Advances in the mechanics of undamageable materials: General three-dimensional formulation

The theory of undamageable materials is extended to general states of deformation and damage. Undamageable materials are hypothetical materials that do not undergo any damage processes under the action of forces within the framework of continuum damage mechanics. In these types of materials, the damage variable remains zero throughout the deformation process. The authors developed previously the theory of undamageable materials for the one-dimensional case using scalars. In this work, the general three-dimensional formulation is presented using tensors. In this regard, a system of nonlinear partial differential equations governing the mechanics of undamageable materials is obtained. An attempt is made to solve the governing system using one single simplifying assumption. It is hope that the theoretical formulation presented in this work will open the way for future development of these types of new materials in practical applications.