Deformation of Damaged Elastic-Brittle Isotropic Materials with a Fixed Concentration of Microdefects in a Complex Stress State

The character of deformation of elastic—brittle isotropic materials weakened by flat microdefects in the form of circular or elliptic microcracks randomly dispersed over volume is studied in the complex stress state. It is assumed that concentration of the microcracks under loading remains constant. Equations of state for such materials are derived depending on the stress state mode and sign of applied stresses. The damaged material is simulated by a linear elastic isotropic medium under all-round compression or tension and under biaxial compression, by a linear elastic transversally isotropic medium under biaxial tension, and by a non-linear orthotropic medium under compression along one axis and tension along another axis. To determine compliance characteristics entering into the equations of state, the continual model of a cracked medium and a method based on the equivalence principle of deformation energy of this medium are used. A numerical example is presented.