Solids with Dry Microcracks

Abstract

The theories of macroscopic properties of cracked solids predict the modification of the stiffness and the change of anisotropy orientation caused by microcracking. Hence, the development of continuum theory dealing with microcrack distribution has an obvious interest for mechanics of materials. Basically, a microcrack is often associated to internal slipping and debonding in matter, e.g., [13], [25]. Following a closed path around the defect, the displacement field has a jump. When the occurrence of microcracks appears with sufficiently high density in some matter, then a continuous volume distribution is a reasonable hypothesis. For a continuous distribution of cracks, displacement and velocity are not single-valued functions of position of a material point M. At least three approaches may be proposed to construct the theory of microcrack continuous distribution: statistical models, micromechanical models, and continuum models [100]. The statistical models, based on statistical physics, are beyond the scope of this book. The micromechanical models consider a basic “microscopic cell” including the crack. In these models, the contact mechanics theory and the homogenization method are applied to each crack in order to account for the influence of crack on the global material properties, e.g., [131]. The continuum models are based on continuum mechanics accounting for discontinuity of scalar and vector fields [163].