Sadik Souhayl, Yavari Arash
School of Civil and Environmental Engineering , Georgia Institute of Technology , Atlanta, GA 30332, USA.
School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA; The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA.
Proc Math Phys Eng Sci. 2016 Nov;472(2195):20160659. doi: 10.1098/rspa.2016.0659.
In this paper, we are concerned with finding exact solutions for the stress fields of nonlinear solids with non-symmetric distributions of defects (or more generally finite eigenstrains) that are small perturbations of symmetric distributions of defects with known exact solutions. In the language of geometric mechanics, this corresponds to finding a deformation that is a result of a perturbation of the metric of the Riemannian material manifold. We present a general framework that can be used for a systematic analysis of this class of anelasticity problems. This geometric formulation can be thought of as a material analogue of the classical theory in nonlinear elasticity. We use the present small-on-large anelasticity theory to find exact solutions for the stress fields of some non-symmetric distributions of screw dislocations in incompressible isotropic solids.
在本文中，我们关注的是寻找具有缺陷非对称分布（或更一般地，有限本征应变）的非线性固体应力场的精确解，这些缺陷分布是具有已知精确解的对称缺陷分布的小扰动。用几何力学的语言来说，这相当于找到一种变形，它是黎曼材料流形度量扰动的结果。我们提出了一个通用框架，可用于对此类滞弹性问题进行系统分析。这种几何公式可以被认为是非线性弹性中经典理论的材料类似物。我们使用当前的小对大滞弹性理论来寻找不可压缩各向同性固体中一些螺旋位错非对称分布的应力场精确解。
