Interpolating Modified Moving Least Squares based element free Galerkin method for fracture mechanics problems

Interpolating Modified Moving Least Squares (IMMLS) based element-free Galerkin method (EFGM) is a simple, robust technique which addresses the limitations of classical Moving Least Squares Approximation (MLSA) based EFGM and is well-demonstrated for tissue deformation. However, its application to fracture mechanics featuring strong discontinuities has not been explored. To address this gap, the present work explores isotropic and orthotropic thermoelastic Linear Elastic Fracture Mechanics (LEFM) cases - with initial isotropic and orthotropic LEFM formulations extended to respective thermoelastic cases - and an isotropic Elastoplastic Fracture Mechanics (EPFM) case employing isotropic bilinear stress-strain curve. The results including field -variables and stress intensity factors (SIFs) are corroborated with converged finite element method (FEM) results; in addition, the results also include classical-MLSA results for a comparative study. L2 norms with respect to FEM indicate an overall close correspondence with a better match for primary variables than secondary variables - indicating the efficacy of IMMLS technique for fracture mechanics. In comparison with classical MLSA-based EFGM results, IMMLS-based EFGM (IN-EFGM) results are nearly similar. However, the advantages demonstrated by IMMLS technique over the classical MLSA-based EFGM in enforcing essential boundary conditions, a larger set of admissible nodal configuration and lesser computational time render IN-EFGM as a potential tool for fracture mechanics.

Automated summary

The Interpolating Modified Moving Least Squares (IMMLS) based element-free Galerkin method (EFGM) is a technique that addresses the limitations of classical methods and has been well-demonstrated in tissue deformation. However, its use in fracture mechanics has not been explored. This study investigates the application of IMMLS in isotropic and orthotropic thermoelastic Linear Elastic Fracture Mechanics (LEFM) cases as well as an isotropic Elastoplastic Fracture Mechanics (EPFM) case. The results show that IMMLS has a close correspondence with the finite element method (FEM) results and offers advantages in enforcing boundary conditions, nodal configuration, and computational time, making it a potential tool for fracture mechanics.