Three-Dimensional Mixed-Mode Crack Growth Modeling in Electro-Magneto-Thermo-Elastic Coupled Viscoplastic Multiphase Composites by Time-Domain Hypersingular Integral Equation Method

Abstract

Electro-magneto-thermo-elastic coupled viscoplastic multiphase composites (EMTE-CVP-MCs) typically exhibit pronounced nonlinear response under sufficiently higher electro-magneto-thermo-elastic (EMTE) coupled incremental loading conditions. These extended incremental loads are causing higher extended incremental stresses than under corresponding static extended incremental loads and may induce crack initiation, crack growth and finally lead to fracture or failure of structures. However, relatively little work has been done to the three-dimensional crack growth problem in EMTE-CVP-MCs, because of the present limitations both practical and theoretical. These require us to provide with general precious and accurate theoretical method by use of mathematics tools, and found efficiently numerical method. This work presents a time-domain hypersingular integral equation (TD-HYE) method proposed by the author for modeling three-dimensional mixed-mode crack growth in 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. This crack growth problem is reduced to solving a set of TD-HYEs 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-HYE. Also, analytical solutions of the extended singular incremental stresses gradient and extended incremental integral \( \dot J_i^g \) near the crack front in EMTE-CVP-MCs are provided. In addition, a numerical method of the TD-HYE for a three-dimensional mixed-mode crack subjected to extended incremental loads rate is put forward with the extended incremental displacement discontinuities gradient approximated by the product of basic density functions and polynomials. Finally, several examples are presented to demonstrate the application of the proposed method.