广义耗散固体热力学的变分框架--及其在扩散、损伤和塑性中的应用
A Variational Framework for the Thermomechanics of Gradient-Extended Dissipative Solids -- with Applications to Diffusion, Damage and Plasticity
摘要：
本文提出了一个通用的框架，固体经历非等温过程，在大应变的微观结构不可逆地改变。它概述了率型和增量变分原理的梯度扩展耗散材料中的完全热力耦合。它表明，这些原则产生欧拉方程基本上的宏观和微观平衡，以及能量方程。出发点是将熵和熵率作为正则参数纳入本构能量和耗散函数，它们分别取决于梯度扩展的力学状态及其速率。利用（广义）勒让德变换，可以构造出具有热力和机械驱动力的广义变分原理。在热力学方面，严格区分与熵共轭的量和与熵率共轭的量是必要的。当考虑可能的温度依赖性阈值机制时，具有机械驱动力的制剂特别合适。关于变分一致的增量，我们提出了一个更新计划，使确切的形式的内在耗散，是非常适合考虑绝热过程。结果表明，该算法具有算子分裂的结构。为了强调所提出的框架的广泛适用性，我们建立了三个模型问题的应用程序：Cahn-Hilliard扩散与温度演变，在那里我们提出了一个新的变分原理的物种通量矢量，以及梯度损伤和梯度塑性的热力学。在一个数值例子中，我们研究了交叉剪切带的形成。
英文摘要：
The paper presents a versatile framework for solids which undergo nonisothermal processes with irreversibly changing microstructure at large strains. It outlines rate-type and incremental variational principles for the full thermomechanical coupling in gradient-extended dissipative materials. It is shown that these principles yield as Euler equations essentially the macro- and micro-balances as well as the energy equation. Starting point is the incorporation of the entropy and entropy rate as canonical arguments into constitutive energy and dissipation functions, which additionally depend on the gradient-extended mechanical state and its rate, respectively. By means of (generalized) Legendre transformations, extended variational principles with thermal as well as mechanical driving forces can be constructed. On the thermal side, a rigorous distinction between the quantity conjugate to the entropy and the quantity conjugate to the entropy rate is essential here. Formulations with mechanical driving forces are especially suitable when considering possibly temperature-dependent threshold mechanisms. With regard to variationally consistent incrementations, we suggest an update scheme which renders the exact form of the intrinsic dissipation and is highly suitable when considering adiabatic processes. It is shown that this proposed numerical algorithm has the structure of an operator split. To underline the broad applicability of the proposed framework, we set up three model problems as applications: Cahn-Hilliard diffusion coupled with temperature evolution, where we propose a new variational principle in terms of the species flux vector, as well as thermomechanics of gradient damage and gradient plasticity. In a numerical example we study the formation of a cross shear band.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
