Formulation and computation of geometrically non-linear gradient damage

The aim of this contribution is the extension of a small strain and small deformation formulation of gradient enhanced damage to the geometrically non-linear case. To this end, Non-local Stored Energy densities, (NSE) are introduced as primary variables. Fluxes conjugated to the gradients of the NSE are then computed from balance laws which in the small strain limit correspond to the averaging equation well known in the literature [1-3]. The principal task is then to establish constitutive laws for these newly introduced NSE-fluxes. Thereby, four different options are investigated which are motivated from Lagrange and Euler averaging procedures together with changes of the metric tensors. Issues of the corresponding FE-formulation and its linearization within a Newton-Raphson procedure are addressed in detail. Finally, the four different formulations are compared for the example of a bar in tension whereby large strains are truly envisioned