The purpose of continuum plasticity models is to efficiently predict the behavior of structures beyond their elastic limits. The purpose of multiscale materials science models, among them crystal plasticity models, is to understand the material behavior and design the material for a given target. The current successful continuum hyperelastoplastic models are based in the multiplicative decomposition from crystal plasticity, but significant differences in the computational frameworks of both approaches remain, making comparisons not straightforward. In previous works we have presented a theory for multiplicative continuum elastoplasticity which solved many long-standing issues, preserving the appealing structure of additive infinitesimal Wilkins algorithms. In this work we extend the theory to crystal plasticity. We show that the new formulation for crystal plasticity is parallel and comparable to continuum plasticity, preserving the attractive aspects of the framework: (1) simplicity of the kinematics reaching a parallelism with the infinitesimal framework; (2) possibility of very large elastic strains and unrestricted type of hyperelastic behavior; (3) immediate plain backward-Euler algorithmic implementation of the continuum theory avoiding algorithmically motivated exponential mappings, yet preserving isochoric flow; (4) absence of Mandel-type stresses in the formulation; (5) objectiveness and weak-invariance by construction due to the use of flow rules in terms of elastic corrector rates. We compare the results of our crystal plasticity formulation with the classical formulation from Kalidindi and Anand based on quadratic strains and an exponential mapping update of the plastic deformation gradient.

中文翻译：

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基于加性弹性校正率的乘法有限应变晶体塑性公式：理论与数值实现

连续塑性模型的目的是有效地预测超出其弹性极限的结构的行为。多尺度材料科学模型（其中包括晶体塑性模型）的目的是了解材料行为并为给定目标设计材料。当前成功的连续超弹塑性模型基于晶体可塑性的乘法分解，但两种方法的计算框架仍然存在显着差异，使得比较并不简单。在以前的工作中，我们提出了一种乘法连续弹塑性理论，它解决了许多长期存在的问题，保留了加法无穷小 Wilkins 算法的吸引人的结构。在这项工作中，我们将理论扩展到晶体可塑性。我们表明晶体可塑性的新公式是平行的，可与连续可塑性相媲美，保留了框架的吸引力：（1）运动学的简单性与无穷小框架达到平行；(2) 非常大的弹性应变和不受限制的超弹性行为的可能性；(3) 连续统理论的直接后向欧拉算法实现，避免了算法驱动的指数映射，但保留了等容流；(4) 配方中没有曼德尔型应力；(5) 由于在弹性校正率方面使用流动规则，构造的客观性和弱不变性。