Interpolating Modified Moving Least Squares-based meshless method for large deformation analysis in hyperelastic model

Abstract

This work develops a meshfree interpolation approach based on the Interpolating Modified Moving Least Squares (IMMLS) approximation for the accurate simulation of hyperelastic materials undergoing large deformations. As an enhanced interpolation technique within the family of Element-Free Galerkin (EFG)-type methods, IMMLS provides a flexible numerical framework for problems in which conventional mesh-based approaches often encounter difficulties under severe deformation. Since hyperelastic materials are characterized by highly nonlinear constitutive behavior and can sustain large strains, their response is most appropriately described within the framework of finite deformation theory, making an accurate treatment of such nonlinearity essential for reliable numerical modelling. To assess the capability of the proposed method, the Neo-Hookean model was adopted as a representative constitutive model for large-deformation analysis, while the material parameters were selected from existing literature to ensure consistency and accuracy. The numerical results were compared with reference data reported in previous studies, and the computational implementation was further validated against benchmark solutions obtained in MATLAB. In addition, the broader engineering relevance of the IMMLS approach is discussed through its potential applications, and the present findings are expected to provide a useful basis for future, more detailed investigations in this field.