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Analysis of an interface crack of arbitrary shape in a three-dimensional transversely isotropic magnetoelectrothermoelastic bimaterial—part 2: Numerical method

ABSTRACT The extended displacement discontinuity (EDD) boundary integral equation and boundary-element method are extended and developed to analyze an arbitrarily shaped, planar interface crack in a three-dimensional, transversely isotropic, magnetoelectrothermoelastic bimaterial under combined, thermoelectromagnetomechanical loadings. The fundamental solutions for uniformly distributed EDDs applied over a constant triangular element are obtained through integrating the fundamental solutions for the unit-point EDDs given by Part 1 over the triangular area. To eliminate the oscillatory singularity near the crack front, the Dirac delta function in the integral–differential equations is approximated by the Gaussian distribution function, and accordingly, the Heaviside step function is replaced by the Error function. The extended stress intensity factors without oscillatory singularities, the energy release rate, and the local J-integral in terms of intensity factors are all obtained. To validate the solution, the EDD boundary-element method is proposed. As an application, an elliptical interface crack is numerically simulated. The influences of the applied combined loadings and material-mismatch as well as the ellipticity ratio on the multiphysical response are studied.