Radiated Fields, Energy-Release Rate and Evolution Equation for a Half-Space Eshelby Inclusion

28 May 2009
Xanthippi Markenscoff
In the context of the linear theory of elasticity with eigenstrains, the radiated fields, including inertia effects, and the energy-release rates (“driving forces”) of a spherically expanding and a plane inclusion with constant dilatational eigenstrains are calculated. The fields of a plane boundary with dilatational eigenstrain moving from rest in general motion are calculated by a limiting process from the spherical ones, as the radius tends to infinity, which yield the time-dependent tractions that need to be applied on the lateral boundaries for the global problem to be well-posed. The energy-release rate required to move the plane inclusion boundary (and to create a new volume of eigenstrain) in general motion is obtained here for a superposed loading of a homogeneous uniaxial tensile stress. This provides the relation of the applied stress to the boundary velocity through the energy-rate balance equation, yielding the “equation of motion” (or “kinetic relation”) of the plane boundary under external tensile axial loading. This energy-rate balance expression is the counterpart to the Peach-Koehler force on a dislocation plus the “self-force” of the moving dislocation.
  • Differential Equations and Applications Seminar