Vector-based discrete element method for solid elastic materials

This paper presents the vector-based discrete element method applied to two-dimensional elastic bodies, including details of formulation, its implementation on graphics processing units (GPUs) for accelerating simulations and validation cases. Simulation of elastic bodies has traditionally been realised through continuum-mechanics based methods such as finite elements while using discrete element methods have been restricted to small spatial and temporal scales due to the relatively high computational cost. The vector-based discrete element method, or V-model, overcomes the limitations of both traditional continuum-based mechanics and discrete element approaches to enable the possibility to model additional physics such as cracking, recombination and rupture in future studies. In this study we develop and compare CPU and GPU implementations for elastic bodies under deformation only with both static and dynamic validation studies to assess the performance of the method. Results demonstrate the ability of the method to model linear deformation within 1% of the analytical solution and provide qualitative representation of non-linear deformation. The spatial rate of convergence with decreasing particle size is demonstrated to be approximately first order with a methodology to clarify selection of time step size. This paper presents the first implementation of the V-model on GPUs to model elastic bodies demonstrating a 20x speed-up over the CPU implementation and is applied to the stochastic modelling of material properties in a deforming beam.