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A new energy-momentum time integration scheme for non-linear thermo-mechanics

机译：非线性热电机的新能量动力时间集成方案

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The aim of this paper is the design a new one-step implicit and thermodynamically consistent Energy-Momentum (EM) preserving time integration scheme for the simulation of thermo-elastic processes undergoing large deformations and temperature fields. Following Bonet et al. (2020), we consider well-posed constitutive models for the entire range of deformations and temperature. In that regard, the consideration of polyconvexity inspired constitutive models and a new tensor cross product algebra are shown to be crucial in order to derive the so-called discrete derivatives, fundamental for the construction of the algorithmic derived variables, namely the second Piola-Kirchoff stress tensor and the entropy (or the absolute temperature). The proposed scheme inherits the advantages of the EM scheme recently published by Franke et al. (2018), whilst resulting in a simpler scheme from the implementation standpoint. A series of numerical examples will be presented in order to demonstrate the robustness and applicability of the new EM scheme. Although the examples presented will make use of a temperature based version of the EM scheme (using the Helmholtz free energy as the thermodynamical potential and the temperature as the thermodynamical state variable), we also include in an Appendix an entropy-based analogue EM scheme (using the internal energy as the thermodynamical potential and the entropy as the thermodynamical state variable). (C) 2020 Elsevier B.V. All rights reserved.
机译：本文的目的是设计一种新的一步隐式和热力学一致的能量动力（EM）保留时间集成方案，用于模拟经历大变形和温度场的热弹性过程。以下Bonet等人。 （2020），我们考虑了整个变形和温度范围的构成型模型。在这方面，考虑到的聚变性激发了本构模型和新的张量横向产品代数被认为是至关重要的，以获得所谓的离散衍生物，算法衍生变量的构建的基础，即第二型Piola-Kirchoff压力张量和熵（或绝对温度）。拟议的计划继承了最近发表的EM计划的优势。 （2018），同时从实现的角度出现了更简单的方案。将提出一系列数值示例，以证明新EM计划的稳健性和适用性。尽管所提出的示例将利用基于温度的EM方案版本（使用Helmholtz自由能作为热力学电位和温度作为热力学状态变量），但我们还包括附录基于熵的类似物EM方案（使用内部能量作为热力学电位和熵作为热力学状态变量）。 （c）2020 Elsevier B.v.保留所有权利。

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