On the decomposition of the damage variable in continuum damage mechanics

• Published in: Acta mechanica Vol. 228; no. 7; pp. 2499 - 2517
• Main Authors: Voyiadjis, George Z., Kattan, Peter I.
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 01.07.2017; Springer; Springer Nature B.V
• Subjects: Classical and Continuum Physics; Continuum damage mechanics; Control; Cracks; Decomposition; Defects; Deformation; Dynamical Systems; Engineering; Engineering Thermodynamics; Fracture mechanics; Heat and Mass Transfer; Mathematical analysis; Mechanical properties; Original Paper; Plane stress; Scalars; Solid Mechanics; Solids; Tensors; Theoretical and Applied Mechanics; Variables; Vibration; Voids
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-017-1836-1

Refinements and generalizations of the decomposition of the damage variable are presented within the framework of continuum damage mechanics. It is assumed that damage in a solid is due mainly to cracks and voids. The classical decomposition of the damage variable into a damage part due to cracks and another damage part due to voids is examined and extended consistently and mathematically. This is further elaborated upon by considering a solid with three types of defects: cracks, voids, and a third defect that is unspecified. Initially, the decomposition issues are carried out in one dimension using scalars. But this is generalized subsequently for the general case of three-dimensional deformation and damage using tensors. Finally, the special case of plane stress is illustrated as an example. It is shown that in the case of plane stress, two explicit decomposition equations are obtained along with a third implicit coupling equation that relates the various “crack” and “void” damage tensor components.