Abstract

We study simple one-dimensional waves (Riemann waves) in an incompressible anisotropic elastoplastic medium with hardening. The motion is parallel to the planes of constant phase. We show that there exist two types of such waves: fast and slow waves, whose velocities are different everywhere except for some points in the plane of stress components. The medium is assumed to be nonlinear and defined by its elastic properties as well as by conditions for the formation of plastic deformations. We find the velocities of the characteristics that carry the Riemann waves, and analyze the evolution of the Riemann waves and the overturning conditions for these waves.

中文翻译：

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具有硬化的不可压缩各向异性弹塑性介质中的简单一维波

摘要

我们在具有硬化性的不可压缩各向异性弹塑性介质中研究简单的一维波（黎曼波）。该运动平行于恒定相位的平面。我们显示出这种波存在两种类型：快波和慢波，除了应力分量平面中的某些点外，其他所有位置的速度都不同。假定该介质是非线性的，并由其弹性特性以及塑性变形形成的条件来定义。我们找到了携带黎曼波的特征的速度，并分析了黎曼波的演变以及这些波的倾覆条件。