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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >A model for the evolution of laminates in finite-strain elastoplasticity
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A model for the evolution of laminates in finite-strain elastoplasticity

机译：层板的有限应变弹塑性演化模型

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We study the time evolution in elastoplasticity within the rate-independent framework of generalized standard materials. Our particular interest is the formation and the evolution of microstructure. Providing models where existence proofs are possible is a challenging task since the presence of microstructure comes along with a lack of convexity and, hence, compactness arguments cannot be applied to prove the existence of solutions. In order to overcome this problem, we will incorporate information on the microstructure into the internal variable, which is still compatible with generalized standard materials. More precisely, we shall allow for such microstructure that is given by simple or sequential laminates. We will consider a model for the evolution of these laminates and we will prove a theorem on the existence of solutions to any finite sequence of time-incremental minimization problems. In order to illustrate the mechanical consequences of the theory developed some numerical results, especially dealing with the rotation of laminates, are presented. The authors study the time evolution in elastoplasticity within the rate-independent framework of generalized standard materials. Their particular interest is the formation and the evolution of microstructure. Providing models where existence proofs are possible is a challenging task since the presence of microstructure comes along with a lack of convexity and, hence, compactness arguments cannot be applied to prove the existence of solutions. In order to overcome this problem, they will incorporate information on the microstructure into the internal variable, which is still compatible with generalized standard materials. More precisely, they hall allow for such microstructure that is given by simple or sequential laminates. The authors will consider a model for the evolution of these laminates and will prove a theorem on the existence of solutions to any finite sequence of time-incremental minimization problems. In order to illustrate the mechanical consequences of the theory developed some numerical results, especially dealing with the rotation of laminates, are presented.
机译：我们在广义标准材料的速率无关框架内研究弹塑性的时间演化。我们特别感兴趣的是微观结构的形成和演化。在可能的情况下提供存在模型的模型是一项艰巨的任务，因为微观结构的存在伴随着凸度的缺乏，因此，紧密度参数不能用于证明解的存在。为了克服这个问题，我们将有关微观结构的信息纳入内部变量中，该变量仍与通用标准材料兼容。更准确地说，我们应考虑由简单或顺序的层压板提供的这种微观结构。我们将考虑这些叠层的演化模型，并证明一个关于时间递增最小化问题的有限序列解的存在性的定理。为了说明该理论的机械结果，提出了一些数值结果，尤其是处理层压板的旋转时。作者研究了广义标准材料在与速率无关的框架内弹塑性的时间演变。他们特别感兴趣的是微观结构的形成和演化。提供可能的存在证明的模型是一项艰巨的任务，因为微观结构的存在伴随着缺乏凸度，因此，紧密度参数不能用于证明解的存在。为了克服这个问题，他们会将有关微结构的信息整合到内部变量中，该变量仍与通用标准材料兼容。更准确地说，它们允许由简单或顺序的层压板提供的这种微观结构。作者将考虑这些层压板的演化模型，并将证明关于时间递增最小化问题的任何有限序列的解的存在性的定理。为了说明该理论的机械结果，提出了一些数值结果，尤其是处理层压板的旋转时。

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