A stable and convergent Lagrangian particle method with multiple nodal stress points for large strain and material failure analyses in manufacturing processes

This paper presents a new Lagrangian particle method for the simulation of manufacturing processes involving large strain and material failure. The starting point is to introduce some stabilization terms as a means of circumventing the onerous zero-energy deformation in the Lagrangian particle method. The stabilization terms are derived from the approximate strain vector by the combination of a constant and strain derivatives, which leads to a multiple nodal stress points algorithm for stabilization. The resultant stabilized Lagrangian particle formulation is a non-residual type that renders no artificial control parameters in the stabilization procedure. Subsequently, the stabilized formulation is supplemented by an adaptive anisotropic Lagrangian kernel and a bond-based material failure criterion to sufficiently prevent the tension instability and excessive straining problems. Several numerical examples are presented to examine the effectiveness and accuracy of the proposed method for modeling large strain and material failure in manufacturing processes.