Abstract This paper deals with continuous description of elasto-plastic materials with lattice defects such as dislocations and disclinations, and grain boundaries. The behaviour of crystalline solids containing defects is described by non-local fields that are smooth over an interatomic length scale and at times of micro-seconds. The dislocation and disclination densities are appropriate measures of incompatibilities of the plastic distortion and of the plastic connection relative to plastic distortion, respectively. The grain boundaries will be simulated in terms of an array of disclination dipoles. The heterogeneous initial disclinations are a source of dislocations. These lattice defects, stress, strain and the displacement vector will be provided by solving initial and boundary value problems in elasto-plastic bodies, which involve dissipative evolution equations for plastic distortion and disclination tensor. The numerical procedure and corresponding algorithms to solve the variational formulation of the initial and boundary value problems are provided. The results of numerical simulations are analyzed and a number of graphs illustrate the elasto-plastic behaviour of the sheet when a shear stress is applied on one of its edge.

中文翻译：

---

具有显微结构缺陷的晶体材料中基于向错的晶界模型

摘要 本文涉及具有位错和向错等晶格缺陷和晶界的弹塑性材料的连续描述。包含缺陷的结晶固体的行为由在原子间长度尺度和微秒时间平滑的非局部场描述。位错和向错密度分别是塑性变形和塑性连接相对于塑性变形的不相容性的适当量度。晶界将根据向错偶极子阵列进行模拟。异质初始向错是位错的来源。这些晶格缺陷、应力、应变和位移矢量将通过求解弹塑性体中的初值和边界值问题来提供，其中涉及塑性变形和向错张量的耗散演化方程。给出了求解初值和边值问题的变分公式的数值程序和相应的算法。对数值模拟的结果进行了分析，许多图表说明了当剪切应力施加在其边缘之一时，板的弹塑性行为。