Use of fabric tensors in damage and healing mechanics of materials

A mathematical formulation incorporating the relationship between the damage tensor, healing tensor, and fabric tensors is presented. This formulation provides for a direct link between the subjects of Damage and Healing Mechanics using Fabric Tensors. A new damage-healing tensor is introduced that is based on the fabric of the material. This new tensor is pivotal in characterizing the micro-structure of the material, especially the distributions of micro-cracks and other micro defects. It is noted that the theory applies to linear elastic materials but can be generalized to other constitutive models incorporating inelastic behavior. As examples, the authors solve three cases, namely those of plane stress, plane strain, and isotropic elasticity. The case of plane stress assumes plane damage and plane healing as will be illustrated in the equations. Similarly, the case of plane strain is also illustrated. The case of isotropic elasticity assumes the presence of isotropic damage and isotropic healing. As an illustration, a numerical example is shown for a certain micro-crack distribution. Finally, experimental results are shown to illustrate the relationship between the fabric tensor parameters and the components of the damage and healing tensors. Finally, the evolution of damage and healing are discussed based on sound thermodynamic principles.