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On a numerical implementation of a formulation of anisotropic continuum elastoplasticity at finite strains

机译：有限应变各向异性连续弹塑性公式的数值实现

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In a recent theoretical study [see C. Sansour, I. Kar aj, J. Soric, A formulation of anisotropic continuum elastoplasticity at finite strains. Part 1: Modelling, International Journal of Plasticity 22 (2006) 2346-2365], a constitutive model for anisotropic elastoplasticity at finite strains has been developed. The model is based on the multiplicative decomposition of the deformation gradient. The stored energy function as well as the flow rule has been considered as quadratic functions of their arguments. In both cases, the list of arguments is extended to include structural tensors which describe the anisotropy of the material response at hand. Non-linear isotropic hardening is considered as well. In this paper, the integration of the constitutive law is presented. The associative flow rule is integrated using the exponential map which preserves the plastic incompressibility condition. The numerical treatment of the problem is fully developed and expressions related to the local iteration and the consistent tangent operator are considered in detail. It is shown that while the consistent linearisation of the model is quite complicated, it still can be achieved if various intriguing implicit dependencies are identified and correctly dealt with. Various numerical examples of three-dimensional deformations of whole structural components are presented. The examples clearly illustrate the influence of anisotropy on finite elastoplastic deformations. (C) 2008 Elsevier Inc. All rights reserved.
机译：在最近的理论研究中[参见C. Sansour，I。Kar aj，J。Soric，各向异性应变在有限应变下的连续塑性公式。第1部分：建模，国际可塑性杂志22（2006）2346-2365]，已经开发了有限应变下各向异性弹塑性的本构模型。该模型基于变形梯度的乘法分解。所存储的能量函数以及流量规则已被视为其自变量的二次函数。在这两种情况下，论点列表都被扩展为包括描述当前材料响应各向异性的结构张量。还考虑非线性各向同性硬化。本文提出了本构法的整合。关联流规则使用保留塑料不可压缩条件的指数图进行集成。对该问题的数值处理得到了充分发展，并详细考虑了与局部迭代和一致切线算符有关的表达式。结果表明，虽然模型的一致线性化非常复杂，但是如果能够识别并正确处理各种有趣的隐式依赖关系，仍然可以实现。给出了整个结构部件的三维变形的各种数值示例。这些例子清楚地说明了各向异性对有限弹塑性变形的影响。 （C）2008 Elsevier Inc.保留所有权利。

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