A Novel TLSPH Approach for Modeling Damage in Elastic Solids

Crack initiation and propagation present significant challenges in solid mechanics, necessitating reliable and efficient computational methods for accurate simulations. Traditional mesh-based approaches face limitations such as computational inefficiency and mesh dependence. Meshless methods, particularly smoothed particle hydrodynamics (SPH), offer an alternative by eliminating mesh-related issues and simplifying the simulation of discontinuities. SPH, originally developed for astrophysical applications, has been successfully adapted for fluid and solid mechanics, including fracture mechanics. This article introduces a total Lagrangian smoothed particle hydrodynamics (TLSPH) model for crack modeling, addressing the limitations of existing SPH and other methods. In proposed method, interactions between particle pairs are characterized by “stretch” and an interaction is eliminated when the stretch exceeds a threshold value. The mitigation of damage-induced instabilities is performed via enhancing the numerical diffusion and applying velocity filtering in damaged area. The capability of in-house TLSPH code is first demonstrated through simulations of 2D and 3D undamaged cantilever beams under large deformations. The accuracy of the novel damage model is validated by modeling Kalthoff-Winkler experiment in 2D and 3D and dynamic crack branching case in 2D. The results highlight the effectiveness and computational efficiency of the proposed TLSPH damage model.