On the development of a hybrid particle method using the differential formulation

An extension of the Dual Particle Dynamics (DPD) method is introduced for the differential (strong) formulation in solid mechanics. Similar to the DPD, the new approach, termed the Hybrid Particle Method, employs two different types of particles or interpolation points, namely the motion points (mps) and stress points (sps). Momentum is balanced at the mps, while stresses and other field variables are calculated and tracked at both the sps and mps. A new momentum mixture rule is introduced which allows the Hybrid Particle Method to span the entire range from pure co-locational (mps only) to the pure DPD as well as variations and combinations of the two approaches. In one dimension, the accuracies of both the momentum balance and stress calculations are examined in detail. Co-locational (mps only) approaches are shown to be extremely noisy for wave propagation problems. However, accurate stresses are obtained at both mps and sps. A series of one dimensional results are shown to demonstrate the validity of the formulation. A discussion on the Hybrid Particle Method for two- and three-dimensional analyses is given, including some preliminary two-dimensional results. Issues concerning the modeling of very large deformations using the Hybrid Particle Method are also outlined.