Analyticity of solutions to thermo-elastic-plastic flow problem with microtemperatures,ZAMM - Journal of Applied Mathematics and Mechanics

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Analyticity of solutions to thermo-elastic-plastic flow problem with microtemperatures
ZAMM - Journal of Applied Mathematics and Mechanics ( IF 2.3 ) Pub Date : 2021-06-15 , DOI: 10.1002/zamm.202000346
Moncef Aouadi ₁ , Mohamed Ben Bettaieb ₂ , Farid Abed‐Meraim ₂

Affiliation

In this paper, we study some qualitative and numerical properties of new equations including the coupled effects of thermal elastic-plastic theory with microtemperatures. We establish the necessary and sufficient conditions to guarantee that the model dissipates energy. The one-dimensional case, which corresponds to isotropic hardening problem, is chosen in order to present some qualitative and numerical properties. With the help of the semigroup theory of linear operators, we prove the well-posedness of the one-dimensional problem corresponding to plastic flow. Then, we show that the associated

C_{0} -

semigroup is not analytical in general, except for a special case. The exponential stability of the solutions is kept in all cases. Finally, a numerical tool, based on the finite element method, is developed to validate the proposed model and to show its capability. Particular attention is paid to the consideration of the elastoplastic behavior in the development of this tool.

中文翻译：

微温热弹塑性流动问题解的解析性

在本文中，我们研究了新方程的一些定性和数值性质，包括热弹塑性理论与微观温度的耦合效应。我们建立了保证模型耗散能量的充要条件。选择对应于各向同性硬化问题的一维情况是为了呈现一些定性和数值特性。借助线性算子的半群理论，我们证明了塑性流动对应的一维问题的适定性。然后，我们证明关联的