Handbook of Damage Mechanics: Nano to Macro Scale for Materials and Structures

Abstract

This chapter includes two main topics in isotropic and anisotropic damage mechanics. In the first topic, various new proposed damage variables are introduced, examined, and compared. The scalar case pertaining to isotropic damage is investigated, and several types of new damage variables are proposed. The damage variables introduced in this part can be applied to elastic materials including homogeneous materials like metals and heterogeneous materials like composite laminates. More over, higher-order strain energy forms are proposed. These higher-order strain energy forms along with some of the proposed damage variables are used in trying to lay the theoretical groundwork for the design of undamageable materials, i.e., materials that cannot be damaged where the value of the damage variable remains zero throughout the deformation process. The second topic presents a new concept of anisotropic damage that is examined within the framework of continuum damage mechanics. New proposed damage tensors are studied in order to investigate the damage effect variables in the mechanical behavior of materials. In addition, new hybrid damage tensors are proposed and defined in terms of the damage effect tensor and the new proposed damage tensors. Accordingly, this study demonstrates that most of the new proposed damage tensors are verified within the framework of continuum damage mechanics.