LAUSR

Abstract In this work, the Finite Particle Method (FPM) which is a typical meshfree particle method is formulated for static deformation and plastic flow problems. The novel formulation utilizes the Lagrangian-type kernel, which guarantees the method being free from the tension instability. A pseudo-viscosity is introduced into the particle system to prevent the hourglass phenomenon in the numerical procedure. The nonlinear system of governing equations is solved with implicit time integration scheme. For numerical efficiency the Jacobian-Free Newton-Krylov (JFNK) method is applied to obtain the solution for each time step. Numerical examples are provided to demonstrate the validity and the effectiveness of the method in capturing finite deformation with moderate distortion.