TRANSIENT ELASTIC FIELD DUE TO A SPHERICAL DYNAMIC INCLUSION WITH AN ARBITRARY TIME PROFILE
Yozo Mikata · The Quarterly Journal of Mechanics and Applied Mathematics · 1993
The elastodynamic field of an infinite isotropic elastic medium is investigated when a spherical portion of the medium experiences a dynamic phase transformation. The phase transformation is modelled as a spatially uniform eigenstrain over a sphere multiplied by an arbitrary function of time. The objective is to determine the elastic fields inside and outside the sphere when the dynamic eigenstrain is given. Using a Green's-function approach, an exact closed-form solution is obtained for this problem. As special cases, a time-harmonic solution as well as an elastodynamic response of the medium due to a sudden phase transformation are discussed.