A non-local extension of Gurson-based ductile damage modeling

The purpose of this work is the development and numerical implementation of a non-local extension of existing Gurson-based modeling for isotropic ductile damage and attendant crack growth. In the current work, this extension is based on a generalization of Gurson-based ductile damage modeling formally analogous to that of Needleman and Tvergaard as based on a (local) effective damage parameter f* which accounts in their case in an effective fashion for the effect of void coalescence on yield behaviour. Here, the corresponding generalized effective damage parameter ν is introduced in order to delocalize the model damage process. To this end, ν is modeled in this work as a scalar-valued continuum microstructural field or generalized phase field via a recent thermodynamic approach to the modeling of such fields. In the last part of the work, the complete model for coupled damage-deformation is implemented numerically using the finite element method and utilized to investigate the damage behaviour of an inhomogeneous steel block in simple tension. The corresponding simulation results demonstrate in particular that delocalization of the model damage process also leads to minimization of mesh-dependence. For simplicity, the current formulation is restricted to the case of small strain and isothermal conditions.