论文标题
混合边界条件是动态完美塑性中耗散边界条件的极限
Mixed boundary conditions as limits of dissipative boundary conditions in dynamic perfect plasticity
论文作者
论文摘要
本文介绍了完美可塑性的动态模型的良好姿势，并具有混合边界条件，用于一般封闭和凸弹性集。证明依赖于对[7]中获得的松弛耗散边界条件的完美可塑性模型解决方案的渐近分析。主要问题之一是扩展了应力和塑料菌株之间的理论二元性配对，以及对不一定有界限的更一般环境的凸性不等式。完整的答案是在纯的Dirichlet和纯净的Neumann案件中给出的。对于一般的混合边界条件，在弹性集和参考配置的其他几何假设下，在尺寸$ 2 $和3 $中给出了部分答案。
This paper addresses the well posedness of a dynamical model of perfect plasticity with mixed boundary conditions for general closed and convex elasticity sets. The proof relies on an asymptotic analysis of the solution of a perfect plasticity model with relaxed dissipative boundary conditions obtained in [7]. One of the main issues consists in extending the measure theoretic duality pairing between stresses and plastic strains, as well as a convexity inequality to a more general context where deviatoric stresses are not necessarily bounded. Complete answers are given in the pure Dirichlet and pure Neumann cases. For general mixed boundary conditions, partial answers are given in dimension $2$ and $3$ under additional geometric hypothesis on the elasticity set and the reference configuration.
