Eshelby energy-momentum tensor

Summary

The Eshelby energy-momentum tensor is a second-order tensor built from the strain energy density and the stress of an elastic body. Its divergence vanishes at equilibrium in a homogeneous hyperelastic material without body forces. So its flux through a closed surface is zero unless the surface encloses a defect. The flux around a defect, such as a crack tip, a dislocation or an inclusion, is the configurational force on it. This force is the rate of decrease of energy when the defect moves. The J-integral of fracture mechanics is the flux of its first row around a crack tip.