Automatic Differentiation for Numerically Exact Computation of Tangent Operators in Small- and Large-Deformation Computational Inelasticity

Abstract

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.