyu Luo","doi":"10.1177/10812865241238985","DOIUrl":"https://doi.org/10.1177/10812865241238985","url":null,"abstract":"Soft materials exhibit significant nonlinear geometric deformations and stress–strain relationships under external forces. This paper explores weakly nonlinear elasticity theories, including Landau’s and Murnaghan’s formulations, advancing understanding beyond linear elasticity. We establish connections between these methods and extend strain-energy functions to the third and fourth orders in power of [Formula: see text], where [Formula: see text] and [Formula: see text], and [Formula: see text] is the perturbation to the deformation gradient tensor [Formula: see text]. Furthermore, we address simplified strain-energy functions applicable to incompressible materials. Through this work, we contribute to a comprehensive understanding of nonlinear elasticity and its relationship to weakly nonlinear elasticity, facilitating the study of moderate deformations in soft material behavior and its practical applications.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"131 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140811880","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}
Pub Date : 2024-04-26DOI: 10.1177/10812865241242432
Yang Liu, Xiang Yu, Luis Dorfmann
In this paper, we present a dimensional reduction to obtain a one-dimensional model to analyze localized necking or bulging in a residually stressed circular cylindrical solid. The nonlinear theory of elasticity is first specialized to obtain the equations governing the homogeneous deformation. Then, to analyze the nonhomogeneous part, we include higher-order correction terms of the axisymmetric displacement components leading to a three-dimensional form of the total potential energy functional. Details of the reduction to the one-dimensional form are given. We focus on a residually stressed Gent material and use numerical methods to solve the governing equations. Two loading conditions are considered. First, the residual stress is maintained constant, while the axial stretch is used as the loading parameter. Second, we keep the pre-stretch constant and monotonically increase the residual stress until bifurcation occurs. We specify initial conditions, find the critical values for localized bifurcation, and compute the change in radius during localized necking or bulging growth. Finally, we optimize material properties and use the one-dimensional model to simulate necking or bulging until the Maxwell values of stretch are reached.
{"title":"Reduced model and nonlinear analysis of localized instabilities of residually stressed cylinders under axial stretch","authors":"Yang Liu, Xiang Yu, Luis Dorfmann","doi":"10.1177/10812865241242432","DOIUrl":"https://doi.org/10.1177/10812865241242432","url":null,"abstract":"In this paper, we present a dimensional reduction to obtain a one-dimensional model to analyze localized necking or bulging in a residually stressed circular cylindrical solid. The nonlinear theory of elasticity is first specialized to obtain the equations governing the homogeneous deformation. Then, to analyze the nonhomogeneous part, we include higher-order correction terms of the axisymmetric displacement components leading to a three-dimensional form of the total potential energy functional. Details of the reduction to the one-dimensional form are given. We focus on a residually stressed Gent material and use numerical methods to solve the governing equations. Two loading conditions are considered. First, the residual stress is maintained constant, while the axial stretch is used as the loading parameter. Second, we keep the pre-stretch constant and monotonically increase the residual stress until bifurcation occurs. We specify initial conditions, find the critical values for localized bifurcation, and compute the change in radius during localized necking or bulging growth. Finally, we optimize material properties and use the one-dimensional model to simulate necking or bulging until the Maxwell values of stretch are reached.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"19 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140801136","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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