Decomposition of healing tensor: In continuum damage and healing mechanics

The decomposition of the healing variable (in the case of scalars) and the healing tensor (in the case of tensors) is carried out systematically and consistently. In this respect, the classical linear healing model is adopted in this work. The decomposition of healings includes the healing variable/tensor of cracks and the healing variable/tensor for voids. A third defect type is considered wherever mathematically possible. Thus a complete treatment of the decomposition of the healing tensor is presented covering both the one-dimensional and three-dimensional aspects. As an illustrative example, the case of plane stress, plane damage, and plane healing is solved. In this case, it is concluded that two distinct decomposition equations are obtained as well as one single coupling formula. The coupling equation is an expression that relates the various healing tensor components and damage tensor components for cracks and voids Furthermore; it is shown that there is no coupling in the one-dimensional case.