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Dissipative boundary conditions and entropic solutions in dynamical perfect plasticity
Journal de Mathématiques Pures et Appliquées ( IF 2.3 ) Pub Date : 2021-02-17 , DOI: 10.1016/j.matpur.2021.02.001
Jean-François Babadjian , Vito Crismale

We prove the well–posedness of a dynamical perfect plasticity model under general assumptions on the stress constraint set and on the reference configuration. The problem is studied by combining both calculus of variations and hyperbolic methods. The hyperbolic point of view enables one to derive a class of dissipative boundary conditions, somehow intermediate between homogeneous Dirichlet and Neumann ones. By using variational methods, we show the existence and uniqueness of solutions. Then we establish the equivalence between the original variational solutions and generalized entropic–dissipative ones, derived from a weak hyperbolic formulation for initial–boundary value Friedrichs' systems with convex constraints.



中文翻译:

动态完美可塑性的耗散边界条件和熵解

我们在应力约束集和参考构型的一般假设下证明了动力学完美可塑性模型的适定性。通过结合变分演算和双曲线方法来研究该问题。双曲观点使人们能够推导一类耗散边界条件,这些条件介于均质Dirichlet和Neumann条件之间。通过使用变分方法,我们显示了解的存在性和唯一性。然后,我们建立了原始变分解与广义熵-耗散解之间的等价关系,后者是针对凸约束的初值-边界值Friedrichs系统的弱双曲公式得出的。

更新日期:2021-03-02
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