Computational simulation of solids has experienced a rapid development since the formulation of the finite element method (FEM). However a number of problems cannot be properly solved by using the FEM because a severe mesh distortion in computations of Lagrangian scheme may arise for very large displacements, high speed impact, fragmentation, particulate solids, fluid-structure interaction, … leading to lack of consistency between the numerical and the physical problem. The discretization of the problem domain with nodal points without any mesh connectivity, would be useful to overcome this difficulty. Moreover the discrete nature of continuum matter – usually observed at the microscale – allows to adopt such a kind of discretization that is natural for granular materials and enables us to model very large deformations, handle damage – such as fracture, crushing, fragmentation, clustering – thanks to the variable interaction between particles. In the context of meshless methods, smoothed particle hydrodynamics (SPH) is a meshfree particle method based on Lagrangian formulation, that has been widely applied to different engineering fields. In the present paper a unified computational potential-based particle method for the mechanical simulation of continuum and granular materials under dynamic condition, is proposed and framed in the SPH-like approaches. The particle-particle and particle-boundary interaction is modelled through force functionals related to the nature of the material being analyzed (solid, granular, …); large geometrical changes of the mechanical system, such as fracture, clustering, granular flow can be easily modelled. Some examples are finally proposed and discussed to underline the potentiality of the approach.
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