Investigation of aspects of an implicit dynamic material point method implementation

The Material Point Method (MPM) has been shown to be a useful Finite Element (FE) variant for simulating large-strain problems in geotechnical applications. This paper presents the development and implementation of an implicit dynamic MPM code, as opposed to the widely used explicit scheme. In this implementation, Newmark time integration is utilised to update the kinematic variables. The implicit MPM algorithm is tested via two well-known numerical examples: single-point vibration and continuum bar vibration, for which analytical solutions are also available. In terms of improving algorithm accuracy, kinematic variable updates and stress update order are discussed. In terms of energy conservation, it is suggested that care should be taken when applications with a small E/rho ratio are considered with implicit MPM, based on observations made for the two benchmark examples.