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Variationally consistent modeling of finite strain plasticity theory with non-linear kinematic hardening

机译：运动非线性有限应变塑性理论的变分一致建模

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摘要

Variational constitutive updates provide a physically and mathematically sound framework for the numerical implementation of material models. In contrast to conventional schemes such as the return-mapping algorithm, they are directly and naturally based on the underlying variational principle. Hence, the resulting numerical scheme inherits all properties of that principle. In the present paper, focus is on a certain class of those variational methods which relies on energy minimization. Consequently, the algorithmic formulation is governed by energy minimization as well. Accordingly, standard optimization algorithms can be applied to solve the numerical problem. A further advantage compared to conventional approaches is the existence of a natural distance (semi metric) induced by the minimization principle. Such a distance is the foundation for error estimation and as a result, for adaptive finite elements methods. Though variational constitutive updates are relatively well developed for so-called standard dissipative solids, i.e., solids characterized by the normality rule, the more general case, i.e., generalized standard materials, is far from being understood. More precisely, (Int. J. Sol. Struct. 2009,46:1676-1684) represents the first step towards this goal. In the present paper, a variational constitutive update suitable for a class of nonlinear kinematic hardening models at finite strains is presented. Two different prototypes of Armstrong-Frederick-type are re-formulated into the aforementioned variationally consistent framework. Numerical tests demonstrate the consistency of the resulting implementation.
机译：变体本构更新为材料模型的数值实现提供了物理和数学上合理的框架。与诸如返回映射算法之类的常规方案相比，它们直接且自然地基于潜在的变分原理。因此，所得的数值方案继承了该原理的所有特性。在本文中，重点是依赖于能量最小化的一类这类变分方法。因此，算法公式也受能量最小化的支配。因此，可以使用标准的优化算法来解决数值问题。与常规方法相比，另一个优点是存在由最小化原理引起的自然距离（半度量）。这样的距离是误差估计的基础，因此是自适应有限元方法的基础。尽管对于所谓的标准耗散固体（即以正态性规则为特征的固体）开发了相对较好的变体本构更新，但更普遍的情况（即广义的标准材料）尚无法理解。更准确地说，（Int。J. Sol。Struct。2009,46：1676-1684）代表了朝着这一目标迈出的第一步。在本文中，提出了适用于一类在有限应变下的非线性运动硬化模型的变分本构更新。将两个不同的Armstrong-Frederick型原型重构为上述变化一致的框架。数值测试证明了所得实现的一致性。

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