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

Abstract

Summary 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. Copyright © 2015 John Wiley & Sons, Ltd.

A unified approach for static and dynamic fracture failure in solids and granular materials by a particle method

“…(5) provides a tangential force as the minimum value between the dynamic friction and the viscosity action. The present authors have verified that the function infl ( ) a r , for a given particles arrangement, is almost independent of the particles arrangement in the space and depends on infl r only [24]. On the other hand, the Poisson's coefficient tends to 1/3 as the influence radius increases, irrespective of the particles layout used to represent the domain of the problem of interest.…”

A Particle-Based Cohesive Crack Model for Brittle Fracture Problems

“…Effective numerical modeling of the fracture process is important for assessing the safety, reliability, and structural performance of engineering structures. For modeling the fracture process, a number of numerical methods are often employed, such as the finite element method (FEM) [ 1 ], the extended finite element method (XFEM) [ 2 ], meshless methods [ 3 ], the particle finite element method (PFEM) [ 4 ], molecular dynamics [ 5 ], the particle method [ 6 ], and atomistic methods [ 7 , 8 ]. Among them, the atomistic method is able to provide great insight into the nanoscopic mechanism of fracture initiation and propagation since fracture problems essentially take place at the atomic level of materials by means of the breakage of bonds [ 9 , 10 ].…”

Modelling of Granular Fracture in Polycrystalline Materials Using Ordinary State-Based Peridynamics

“…CPM is especially useful for complex fracture patterns such as crack branching and coalescence. Other promising techniques used for fracture modelling include smoothed particle hydrodynamics [36,37,38], molecular dynamics [39], the discrete element method [40], and the force potential-based particle method [41]. Although the aforementioned approaches may have certain advantages for particular conditions, in this study peridynamics was chosen for modelling granular fracture in polycrystalline materials.…”