Symmetry-preserving return mapping algorithms and incrementally extremal paths: A unification of concepts
Symmetry-preserving return mapping algorithms and incrementally extremal paths: A unification of concepts
复制标题
保持对称的返回映射算法和增量极值路径：概念的统一
DOI：
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发表时间：
1989
期刊：
影响因子：
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通讯作者：
J. B. Martin
中科院分区：
文献类型：
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作者：
M. Ortiz;J. B. Martin
在这项工作中，我们试图描述弹塑性应力更新算法保持材料响应固有对称性的条件。从数值的角度来看，目的是确定应力更新算法在什么条件下应用于服从正态分布的材料时产生对称一致的切线。对于理想塑性固体，我们证明了只有全隐式或最近点返回映射算法是保持对称性的。对于硬化塑性，除非对本构方程施加适当的限制，否则通常不能保持对称性。我们证明，这些限制相当于存在一个伪内能函数，它作为塑性流动方向和硬化模数的联合势。鉴于基于增量极值路径的完整方法也产生具有潜在结构的更新规则，因此在对称切线中，我们解决了这两种方法之间是否存在任何联系的问题。我们证明了完整方法和全隐式算法确实是可以对应的。
In this work we seek to characterize the conditions under which an elastic–plastic stress update algorithm preserves the symmetries inherent to the material response. From a numerical standpoint, the aim is to determine under what conditions a stress update algorithm produces symmetric consistent tangents when applied to materials obeying normality. For the ideally plastic solid we show that only the fully implicit or closest point return mapping algorithm is symmetry preserving. For hardening plasticity, symmetry cannot be preserved in general unless suitable restrictions are imposed on the constitutive equations. We show that these restrictions amount to the existence of a pseudo-internal energy function acting as a joint potential for both the direction of plastic flow and the hardening moduli. In view of the fact that holonomic methods based on incrementally extremal paths also result in update rules possessing a potential structure and, hence, in symmetric tangents, we address the question of whether any connections exist between the two approaches. We show that holonomic methods and the fully implicit algorithm may indeed be brought into correspondence.