3D Path independent integral for thermoelastic and magnetostriction problem

In this work, a universal path independent integral Ju  that represents the energy release rate or flux during crack extension in a homogeneous and isotropic material, has been derived for straight crack subjected to multiple loads. This version of integral includes the effect of elastic strain, Eigen strain, thermal strain, body forces and magnetic strain. Particularly focus is made on thermo-mechanical and magnetic strains. The 3D J-integral expression represents the energy release rate in the combined thermoelastic field with magnetostriction characteristics. This integral is applicable to the real field problems concerning medium in an electric field where the multiphysics of heat generation and magnetic field are involved. 3D finite element analysis of edge cracked magnetostrictive specimen has been carried out to demonstrate the efficacy of the integral expressions.