Finite element implementation of a non-local particle method for elasticity and fracture analysis

• A new finite element implementation scheme for non-local particle methods is proposed.
• 10-particles element is developed to describe both local pair-wise and non-local multi-body particle interactions.The new scheme is verified to be accurate, efficient and robust in simulating elastic and fracture problems.

A finite element formulation for a non-local particle method is proposed in this paper for elasticity and fracture analysis of 2D solids. The model is based on a new particle method which incorporates a non-local multi-body particle interaction into the conventional pair-wise particle interactions. The non-local particle method is capable of modeling solids with arbitrary Poisson׳s ratio. Finite element formulation is proposed for the implicit solution of elasticity and fracture problems under static/quasi-static conditions, which is very efficient compared to the direct explicit solution in particle dynamics. Energy minimization principle is used to develop a new finite element with both local pair-wise and non-local multi-body particle interactions. The developed finite element formulation is verified with classical finite element simulation of some benchmark problems. Fracture simulation using the proposed particle-based finite element formulation is demonstrated. Some conclusions and future work is drawn based on the current investigation.