2. Undamageable Materials and Damage Processes in Series and in Parallel

This chapter introduces a new study in the field of continuum damage mechanics and includes two main topics. In the first topic, both the concepts of Voyiadjis-Kattan materials and undamageable materials are introduced. The Voyiadjis-Kattan material of order n is defined as a nonlinear elastic material that has a higher-order strain energy form in terms of n. The undamageable material is obtained as the limit of the Voyiadjis-Kattan material of order n as n goes to infinity. The relations of these types of materials to other nonlinear elastic materials from the literature are outlined. Also, comparisons of these types of materials with rubber materials are presented. It is hoped that these proposed new types of materials will open the way to new areas of research in both damage mechanics and materials science.

The second topic lays special emphasis on the order and sequence of damage processes occurring in materials. These processes can occur in series or in parallel. For example, in a metallic material, the evolution of micro-cracks and the evolution of micro-voids are considered as two separate damage processes. These two different evolutions can occur simultaneously or they can occur following each other. Another example would be matrix cracking and debonding in a composite material. These two different damage processes can occur simultaneously in parallel or sequentially in series. Three-dimensional states of deformation and damage are also presented using the concepts discussed in this work.