Homogenization of a finite plasticity model of layered structures with two slip systems

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Real World Applications Pub Date : 2025-02-08 DOI:10.1016/j.nonrwa.2025.104326

Akira Ishikawa , Karel Svadlenka

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引用次数: 0

Abstract

This paper investigates a homogenization problem for composite crystalline materials consisting of two distinct types of parallel layers with two plastic systems. In particular, one of the layers undergoes only local rotations while the other allows rotation and plastic deformation along two different slip directions. We take the

Γ

-convergence approach and derive the full homogenized energy in the case of orthogonal slip systems. We also provide additional insight into the problem with general angle between slip directions. The analysis builds upon the work of Christowiak and Kreisbeck (2017), which addresses the problem with a single slip system, and is based on a modification of the classical construction of laminate microstructures. However, several nontrivial difficulties arise due to nonconvex constraints being present in the composite energy. Our motivation is to supply a further step towards understanding real materials which show an interplay of multiple directions of slip.

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双滑移层状结构有限塑性模型的均质化

本文研究了由两种不同类型的平行层和两种塑性体系组成的复合晶体材料的均匀化问题。特别是，其中一层只经历局部旋转，而另一层允许沿两个不同的滑移方向旋转和塑性变形。我们采用Γ-convergence方法，推导出正交滑移系统的完全均匀化能量。我们还对滑移方向之间的一般角度问题提供了额外的见解。该分析建立在Christowiak和Kreisbeck（2017）的工作基础上，该工作解决了单滑移系统的问题，并基于对层压板微结构的经典构造的修改。然而，由于在复合能量中存在非凸约束，出现了一些重要的困难。我们的动机是为理解真实材料提供进一步的步骤，这些材料显示了多个滑动方向的相互作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Nonlinear Analysis-Real World Applications 数学-应用数学

CiteScore

3.80

自引率

5.00%

发文量

176

审稿时长

59 days

期刊介绍： Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems. The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.