Continuum Damage Based on Elastic Projection Operators

The general formulation for continuum damage, as for plasticity, is so broad that specific conclusions can be made only if simplifying assumptions are made. Experimental data do not support the simplification of isotropic damage. Here, the elasticity tensor is expressed in terms of projection operators and principal elasticities which are altered with damage. A subspace is used to define a damage mode. The result is a theory that predicts a limited amount of anisotropic damage and represents a natural generalization of isotropic damage. The further assumption that a different damage function holds for each mode results in a number of damage surfaces with the lower bound forming the composite damage surface. It is also postulated that a characteristic set of cracks is associated with each mode. Each set is assumed to consist of an isotropic distribution of cracks with a representative crack dimension. However, the set for one mode may be different from the next set so, overall, the crack distribution need not be isotropic nor of one characteristic average dimension. The use of these assumptions results in the uncoupling of damage modes and evolution equations for crack growth and for the principal values of the elasticity tensor. Furthermore, the possible connection between dilatation and the rotation of projection operators is illustrated with a load path based on triaxial compression.