Automatic Differentiation for Numerically Exact Computation of Tangent Operators in Small‐ and Large‐Deformation Computational Inelasticity
Automatic Differentiation for Numerically Exact Computation of Tangent Operators in Small‐ and Large‐Deformation Computational Inelasticity
复制标题
小变形和大变形计算非弹性中切算子数值精确计算的自动微分
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
G. Hansen
中科院分区：
文献类型：
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作者：
Qiushi Chen;J. Ostien;G. Hansen
计算机软件工具和技术的进步已经改变了开发有限元代码和相关材料模型的方式。在这项工作中，我们提出了一个数值上精确的方法来计算灵敏度所需的构造局部一致的切线算子在计算非弹性的应用。在积分点水平上积分材料模型时，由本构方程导数产生的切线算子是实现二次收敛的必要条件。与基于有限差分的数值方法不同，在这项工作中提出的方法是基于一个精确的微分技术称为自动微分（AD）。该方法是有效的，稳健的，易于纳入。通过对复杂材料模型的小变形和大变形非弹性问题的数值算例，验证了该方法的有效性和适用性。
Advances in computer software tools and technologies have transformed the way in which finite element codes and associated material models are developed. In this work, we propose a numerically exact approach for computing the sensitivites required to construct local consistent tangent operators in computational inelasticity applications. The tangent operators that come from the derivatives of constitutive equations are necessary for achieving quadratic convergence in integrating material models at the integration point level. Unlike finite difference-based numerical methods, the approach proposed in this work is based on an exact differentiation technique called automatic differentiation (AD). The method is efficient, robust and easy to incorporate. Numerical examples in both small- and large-deformation inelasticity problems with complicated material models are presented to illustrate the efficiency and applicability of the proposed method.