The article focuses on non-uniqueness, bifurcation and stability conditions in elasto-viscoplastic boundary value problems when inertia terms are neglected. Analytical and numerical studies are presented to investigate the capability of an elasto-viscoplastic model to regularize the behavior in the occurrence of strain localization with respect to number of strain bands formed and mesh dependency. It is found that elasto-viscoplasticity in a Cauchy medium neither restores the uniqueness of the solution nor provides mesh independent results. A high value of the viscosity parameter can sometimes provide results that are mesh independent, up to a certain limit strain, as it actually modifies the response of the constitutive law by an ad-hoc increase of its hardening branch. On the contrary, coupling elasto-viscoplasticity with a second gradient model that introduces an internal length parameter reproduces realistically the rate dependent behavior and regularizes the results.

本文重点研究了忽略惯性项时弹粘塑性边值问题中的非唯一性、分岔和稳定性条件。提出了分析和数值研究，以研究弹粘塑性模型的能力，以根据形成的应变带数量和网格依赖性来规范应变局部化发生中的行为。发现柯西介质中的弹粘塑性既不能恢复解的唯一性，也不能提供与网格无关的结果。粘度参数的高值有时可以提供与网格无关的结果，直至达到一定的极限应变，因为它实际上通过特别增加其硬化分支来修改本构定律的响应。相反，