Shear Band Patterns by Boundary Integral Equations

Large strain effects are important in a number of engineering problems, and they can influence the behaviour of microelectromechanical systems, geological formations, biological tissues, and structural elements, such as seismic insulators and rubber bearings. High levels of pre-stress may induce shear bands in materials like metals, polymers, granular solids. Here, boundary integral equations are presented to analyse perturbations in terms of small elastic deformations superimposed upon an arbitrary, homogeneous strain. Plane strain deformations of an incompressible elastic solid are considered, within the elliptic range, assuming the Biot constitutive framework. The integral equations are the means to analyse strain localization as a special case of instability which is induced by perturbations and is found to occur within the elliptic range. The boundary integral equations are based on Green’s functions developed by the Authors for nonlinear incremental elastic deformations.