Mechanical and Civil Engineering Seminar
A persistent shear band is a dominant pattern of localized deformation in a heterogeneous material. It may or may not be the first one to emerge, but it is the prevailing pattern that persists in the end. In unsaturated porous materials, the persistent shear band depends crucially on degree of saturation, since fluid in the pores of a solid imposes a volume constraint on the deformation of the solid. When fluid flow is involved, the persistent shear band also depends on the heterogeneity of a material, which is quantified in terms of the spatial variation of density, degree of saturation, and matric suction. In this lecture, I will present a mathematical framework for coupled solid-deformation/fluid-diffusion in unsaturated porous media considering material and geometric nonlinearities. The framework relies on the continuum principle of thermodynamics to identify an effective or constitutive stress for the solid matrix, and a water retention law that highlights the interdependence of degree of saturation, suction, and porosity of the material. I will discuss the role of heterogeneity, quantified either deterministically or stochastically, on the development of a persistent shear band. This work is inspired by current testing capabilities that allow nondestructive and non-invasive measurement of density and degree of saturation through high resolution imaging.