On the relationship between the Eulerian and Lagrangian descriptions of finite rigid plasticity
On the relationship between the Eulerian and Lagrangian descriptions of finite rigid plasticity
复制标题
有限刚塑性的欧拉和拉格朗日描述之间的关系
DOI：
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发表时间：
1988
期刊：
影响因子：
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通讯作者：
P. Naghdi
中科院分区：
文献类型：
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作者：
J. Casey;P. Naghdi
本文的目的是澄清与有限塑性的拉格朗日（或参考）和欧拉（或空间）应变空间公式之间的关系有关的某些未解决的问题。为了概念简单起见，注意力仅限于硬质塑料材料。首先证明对于硬化参数为标量的本构方程，拉格朗日和欧拉描述是等价的；此外，客观应力率的选择并不重要。鉴于这些发展，结合包含位移张量的更一般（“各向异性”）硬化定律，进一步探讨了客观速率的作用。提出了一种移位张量速率本构方程的形式，其中目标速率的选择是任意的。然后证明了该理论的本构方程的结构——在欧拉和拉格朗日描述中——在目标速率的任意变换下是形式不变的。这里采取的方法与最近一些论文中采用的方法形成鲜明对比，在这些论文中，优先考虑一种或另一种特定的客观利率。
The motivation for the present paper is to clarify certain unresolved issues pertaining to the relation between the Lagrangian (or referential) and Eulerian (or spatial) strain-space formulations of finite plasticity. For conceptual simplicity, attention is confined to rigid-plastic materials. It is shown first that for constitutive equations in which the hardening parameter is a scalar, the Lagrangian and Eulerian descriptions are equivalent; and that, additionally, the choice of objective stress rate is immaterial. In the light of these developments, the role of objective rates is further explored in connection with more general (“anisotropic”) hardening laws which contain a shift tensor. A form of the constitutive equation for the rate of the shift tensor is motivated in which the choice of objective rate is arbitrary. It is then demonstrated that the structure of the constitutive equations of the theory — in both the Eulerian and Lagrangian descriptions — is form-invariant under arbitrary transformations of objective rate. The approach taken here contrasts with that adopted in a number of recent papers in which preference is given to one particular objective rate or another.