A two-surface gradient-extended anisotropic damage model using a second order damage tensor coupled to additive plasticity in the logarithmic strain space

Abstract

The objective of the present paper is to develop a thermodynamically consistent coupled damage-plasticity model at large deformations, which accounts for damage anisotropy. Moreover, a ‘two-surface’ approach allows modeling plasticity and damage independently. Thus, both phenomena are treated as separate dissipative mechanisms, making the model attractive for application to both brittle and ductile materials. The framework is based on Continuum Damage Mechanics. Furthermore, logarithmic strain measures – also known as Hencky strain – are considered for the kinematics, while the decomposition of the total deformation into elastic and plastic parts is based on the additive split. Hence, the derivation of the model and its conjugated quantities takes place in the logarithmic strain space, but these are subsequently transformed to their Lagrangian counterparts to be applicable in standard finite element formulations. Consequently, the transformation of constitutively dependent quantities such as stresses, but also the various associated material sensitivities, are addressed here. Another main aspect of this work is the gradient-extension of the presented model in order to cure mesh sensitivity in case of material softening. To this end, a novel gradient extension is derived using the invariants of the second order damage tensor, which is based on the micromorphic approach. In addition to the theoretical framework, special attention is paid to the finite element implementation, the formulation of the local residuals, and additionally the computation of the material tangents to achieve quadratic convergence rate within the Newton–Raphson scheme. Single element studies as well as representative structural examples investigate the model’s response to various loading scenarios, the effect of damage anisotropy and further highlight its ability to provide mesh-independent results while undergoing large deformations.