Abstract The commutative-symmetrical elastic-plastic stretch-tensor product and the multiplicative Bilby-Kroner-Lee decompositions of a deformation gradient are compared to one another in particular with respect to the corresponding time derivatives and tensor rates. It turns out that these multiplicative deformation-tensor models differ with respect to the elastic response just for a Lagrangean point of view and coincide for an Eulerian perspective. The uniqueness of the constitutive equations requires symmetric plastic-flow rules for commutative-symmetrical elastic-plastic stretch-tensor products and non-symmetric plastic-flow rules for multiplicative Bilby-Kroner-Lee formulations. Further, the author discusses whether a plastic rotation tensor—implied from a non-symmetric plastic-flow rule—is appropriate for a proper finite-plasticity formulation of polycrystalline metals and whether at all a plastic rotation is a material-dependent property in this context. A proper elasto-plasticity/ -inelasticity model may be constituted for a symmetric plastic-flow rule in conjunction with a commutative-symmetrical elastic-plastic stretch-tensor product, which inherently includes even the simultaneous modeling of finite-elastic and finite-plastic/ -inelastic orthotropy.

中文翻译：

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交换对称弹塑性拉伸张量积及其速率

摘要 将变形梯度的交换对称弹塑性拉伸张量积和乘法 Bilby-Kroner-Lee 分解相互比较，特别是在相应的时间导数和张量速率方面。事实证明，这些乘法变形张量模型仅就拉格朗日角度而言在弹性响应方面有所不同，而在欧拉角度上则是一致的。本构方程的唯一性要求交换对称弹塑性拉伸张量积的对称塑性流动规则和乘法 Bilby-Kroner-Lee 公式的非对称塑性流动规则。更多，作者讨论了塑性旋转张量（由非对称塑性流动规则隐含）是否适用于多晶金属的适当有限塑性公式，以及在这种情况下，塑性旋转是否完全取决于材料。一个适当的弹塑性/非弹性模型可以为对称塑性流动规则与交换对称弹塑性拉伸张量积一起构成，它本质上甚至包括有限弹性和有限塑性/ - 非弹性正交各向异性。