TRANSIENT, ASYMPTOTIC, ELASTODYNAMIC ANALYSIS - A SIMPLE METHOD AND ITS APPLICATION TO MIXED-MODE CRACK-GROWTH

When a moving singularity in a linearly elastic solid admits, in its steady state, an asymptotic eigen-expansion of variable-separable type, its asymptotic expansion in an unsteady state can be obtained systematically. A simple, straightforward method is presented here for deriving the transient, asymptotic, elastodynamic local fields near such moving singularities. The method makes use of the steady-state solution, and turns a transient problem into finding the particular solutions of a set of second-order ordinary differential equations, which have constant coefficients and nonhomogeneous terms involving only cosine and sine functions. The method is employed to obtain transient plane elastodynamic near-tip fields for a crack growing in a homogeneous, isotropic and linearly elastic solid. The fields are given in terms of two displacement potentials, applicable to general mixed-mode crack growth cases, from which crack-tip stress and deformation fields can be readily derived. Such transient solutions will be useful in numerical simulation as well as experimental interpretation of dynamic crack propagation events.