Formulation and computation of geometrically non-linear gradient damage

The aim of this contribution is the extension of a small strain and small d eformation formulation of gradient enhanced damage to the geometrically non -linear case. To this end, Non-local Stored Energy densities, (NSE) are int roduced as primary variables. Fluxes conjugated to the gradients of the NSE are then computed from balance laws which in the small strain limit corres pond to the averaging equation well known in the literature [1-3]. The prin cipal task is then to establish constitutive laws for these newly introduce d NSE-fluxes. Thereby, four different options are investigated which are mo tivated from Lagrange and Euler averaging procedures together with changes of the metric tensors. Issues of the corresponding FE-formulation and its l inearization within a Newton-Raphson procedure are addressed in detail. Fin ally, the four different formulations are compared for the example of a bar in tension whereby large strains are truly envisioned. Copyright (C) 1999 John Wiley & Sons, Ltd.