A novel Volume-Compensated Particle method (VCPM) for elasticity and plasticity analysis

A new Volume-Compensated Particle model (VCPM) is proposed for the general solution of elasticity and plasticity problems, which only requires the determination of uniaxial constitutive laws between particles. First, the entire simulation domain is discretized into mass particles. Pair-wise potential between particles and a multi-body potential among many neighboring particles are introduced for the volume conservation (i.e. Poisson's effect) under general loading conditions. Following this, the discussion for the determination of potential coefficients under elasticity is given and it is observed that the introduced multi-body potential term compensate the solid volumetric deformation using the classical lattice theory. Next, the discussion is extended to plasticity conditions and the determination of model parameters is discussed in details. Many classical solid mechanics problems are used to verify the proposed VCPM methodology. Finally, some conclusions and future work are given based on the proposed study.