Moving singularities in elasto-diffusive solids with applications to fracture propagation

Solutions are derived for steady-state motion of a singularity class, which includes point sources and dislocations, through a medium in which the elastic stress-field can evolve with time due to the diffusion of an internal second-phase species, such as a pore-fluids and lattice impurity concentrations in a crystalline solid, or the transfer of heat. The technique is to integrate the known influence functions for a stationary singularity. Attention is focused on the most tractable aspect, namely the stress field on the trajectory of motion: this suffices for simulation of growing shear and tensile fractures (e.g. in a porous fluid-saturated solid). Continuous densities of fluid sources and point discontinuities (dislocations) are suitably distributed (as determined by solving the resulting singular integral equations) to satisfy solid stress and fluid pressure or flow conditions on the fracture surfaces. Alternative methods for finding the complete dislocation influence function are discussed and comparisons with existing source solutions are made. Substantial stabilization effects are found in fracture propagation.