A gradient-extended two-surface damage-plasticity model for large deformations. (June 2020) - Brepols, Tim; Wulfinghoff, Stephan; Reese, Stefanie
Abstract: This work is concerned with the theoretical development, algorithmic implementation and numerical investigation of a novel thermodynamically consistent 'two-surface' gradient-extended damage-plasticity model for arbitrarily large deformations. It can be considered the geometrically nonlinear version of a corresponding model for small deformations which was presented recently (Brepols et al., (2017; 2018)). The terminology 'two-surface' stems from the fact that damage and plasticity are treated in the model as truly distinct but coupled dissipative mechanisms, meaning that individual damage loading and plastic yield criteria as well as appropriate loading/unloading conditions are used in the formulation, respectively. Such an approach makes the model flexibly adaptable to various situations in which the material under consideration shows either a more brittle- or ductile-like damaging behavior. Nonlinear Armstrong-Frederick kinematic hardening, nonlinear Voce isotropic hardening as well as nonlinear damage hardening are accounted for in the presented formulation that relies exclusively on symmetric internal variables, being beneficial, e.g., from the computational point of view. The model is formulated in the framework of Continuum Damage Mechanics and its gradient-extension is derived on the basis of the micromorphic approach according to Forest (2009, 2016). As such, it allows for the computation of mesh-insensitive results in finite element simulations involving material softening which is practically confirmed by means of several structural example problems. Furthermore, many other interesting aspects are highlighted, as, e.g., the model's implementation into finite elements, the computation of the algorithmically consistent tangent operators necessary to retain a quadratic rate of convergence in a global Newton-Raphson scheme, or a suitable time-integration of the model's evolution equations at the integration point level. Highlights: A novel thermodynamically-consistent gradient-extended damage-plasticity model for large deformations is presented. The model uses a 'two-surface' strategy in which 'damage' and 'plasticity' are treated as distinct dissipative mechanisms. The model accounts for nonlinear isotropic and kinematic hardening as well as nonlinear damage hardening. The model formulation is based exclusively on symmetric tensorial internal variables, which has many advantages. The model's algorithmic implementation and its mesh regularization properties are investigated and discussed in detail.