A new total-Lagrangian smooth particle hydrodynamics approximation for the simulation of damage and fracture of ductile materials

Smooth particle hydrodynamics (SPH) is gaining popularity for the simulation of solids subjected to machining, wear, and impacts. Its attractiveness is due to its abilities to simulate problems, involving large deformations resulting from the absence of mesh as well as the development of the total-Lagrangian version of SPH (TLSPH) to solve tensile instabilities and an hourglass control algorithm to reduce rank-deficiency problems. However, when TLSPH is used with continuum damage mechanics, nonphysical residual forces can emerge and lead to instabilities. To solve this issue, the “pseudospring” method that scales the kernel function with damage was proposed by Chakraborty and Shaw. This method preserves local linear momentum and is stable for elastic solids but can generate instabilities when solids damage after experiencing high plastic strains. In this contribution, we present a new TLSPH approximation that conserves both linear and angular momenta, which is suitable for the simulation of damage and fracture of ductile materials. Using single-edge notched samples and tensile tests, we show that this approximation is stable whatever the stress/strain state and is in good agreement with finite element simulations and experimental results.