Cracks in Cosserat Continuum—Macroscopic Modeling

Abstract

Modeling of particulate and layered materials (e.g., concrete and rocks, rock masses) by Cosserat continua involves characteristic internal lengths which can be commensurate with the microstructural size (the particle size or layer thickness). When fracture propagation in such materials is considered, the criterion of their growth is traditionally based on the parameters of the crack-tip stress singularities referring to the distances to the crack tip smaller than the characteristic lengths and hence smaller than the microstructural size. This contradicts the very notion of continuum modeling which refers to the scales higher than the microstructural size. We propose a resolution of this contradiction by considering an intermediate asymptotics corresponding to the distances from the crack tip larger than the microstructural sizes (the internal Cosserat lengths) but yet smaller than the crack length. The approach is demonstrated using examples of shear crack in particulate and bending crack in layer materials.