Eshelby instability pressure for nucleation of a phase change defect

摘要

The existence of a nucleation instability is demonstrated at the vanishing of the path-independent M integral in linear anisotropic elasticity so that a region that is arbitrarily small can grow at constant potential energy. It yields a quadratic equation for the critical pressure to balance the Eshelby dissipation and nucleate an inclusion undergoing both change in density and change in bulk modulus, and is independent of the radius of the defect. Regarding the shape of nucleation, the expression from Noether's theorem allows also a symmetry breaking mode as a penny-shape "pancake", and by comparison of the M integrals for the pancake and the sphere, it would require a greater loss of potential energy of the system to nucleate a pancake, but less to grow it larger.