Meshfree Stabilized Collocation Method for Large Deformation Analysis of Hyperelastic Materials

ABSTRACT The analysis of large deformation problems of hyperelastic materials is challenging due to strong nonlinearities arising from both material behavior and geometric effects. Traditional Finite Element Method (FEM) often requires remeshing or element deletion to address element distortion during large deformations. In this study, a meshfree numerical method based on the stabilized collocation method (SCM) is developed to analyze large deformations in hyperelastic materials. This method constructs shape functions based on reproducing kernel approximations and achieves accurate integration within local subdomains through low‐order Gaussian quadrature. As a result, the condition number of the stiffness matrix is reduced, and the numerical stability is improved. The integration subdomains are determined by the positions of particles, and the deformation of the domain is described by the motion of particles. During large deformations, the subdomains remain regular and undeformed; therefore, remeshing is not required, and the computational efficiency is improved. Within a total Lagrangian framework and combined with a Newton–Raphson iterative solution strategy, the proposed SCM efficiently solves the nonlinear equilibrium equations. A series of two‐ and three‐dimensional examples, including tension, compression, shear, bending, and torsion, are presented. The results show that the SCM can handle larger deformations than the FEM without convergence difficulties and can achieve improved accuracy and numerical stability compared with Reproducing Kernel Collocation Method (RKCM) as well as higher computational efficiency than Reproducing Kernel Particle Method (RKPM).