On the Single-Point Calculation of Stress–Strain Data under Large Deformations with Stress and Mixed Control

Abstract

Stress–strain data with a given constitutive model of material can be calculated directly at a single material point. In this work, we propose a framework to perform single-point calculations under large deformations with stress and mixed control, to test and validate sophisticated constitutive models for materials. Inspired by Galerkin–FFT methods, a well-defined mask projector is used for stress and mixed control, and the derived nonlinear equations are solved in Newton iterations with Krylov solvers, simplifying implementation. One application example of the single-point calculator in developing sophisticated models for anisotropic single crystal rate-independent elastoplasticity is given, illustrating that the proposed algorithm can simulate asymmetrical deformation responses under uni-axial loading. Another example for artificial neural network models of the particle reinforced composite is also given, demonstrating that the commonly used machine learning or deep learning modeling frameworks can be directly incorporated into the proposed calculator. The central difference approximation of the tangent is validated so that derivative-free calculations for black-box constitutive models are possible. The proposed Python-coded single-point calculator is shown to be capable of quickly building, testing, and validating constitutive models with sophisticated or implicit structures, thus boosting the development of novel constitutive models for advanced solid materials.