Thermo-mechanically coupled gradient-extended damage-plasticity modeling of metallic materials at finite strains

Abstract For various engineering applications, the analysis and prediction of damage onset and propagation within ductile materials under thermo-mechanical loading conditions play a crucial role. However, finite element modeling of the influence of the temperature on plastic flow and damage evolution and the back-coupling of theses dissipative processes on the temperature field remains a challenging task, until today. To this end, a thermo-mechanically coupled two-surface damage-plasticity theory is derived in a thermodynamically consistent manner for large deformations. It can be considered as the thermo-mechanically coupled extension of a corresponding isothermal model, which was proposed recently by Brepols et al. (2020). In this novel theory, the heat generation associated with thermo-elastic coupling and irreversible processes (i.e. damage and plasticity) is derived from the first law of thermodynamics. To overcome the mesh-dependence of conventional local damage models, a gradient-extension based on the micromorphic approach of Forest (2009, 2016) is employed. Besides the theoretical development, the algorithmic implementation into finite elements is discussed, including the computation of the required tangent operators via automatic differentiation. Finally, the fully coupled multi-physical formulation is verified regarding mesh-insensitive predictions of e.g. strain localization, local heat accumulation, material and thermal-softening, as well as crack propagation and back-coupling effects on the temperature field. Quantitative and qualitative comparisons of the model’s predictions to experimental data reveal the promising potential of the numerically robust and flexible theory.