Multiscale Modeling of Complex Dynamic Problems: An Overview and Recent Developments

Abstract

International audienceMultiscale modeling aims to solve problems at the engineering (macro) scale while considering the complexity of the microstructure with minimum cost. Generally, two scales are considered in multiscale modeling: small scale, which is designed to capture the mechanical phenomena at the atomistic, molecular or molecular cluster level, and large scale which is connected to continuous description. For each scale, well-established numerical methods have been developed over the years to handle the relevant phenomena. As a first part of this paper, the most popular numerical methods, used at different scales, as well as the coupling approaches between them are classified, according to their features and applications, so that the place of those used in multiscale modeling can be distinguished. Subsequently, the class of concurrent discrete–continuum coupling approaches, which is well adapted for dynamic studies of complex multiscale problems, is reviewed. Several techniques used in this class are also detailed. Among them, the bridging domain (BD) technique is used to develop a discrete–continuum coupling approach, adapted for dynamic simulations, between the Discrete Element Method and the Constrained Natural Element Method (CNEM). This approach is applied to study the BD coupling parameters in dynamics. Several results giving more light on the setting of these parameters in practice are obtained

Harriaren egituraren zenbakizko eredua artezketan

“…Metodo diskretuak, partikula-kopuru handi baten mugimenduak konputatzen dituzten zenbakizko metodoak dira [15,16]. Dinamika molekularra (molecular dynamics, MD) eta DEM dira ezagunenak.…”

“…Integrazio-eskemak (c) iterazio bakoitzean zenbakizko integrazioa burutzen du, hurrengo iterazioan DE bakoitzak izango dituen posizio eta orientazio berriak kalkulatzeko. Tchamwa-Vielgosz eskema aukeratu da, konbergentzia hobetzeko eskemak zenbakizko moteltzea gehitzen baitio [16].…”

Multiresolution molecular mechanics: Adaptive analysis

“…Therefore, continuum approaches leave the physical underpinning of their theory weak [5]. Another reason is the fact that different physical phenomena are in play at each scale; for example, quantum effects are not considered at larger scales but they must be accounted for at the nanoscale [6]. A third reason is because the continuum does not allow the material length to vanish to zero; such as at a crack opening [7].…”

“…employs Perfectly Matched Layers (PML) at the handshake zone between molecular dynamics and continuum to damp out the high frequency waves that cannot be supported by the coarse continuum region [32]. For further information on the literature of multiscale methods, interested readers can see excellent review papers [6,13,[33][34][35][36][37][38][39][40][41].…”

Using the New Fibre Contact Element Method for Dynamic Structural Analysis

“…Methods based on discrete element formulations like the Discrete (or Distinct) Element Method (DEM) are a group of numerical methods in which the models consist in a set of bodies interacting with each other by contact laws. Cohesive links between bodies can be a set of normal springs, normal and transverse springs or beam elements (Jebahi et al 2014).…”