On magneto-thermo-viscoelastic deformation and fracture

A thermodynamic formulation of magneto-thermo-viscoelastic constitutive and fracture theory is developed, accounting for non-linear, thermal and hysteresis effects. State equations and energy flux integral are obtained in consideration of the Helmholtz free energy including the contribution of the free magnetic field as a functional of the histories of deformation, temperature and magnetic induction in the reference configuration. The rate of energy flow towards the crack front per unit crack advance provides the crack driving force in the presence of magneto-thermo-mechanical coupling and hysteresis, which is evaluated through formation of energy-momentum tensor for steady-state crack propagation. A fracture criterion based on the generalized J˜-integral thus formulated overcomes the difficulty encountered by existing treatments and helps to understand the fracture behavior of both conservative and dissipative materials subject to combined magnetic, thermal and mechanical loadings. Reduction of this formulation to finite magneto-thermo-viscoelasticity is provided with polynomial expansion of the Helmholtz free energy functional.