Theory and numerics of a thermodynamically consistent framework for geometrically linear gradient plasticity
Theory and numerics of a thermodynamically consistent framework for geometrically linear gradient plasticity
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DOI：
10.1002/nme.195
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发表时间：
2001-08-30
影响因子：
2.9
通讯作者：
Steinmann, P
中科院分区：
文献类型：
--
作者：
Liebe, T;Steinmann, P
本文介绍了小应变梯度塑性理论的理论和数值计算方法。从经典的局部连续统制定，这未能产生物理意义和数值收敛的结果在本地化计算，一个gravitically动机的梯度塑性制定设想。该模型是基于一个假设的Helmholtz自由能纳入梯度的内部历史变量，屈服条件和最大耗散的假设，从而导致相关的结构。其结果是，共轭的硬化演变的驱动力被确定为准非局部拖曳应力，其中包括除了严格的本地拖曳应力基本上是一个矢量硬化通量的发散。在数值方面，除了线性动量的平衡，算法的一致性条件必须以弱形式求解。因此，关键的问题是确定的积极约束表现出塑性加载，这是解决了一个积极的集搜索算法借用凸非线性规划。此外，提出了不同的离散技术，以比较的FE性能在局部塑性与所提倡的梯度制剂硬化和软化。版权所有（C）2001约翰威利父子有限公司
The paper presents the theory and the numerics of a thermodynamically consistent formulation of gradient plasticity at small strains. Starting from the classical local continuum formulation, which fails to produce physically meaningful and numerically converging results within localization computations, a thermodynamically motivated gradient plasticity formulation is envisioned. The model is based on an assumption for the Helmholtz free energy incorporating the gradient of the internal history variable, a yield condition and the postulate of maximum dissipation resulting in an associated structure. As a result the driving force conjugated to the hardening evolution is identified as the quasi-non-local drag stress which incorporates besides the strictly local drag stress essentially the divergence of a vectorial hardening flux. At the numerical side, besides the balance of linear momentum, the algorithmic consistency condition has to be solved in weak form. Thereby, the crucial issue is the determination of the active constraints exhibiting plastic loading which is solved by an active set search algorithm borrowed from convex non-linear programming. Moreover, different discretization techniques are proposed in order to compare the FE-performance in local plasticity with the advocated gradient formulation both for hardening and softening. Copyright (C) 2001 John Wiley & Sons, Ltd.