Cracks, Shear Bands and Lamellar Inclusions in Homogeneously Prestressed Materials

Localized deformation patterns are experimentally observed to prelude failure in many ductile materials (such as metal, alloy, granular material and plastic) and in quasi–brittle materials (such as concrete and rock). Moreover, the presence of a second phase in composites may promote failure due to stress concentrations at the inclusion boundaries. In order to investigate shear bands nucleation, propagation and interaction with a second phase or a defect, analytical solutions for an infinite nonlinear elastic solid subject to a uniform far–field deformation increment are obtained for the following types of inclusion: i) A crack, revealing features related to the interaction between shear bands and crack tip fields. This solution is also fundamental to the understanding of the shear band problem; ii) A rigid line inclusion, the so-called ‘stiffener’, showing the emergence of shear bands at the stiffener tips in highly deformed ductile materials. For null prestress the solution is shown to match correctly with photoelastic experiments and to predict the fracture patterns for a brittle material containing a stiffener; iii) A pre–existing shear band, showing that the deformation is highly focussed and aligned coaxial to the shear band and the energy release rate to blow up to infinity, for incremental loading occurring when the prestress approaches the elliptic boundary, so that the propagation becomes ‘unrestrainable’. All these analytical results substantiate the experimental observations that shear bands emerge at the inclusion tips and they are preferential near-failure deformation modes.