A damage mechanics model of materials with voids and cracks

In this paper we study a mechanical modeling of complicated materials with damages such as voids, defects, and cracks within the framework of continuum mechanics. We represent the voids, defects, etc. in materials by using the damage tensors based on the effective stress concept and model the cracks on the basis of crack theory, so that discontinuous models can be treated with the help of continuum mechanics method. This modeling is carried out by taking the elastic strain energy of the body with void damages and cracks as the difference between the effective strain energy due to void damages and the complementary energy due to cracks. In the effective space, the complementary energy due to cracks is obtained by the known energy release rate and the effective stiffness properties of materials are derived by using the Green’s theorem. We introduce the concept of the effective stress intensity factors and suggest a method for expressing the I, II, III-type effective stress intensity factors with consideration of crack closure effect. We obtain the expression of the complementary energy and determine the effective stiffness characteristics for various cases of plane open cracks, plane closed cracks, space open elliptic cracks, and space closed elliptic cracks. We analyze the stress and displacement of structural materials with cracks and void damages by using the obtained effective stiffness properties in ANSYS and perform the numerical comparison between the modeling method by the decomposition of total damage variable into void and crack damages and our modeling method by coupling of void damage and crack theory.