The stability of a current carrying beam in an external magnetic field is studied in this paper. The beam is rested on periodic supports and is modelled as a Euler-Bernoulli elastic beam. Based on the linearized stability equation and propagator transfer matrix approach for a multi-span finite length beam the stability equation and solutions of the several boundary value problems are obtained. While the Floquet-Bloch theory is widely used in dynamic problem of phononic and photonic structures conditions, its application to the solution of infinite length beam static stability problem is novel. The stability values of the periodic infinite beam model are in very good agreement with the one of the finite length multi-span beams.
{"title":"STABILITY OF A MULTI-SPAN CURRENT CARRYING BEAM RESTING ON PERIODIC SUPPORTS AND EXPOSED TO AN EXTERNAL MAGNETIC FIELD","authors":"Ara Avetisyan, Karen Ghazaryan, Pier Marzocca","doi":"10.1115/1.4064821","DOIUrl":"https://doi.org/10.1115/1.4064821","url":null,"abstract":"\u0000 The stability of a current carrying beam in an external magnetic field is studied in this paper. The beam is rested on periodic supports and is modelled as a Euler-Bernoulli elastic beam. Based on the linearized stability equation and propagator transfer matrix approach for a multi-span finite length beam the stability equation and solutions of the several boundary value problems are obtained. While the Floquet-Bloch theory is widely used in dynamic problem of phononic and photonic structures conditions, its application to the solution of infinite length beam static stability problem is novel. The stability values of the periodic infinite beam model are in very good agreement with the one of the finite length multi-span beams.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"57 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140440413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Asesh Patra, Atul Kumar Sharma, D. Joglekar, M. Joglekar
This study focuses on investigating hard magnetic soft materials, characterized by magneto-active polymers containing magnetically polarized particles as fillers. The research utilizes the Gent model of hyperelasticity to analyze the propagation of Lamb waves in a magnetically induced deformed compressible plate. In this investigation we explore both finite deformations and incremental wave propagation in nonlinear hard-magnetic soft materials. The main objective is to formulate the elastic tensor and relevant wave equations within the framework of Lagrangian space. To assess the dispersion characteristics of the guided wave, the study introduces and discusses an extension of the Semi Analytical Finite Element (SAFE) method. Using this numerical approach, the research further examines the effects of magnetic flux densities and its orientation with respect to wave propagation direction on the dispersion characteristics of the fundamental Lamb modes. The study starts by examining the limiting case of the neo-Hookean material model to explain such inherent dependencies. These dependencies are then further emphasized by including the strain-stiffening effect that the Gent material model describes. The research findings reveal the presence of a threshold applied magnetic flux, beyond which the Gent-type material may undergo a snap-through instability, resulting in changes in the dispersion characteristics of the fundamental symmetric Lamb mode.
{"title":"Propagation of the fundamental Lamb modes in strain stiffened hard-magnetic soft plates","authors":"Asesh Patra, Atul Kumar Sharma, D. Joglekar, M. Joglekar","doi":"10.1115/1.4064789","DOIUrl":"https://doi.org/10.1115/1.4064789","url":null,"abstract":"\u0000 This study focuses on investigating hard magnetic soft materials, characterized by magneto-active polymers containing magnetically polarized particles as fillers. The research utilizes the Gent model of hyperelasticity to analyze the propagation of Lamb waves in a magnetically induced deformed compressible plate. In this investigation we explore both finite deformations and incremental wave propagation in nonlinear hard-magnetic soft materials. The main objective is to formulate the elastic tensor and relevant wave equations within the framework of Lagrangian space. To assess the dispersion characteristics of the guided wave, the study introduces and discusses an extension of the Semi Analytical Finite Element (SAFE) method. Using this numerical approach, the research further examines the effects of magnetic flux densities and its orientation with respect to wave propagation direction on the dispersion characteristics of the fundamental Lamb modes. The study starts by examining the limiting case of the neo-Hookean material model to explain such inherent dependencies. These dependencies are then further emphasized by including the strain-stiffening effect that the Gent material model describes. The research findings reveal the presence of a threshold applied magnetic flux, beyond which the Gent-type material may undergo a snap-through instability, resulting in changes in the dispersion characteristics of the fundamental symmetric Lamb mode.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"90 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140451350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jin-ming Zhang, Liangliang Zhang, Xiang Mu, Yang Gao, Ernian Pan
This study employs the Lur'e operator method to derive generalized solutions for orthorhombic quasicrystals, incorporating anisotropy factors as a constraint. The obtained solutions encompass the Lekhnitskii-Hu-Nowacki and Elliott-Lodge formulations. Consequently, our analysis of the fundamental solution within infinite space offers a comprehensive characterization of quasicrystal anisotropy, employing both analytical and numerical approaches. It is noteworthy that the analytical solutions for orthorhombic quasicrystals can be simplified to accommodate hexagonal quasicrystals or conventional orthorhombic crystals, enhancing their versatility for broader engineering applications.
{"title":"Three-dimensional general solutions of orthorhombic quasicrystals with constraints","authors":"Jin-ming Zhang, Liangliang Zhang, Xiang Mu, Yang Gao, Ernian Pan","doi":"10.1115/1.4064788","DOIUrl":"https://doi.org/10.1115/1.4064788","url":null,"abstract":"\u0000 This study employs the Lur'e operator method to derive generalized solutions for orthorhombic quasicrystals, incorporating anisotropy factors as a constraint. The obtained solutions encompass the Lekhnitskii-Hu-Nowacki and Elliott-Lodge formulations. Consequently, our analysis of the fundamental solution within infinite space offers a comprehensive characterization of quasicrystal anisotropy, employing both analytical and numerical approaches. It is noteworthy that the analytical solutions for orthorhombic quasicrystals can be simplified to accommodate hexagonal quasicrystals or conventional orthorhombic crystals, enhancing their versatility for broader engineering applications.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"2 10","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139958181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents an elastic-gap free isotropic higher-order strain gradient plasticity theory that effectively captures dissipation associated to plastic strain gradients. Unlike conventional methods that divide the higher-order stress, this theory focuses on dividing the plastic strain gradient into energetic and dissipative components. The moment stress that arises from minimizing a dissipating potential demonstrates a nonlinear evolution over time, resembling the Armstrong-Frederick nonlinear kinematic hardening rule in classical plasticity. The thermodynamically consistent framework establishes additional dissipation in the dissipation inequality. The energetic moment stress saturates as the effective plastic strain increases during plastic flow. In contrast to the Gurtin-type non-incremental model, the proposed model smoothly captures the apparent strengthening at saturation without causing a stress jump. A passivated shear layer is analytically assessed to demonstrate that the proposed theory exhibits the same amount of dissipation as the existing Gurtin-type model when they show similar shear responses at saturation. It is also shown that the plastic flow remains continuous under non-proportional loading conditions using an intermediately passivated shear layer problem. Finally, the proposed theory is validated against a recent experiment involving combined bending torsion of an L-shaped beam using a 3D finite element solution. Overall, the proposed model provides an alternative approach to evaluating the size effect within the non-incremental isotropic strain gradient plasticity theory without introducing any stress jump.
本文提出了一种无弹性间隙各向同性高阶应变梯度塑性理论，能有效捕捉与塑性应变梯度相关的耗散。与划分高阶应力的传统方法不同，该理论侧重于将塑性应变梯度划分为能量和耗散两部分。耗散势最小化产生的力矩应力随时间呈非线性演变，类似于经典塑性中的阿姆斯特朗-弗雷德里克非线性运动硬化规则。热力学一致框架在耗散不等式中建立了额外的耗散。在塑性流动过程中，随着有效塑性应变的增加，能矩应力达到饱和。与古尔丁型非递增模型相比，所提出的模型能平稳地捕捉到饱和时的明显强化，而不会导致应力跃变。通过对钝化剪切层进行分析评估，证明当两者在饱和时表现出相似的剪切响应时，所提出的理论与现有的 Gurtin 型模型表现出相同的耗散量。研究还表明，利用中间钝化剪切层问题，塑性流动在非比例加载条件下保持连续。最后，利用三维有限元求解法，对最近涉及 L 形梁组合弯曲扭转的实验验证了所提出的理论。总之，所提出的模型为评估非递增各向同性应变梯度塑性理论中的尺寸效应提供了另一种方法，而不会引入任何应力跳跃。
{"title":"Elastic-gap free formulation in strain gradient plasticity theory","authors":"Anjan Mukherjee, Biswanath Banerjee","doi":"10.1115/1.4064790","DOIUrl":"https://doi.org/10.1115/1.4064790","url":null,"abstract":"\u0000 This paper presents an elastic-gap free isotropic higher-order strain gradient plasticity theory that effectively captures dissipation associated to plastic strain gradients. Unlike conventional methods that divide the higher-order stress, this theory focuses on dividing the plastic strain gradient into energetic and dissipative components. The moment stress that arises from minimizing a dissipating potential demonstrates a nonlinear evolution over time, resembling the Armstrong-Frederick nonlinear kinematic hardening rule in classical plasticity. The thermodynamically consistent framework establishes additional dissipation in the dissipation inequality. The energetic moment stress saturates as the effective plastic strain increases during plastic flow. In contrast to the Gurtin-type non-incremental model, the proposed model smoothly captures the apparent strengthening at saturation without causing a stress jump. A passivated shear layer is analytically assessed to demonstrate that the proposed theory exhibits the same amount of dissipation as the existing Gurtin-type model when they show similar shear responses at saturation. It is also shown that the plastic flow remains continuous under non-proportional loading conditions using an intermediately passivated shear layer problem. Finally, the proposed theory is validated against a recent experiment involving combined bending torsion of an L-shaped beam using a 3D finite element solution. Overall, the proposed model provides an alternative approach to evaluating the size effect within the non-incremental isotropic strain gradient plasticity theory without introducing any stress jump.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"14 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139958666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The post-buckling behavior of a beam that is subjected to lateral constraints is of relevance to a range of medical and engineering applications, such as endoscopic examination of internal organs, the insertion of a guidewire into an artery in stent procedures, root growth, deep drilling, and more. In this paper we address a disconnect between the existing literature and the reality of these systems, in which the lateral constraints are flexible and experience nonlinear deformations. As a step towards bridging this gap, we consider a beam undergoing planar deformations that is laterally constrained by a non-linear springy wall, i.e. a wall that is laterally pushed by the beam against a non-linear spring. Based on a simplified mathematical model, we obtain closed form analytical solutions, which provide valuable insights and intuition. For example, we show that important features of the behavior, such as transition from point contact to line contact and switching to the next mode, are dictated solely by a non-dimensional force, regardless of all other parameters of the system, and that the full description of the behavior is possible by means of two non-dimensional quantities that describe the relative stiffness of the nonlinear spring compared to that of the beam. The results also highlight the fundamental differences between the behavior with a stiffening spring or with a softening spring, such as the number of attainable modes and the monotonicity of the overall force-displacement relation. These results are then validated by experiments.
{"title":"The post-buckling behavior of a beam constrained by nonlinear springy walls","authors":"Nitzan Judah, Sefi Givli","doi":"10.1115/1.4064684","DOIUrl":"https://doi.org/10.1115/1.4064684","url":null,"abstract":"\u0000 The post-buckling behavior of a beam that is subjected to lateral constraints is of relevance to a range of medical and engineering applications, such as endoscopic examination of internal organs, the insertion of a guidewire into an artery in stent procedures, root growth, deep drilling, and more. In this paper we address a disconnect between the existing literature and the reality of these systems, in which the lateral constraints are flexible and experience nonlinear deformations. As a step towards bridging this gap, we consider a beam undergoing planar deformations that is laterally constrained by a non-linear springy wall, i.e. a wall that is laterally pushed by the beam against a non-linear spring. Based on a simplified mathematical model, we obtain closed form analytical solutions, which provide valuable insights and intuition. For example, we show that important features of the behavior, such as transition from point contact to line contact and switching to the next mode, are dictated solely by a non-dimensional force, regardless of all other parameters of the system, and that the full description of the behavior is possible by means of two non-dimensional quantities that describe the relative stiffness of the nonlinear spring compared to that of the beam. The results also highlight the fundamental differences between the behavior with a stiffening spring or with a softening spring, such as the number of attainable modes and the monotonicity of the overall force-displacement relation. These results are then validated by experiments.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"16 17","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139795884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The post-buckling behavior of a beam that is subjected to lateral constraints is of relevance to a range of medical and engineering applications, such as endoscopic examination of internal organs, the insertion of a guidewire into an artery in stent procedures, root growth, deep drilling, and more. In this paper we address a disconnect between the existing literature and the reality of these systems, in which the lateral constraints are flexible and experience nonlinear deformations. As a step towards bridging this gap, we consider a beam undergoing planar deformations that is laterally constrained by a non-linear springy wall, i.e. a wall that is laterally pushed by the beam against a non-linear spring. Based on a simplified mathematical model, we obtain closed form analytical solutions, which provide valuable insights and intuition. For example, we show that important features of the behavior, such as transition from point contact to line contact and switching to the next mode, are dictated solely by a non-dimensional force, regardless of all other parameters of the system, and that the full description of the behavior is possible by means of two non-dimensional quantities that describe the relative stiffness of the nonlinear spring compared to that of the beam. The results also highlight the fundamental differences between the behavior with a stiffening spring or with a softening spring, such as the number of attainable modes and the monotonicity of the overall force-displacement relation. These results are then validated by experiments.
{"title":"The post-buckling behavior of a beam constrained by nonlinear springy walls","authors":"Nitzan Judah, Sefi Givli","doi":"10.1115/1.4064684","DOIUrl":"https://doi.org/10.1115/1.4064684","url":null,"abstract":"\u0000 The post-buckling behavior of a beam that is subjected to lateral constraints is of relevance to a range of medical and engineering applications, such as endoscopic examination of internal organs, the insertion of a guidewire into an artery in stent procedures, root growth, deep drilling, and more. In this paper we address a disconnect between the existing literature and the reality of these systems, in which the lateral constraints are flexible and experience nonlinear deformations. As a step towards bridging this gap, we consider a beam undergoing planar deformations that is laterally constrained by a non-linear springy wall, i.e. a wall that is laterally pushed by the beam against a non-linear spring. Based on a simplified mathematical model, we obtain closed form analytical solutions, which provide valuable insights and intuition. For example, we show that important features of the behavior, such as transition from point contact to line contact and switching to the next mode, are dictated solely by a non-dimensional force, regardless of all other parameters of the system, and that the full description of the behavior is possible by means of two non-dimensional quantities that describe the relative stiffness of the nonlinear spring compared to that of the beam. The results also highlight the fundamental differences between the behavior with a stiffening spring or with a softening spring, such as the number of attainable modes and the monotonicity of the overall force-displacement relation. These results are then validated by experiments.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"15 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139855729","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The requirement of a non-negative dissipation rate for all possible deformation histories is generally imposed on plastic constitutive relations. This is a constraint analogous to the Coleman-Noll [1] postulate that the Clausius-Duhem inequality needs to be satisfied for all possible deformation histories. The physical basis for the Clausius-Duhem inequality is as a statistical limit for a large number of discrete events for a long time and is not a fundamental physical requirement for small systems for a short time. The relation between the requirement of a non-negative dissipation rate and the Clausius-Duhem inequality is considered. The consequences of imposing a non-negative dissipation rate for all possible deformation histories are illustrated for: (i) a single crystal plasticity framework that accounts for elastic lattice curvature changes as well as elastic lattice straining; and (ii) for discrete defect theories of plasticity, with attention specifically on discrete dislocation plasticity for crystalline solids and discrete shear transformation zone (STZ) plasticity for amorphous solids. Possible less restrictive conditions on the evolution of dissipation in plasticity formulations are considered as are implications for stability. The focus is on open questions and issues.
塑性构造关系通常要求所有可能的变形历史的耗散率均为非负。这一约束条件类似于 Coleman-Noll [1] 假设，即克劳修斯-杜恒不等式需要满足所有可能的变形历史。克劳修斯-杜恒不等式的物理基础是长时间大量离散事件的统计极限，而不是短时间小系统的基本物理要求。我们考虑了非负耗散率要求与克劳修斯-杜恒不等式之间的关系。对所有可能的变形历史施加非负耗散率的后果进行了说明：(i) 考虑到弹性晶格曲率变化和弹性晶格应变的单晶塑性框架；以及 (ii) 离散缺陷塑性理论，特别关注晶体固体的离散位错塑性和非晶体固体的离散剪切变换区（STZ）塑性。研究还考虑了塑性配方中耗散演化的可能限制性较低的条件，以及对稳定性的影响。重点是开放性问题和议题。
{"title":"A Perspective on Plasticity, Dissipation and the 2nd Law of Thermodynamics","authors":"Alan Needleman","doi":"10.1115/1.4064700","DOIUrl":"https://doi.org/10.1115/1.4064700","url":null,"abstract":"\u0000 The requirement of a non-negative dissipation rate for all possible deformation histories is generally imposed on plastic constitutive relations. This is a constraint analogous to the Coleman-Noll [1] postulate that the Clausius-Duhem inequality needs to be satisfied for all possible deformation histories. The physical basis for the Clausius-Duhem inequality is as a statistical limit for a large number of discrete events for a long time and is not a fundamental physical requirement for small systems for a short time. The relation between the requirement of a non-negative dissipation rate and the Clausius-Duhem inequality is considered. The consequences of imposing a non-negative dissipation rate for all possible deformation histories are illustrated for: (i) a single crystal plasticity framework that accounts for elastic lattice curvature changes as well as elastic lattice straining; and (ii) for discrete defect theories of plasticity, with attention specifically on discrete dislocation plasticity for crystalline solids and discrete shear transformation zone (STZ) plasticity for amorphous solids. Possible less restrictive conditions on the evolution of dissipation in plasticity formulations are considered as are implications for stability. The focus is on open questions and issues.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"126 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139870934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The requirement of a non-negative dissipation rate for all possible deformation histories is generally imposed on plastic constitutive relations. This is a constraint analogous to the Coleman-Noll [1] postulate that the Clausius-Duhem inequality needs to be satisfied for all possible deformation histories. The physical basis for the Clausius-Duhem inequality is as a statistical limit for a large number of discrete events for a long time and is not a fundamental physical requirement for small systems for a short time. The relation between the requirement of a non-negative dissipation rate and the Clausius-Duhem inequality is considered. The consequences of imposing a non-negative dissipation rate for all possible deformation histories are illustrated for: (i) a single crystal plasticity framework that accounts for elastic lattice curvature changes as well as elastic lattice straining; and (ii) for discrete defect theories of plasticity, with attention specifically on discrete dislocation plasticity for crystalline solids and discrete shear transformation zone (STZ) plasticity for amorphous solids. Possible less restrictive conditions on the evolution of dissipation in plasticity formulations are considered as are implications for stability. The focus is on open questions and issues.
塑性构造关系通常要求所有可能的变形历史的耗散率均为非负。这一约束条件类似于 Coleman-Noll [1] 假设，即克劳修斯-杜恒不等式需要满足所有可能的变形历史。克劳修斯-杜恒不等式的物理基础是长时间大量离散事件的统计极限，而不是短时间小系统的基本物理要求。我们考虑了非负耗散率要求与克劳修斯-杜恒不等式之间的关系。对所有可能的变形历史施加非负耗散率的后果进行了说明：(i) 考虑到弹性晶格曲率变化和弹性晶格应变的单晶塑性框架；以及 (ii) 离散缺陷塑性理论，特别关注晶体固体的离散位错塑性和非晶体固体的离散剪切变换区（STZ）塑性。研究还考虑了塑性配方中耗散演化的可能限制性较低的条件，以及对稳定性的影响。重点是开放性问题和议题。
{"title":"A Perspective on Plasticity, Dissipation and the 2nd Law of Thermodynamics","authors":"Alan Needleman","doi":"10.1115/1.4064700","DOIUrl":"https://doi.org/10.1115/1.4064700","url":null,"abstract":"\u0000 The requirement of a non-negative dissipation rate for all possible deformation histories is generally imposed on plastic constitutive relations. This is a constraint analogous to the Coleman-Noll [1] postulate that the Clausius-Duhem inequality needs to be satisfied for all possible deformation histories. The physical basis for the Clausius-Duhem inequality is as a statistical limit for a large number of discrete events for a long time and is not a fundamental physical requirement for small systems for a short time. The relation between the requirement of a non-negative dissipation rate and the Clausius-Duhem inequality is considered. The consequences of imposing a non-negative dissipation rate for all possible deformation histories are illustrated for: (i) a single crystal plasticity framework that accounts for elastic lattice curvature changes as well as elastic lattice straining; and (ii) for discrete defect theories of plasticity, with attention specifically on discrete dislocation plasticity for crystalline solids and discrete shear transformation zone (STZ) plasticity for amorphous solids. Possible less restrictive conditions on the evolution of dissipation in plasticity formulations are considered as are implications for stability. The focus is on open questions and issues.","PeriodicalId":508156,"journal":{"name":"Journal of Applied Mechanics","volume":"128 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139810680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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