A framework for geometrically nonlinear continuum damage mechanics

The objective of this work is the derivation of a framework for geometrical ly nonlinear continuum damage mechanics which allows for the description of damage by second order tensors. To this end, so called fictitious undamage d or rather microscopic configurations are considered which are related to the macroscopic configurations by linear tangent maps which allow for the i nterpretation as damage deformation gradients. The corresponding Finger ten sors defined in the macroscopic configuration are then understood as damage d metrics for measuring the free energy for given strains. Thereby, the und erlying motivation is provided by the hypothesis of strain energy equivalen ce between microscopic and macroscopic configurations. Based on the standar d dissipative material approach the constitutive framework is completed by stresses, damage stresses, a damage condition and the associated evolution laws for the damage metric and the internal hardening variable. The relatio nship of the present damage metric based theory to the classical understand ing of damage as an area reduction is highlighted. Finally, a simple protot ype model problem is presented which allows for an efficient and accurate a lgorithmic treatment. Numerical examples demonstrate the applicability of t he proposed framework. (C) 1998 Elsevier Science Ltd. All rights reserved.