A COUPLED THEORY OF DAMAGE MECHANICS AND FINITE STRAIN ELASTOPLASTICITY .1. DAMAGE AND ELASTIC DEFORMATIONS

A coupled theory of elasticity and continuum damage mechanics is formulated here. It is assumed that the material undergoes damage with small elastic strains. The hypothesis of elastic energy equivalence is used in order to produce the proposed coupling. The damage variable used represents average material degradation which reflects the various types of damage at the microscale level like nucleation and growth of voids, cavities, micro-cracks and other microscopic defects. The proposed model is numerically implemented using finite elements with an Updated Lagrangian description. It is also shown how the model can be applied to problems of ductile frActare. The problem of crack initiation in a thin plate with a center crack that is subjected to uniaxial tension is analyzed using the proposed model. The theory is extended to coupling of damage and finite strain plasticity in the companion paper. It is shown there how the model can be used to solve problems in elasto-plastic ductile fracture. © 1990.