Total Lagrangian smoothed particle hydrodynamics for large deformation problems considering Green–Naghdi stress rate

This paper presents the integration of Green–Naghdi’s theory for large deformation elasto-plasticity with Total Lagrangian Smoothed Particle Hydrodynamics (TLSPH) to handle problems in structural dynamic simulations. While the finite element method often encounters challenges such as mesh distortion in large deformation scenarios, the meshless nature of TLSPH effectively handles complex large deformations and structural dynamics. By incorporating Green–Naghdi theory into TLSPH, the proposed method ensures symmetric stress tensors and mitigates spurious stresses by reducing unnecessary skew-symmetric stress components. Through the proposed method, large deformation problems are effectively managed. The method is validated through numerical examples and comparisons with commercial software and experimental data, demonstrating its effectiveness in capturing the large deformation behavior of materials.