A domain decomposition method for granular dynamics using discrete elements and application to railway ballast

Abstract

The paper is devoted to the development of a non overlapping domain decomposition method suited to granular dynamics. The formulation and the efficiency of such a method are well established for structural mechanics. In order to extend this approach to granular systems a so-called primal splitting of the domain is chosen because it is a less intrusive method for software development.Once the interface problem is defined and the solver is slightly enriched with some extra numerical parameters, the method is tested on railway ballast simulations for improving the maintenance of railway tracks. Mathematics Subject ClassificationThe simulation of more and more realistic granular media leads to intensive computations. The size of the simulation increases both in term of number of bodies or particles and of duration of the process to be simulated. The increase of the computations concerns then both the space and the time, because a granular system often exhibits a complex dynamic behavior. Indeed dense collections of grains subjected to dynamic loadings require large-scale samples simulated on a long time to capture the local dynamic crises responsible of the global behavior of the system. Many applications involve such dense assemblies as the sand piles, dunes, blocky rocks, powders. We are here specially interested in a class of applications for which the connectivity of the grains remains almost stable during the studied process, as the masonry of monuments (before collapse) or the railway ballast.The denominations of 'discrete element methods' and 'distinct element methods' (DEM) are commonly used to refer to the pioneering approach of Cundall [11], today implemented in a large range of commercial pieces of software intended to handle non-interpenetrability. Also, because the computation techniques applied in such implementations are close to those of molecular simulations, the denomination of 'molecular dynamics' (MD) method is also used, specially in the domain of granular mechanics [16]. Such an approach is based on regularization strategies both for the dynamics and the interactions between grains. First, the non-interpenetrability constraints are replaced by some stiff 'elastic' repulsion laws which

High performance computing of discrete nonsmooth contact dynamics with domain decomposition

“…Several domain decomposition approaches have been proposed for contact problems, see [8,3,10,9,4,24,3] amongst others, but a few are concerned with multiple contacts in granular media (for an algebraic-like partition, see [17], and for a geometric partitioning of the discrete granular domain, see [5,2,23,30]). Here, we focus on the comparison of two formulations, one similar to FETI approaches, the other closer to additive Schwarz approaches, and of two implementations of the underlying communication scheme.…”

“…The overlapping is rendered by the lack of partition of the unity in (17) in comparison with (7). Here the domain partitioning defines a minimal overlapping between subdomains, since the dynamical operators M E , for E = 1, ..., n sd duplicate the contribution of the interface grains.…”

“…This differs also from the dual partitioning developed in [17], for which a non smooth problem similar to (24) is defined on the global interface composed of contacts, as a standard subdomain. Impulses acting on the boundary grains of a subdomain related to contacts belonging to interconnected subdomains are then taken as boundary conditions without defining a global interface problem as in the NSCDD method.…”

“…The approach described in [23] mainly uses an asynchronous distributed-memory Non-Linear Gauss-Seidel solver (close to the one used in [17] for a synchronous solver and in [18] for an asynchronous version, both for shared-memory architectures. They correspond to the algebraic partitioning of the reduced dynamics, i.e.…”

Effect of Rolling Resistance in Dem Models With Spherical Bodies

“…It has been reported that shape of the grains is of extreme importance [8]. Therefore, complex and realistic shapes are often used in simulation, for example discrete ellipsoids [4], tetrahedrons [18], polyhedrons [1,5] or clumps of smaller spherical particles [6,7,17].…”