Dynamic behaviour of solids and granular materials: a force potential-based particle method

The discrete nature of matter – typically recognised at the microscale – is usually replaced by a continuous model at the macroscale. However, the discrete model of solids can be adopted also at the macroscopic scale, still enabling the description of the main mechanical phenomena; furthermore, the discrete approach, tailored to the scale of observation of interest, allows the multiscale study of solids. The paper presents a general computational particle method – whose particle interaction is modelled through force functionals, related to the nature of the material being analysed (solid, granular or their interaction) – that represents a unified computational mechanical model suitable for a wide class of problems. This force interaction evaluation is also adopted for the boundary-particle and for the particle-particle contacts. It allows to easily assess the dynamic response and failure of solids, granular or their interaction, avoiding the drawbacks of continuous approaches that typically require complex remeshing operations, stress field enrichment or the introduction of discontinuous displacement field for the solution of such problems. Some examples, aimed at demonstrating the versatility of the approach, are finally presented: in particular, the failure of solids under impact and confined particles flows is simulated and the related results discussed.