Anisotropic magneto-electro-elastic fracture mechanics in orthotropic materials: Analysis using efficient interpolating modified MLS-based EFGMs and interaction integral

Abstract

Wendland’s radial basis function-based Interpolating Modified Moving Least Squares (IMMLS) based element-free Galerkin method (EFGM) is an efficient numerical technique which is developed to ameliorate the classical Moving Least Squares Approximation (MLSA) based EFGM. On the other hand, regularized IMMLS-based EFGM (IN-EFGM) is well-explored in tissue deformation and fracture mechanics problems. Anisotropic magneto-electro-elastic (MEE) analysis featuring strong discontinuities is well-established in the finite element method (FEM) and among others. However, MEE analysis has not been explored with in classical MLSA, IN-EFGM, and Wendland’s IMMLS-based EFGM (WiN-EFGM). To address this gap, the present work explores anisotropic MEE fracture mechanics (AMEE-FM) analysis to evaluate the extended stress intensity factors (ESIFs) using interaction integral method using EFGM in general. Benchmark numerical experiments are validated with analytical solutions and amongst the other are performed on simple and complex domains by considering an embedded crack under a steady state condition. The results of field variables in WiN-EFGM and IN-EFGM are corroborated with converged classical MLSA-based EFGM results. The extended stress intensity factors are evaluated using the interaction integral. $L^2$ norm with reference to classical MLSA-based EFGM shows that field variables have an overall better match in WiN-EFGM and IN-EFGM techniques. The field variables in WiN-EFGM have overall nearly same error as compared to IN-EFGM. The potential advantages of efficient WiN-EFGM and IN-EFGM over classical MLSA include ensuring essential boundary conditions, unique solution due to a non-singular moment matrix, and lesser computational time. Thus, interpolating EFGM offers an alternate tool to explore the AMEE fracture mechanics to evaluate the ESIFs.