3D modeling of crack growth in electro-magneto-thermo-elastic coupled viscoplastic multiphase composites

This work presents a time-domain hypersingular integral equation (TD-HIE) method for modeling 3D crack growth in electro-magneto-thermo-elastic coupled viscoplastic multiphase composites (EMTE-CVP-MCs) under extended incremental loads rate through intricate theoretical analysis and numerical simulations. Using Green's functions, the extended general incremental displacement rate solutions are obtained by time-domain boundary element method. Three-dimensional arbitrary crack growth problem in EMTE-CVP-MCs is reduced to solving a set of TD-HIEs coupled with boundary integral equations, in which the unknown functions are the extended incremental displacement discontinuities gradient. Then, the behavior of the extended incremental displacement discontinuities gradient around the crack front terminating at the interface is analyzed by the time-domain main-part analysis method of TD-HIE. Also, analytical solutions of the extended singular incremental stresses gradient and extended incremental integral near the crack fronts in EMTE-CVP-MCs are provided. In addition, a numerical method of the TD-HIE for a 3D crack subjected to extended incremental loads rate is put forward with the extended incremental displacement discontinuities gradient approximated by the product of time-domain basic density functions and polynomials. Finally, examples are presented to demonstrate the application of the proposed method.