An ALE method for penetration into sand utilizing optimization-based mesh motion

Development and experimental validation of an arbitrary Lagrangian‐Eulerian (ALE) method for soil mechanics

“…This section introduces basic equations of ALE continuum mechanics and then outlines the steps of the implemented operator-split ALE finite element solution procedure [15]. A full description is beyond the scope of the paper and is given in [17].…”

“…This process is called rezoning or adaptive remeshing [1] and is a common feature of modern nonlinear Lagrangian finite element codes [2]. With the objective of overcoming the drawbacks of traditional FEM approaches, advanced numerical modeling and simulation tools have received much attention during the past decade, for example discrete element methods [3], [4], material point methods [5], [6], smoothedparticle hydrodynamics [7], [8], coupled Eulerian-Lagrange (CEL) methods [2], [9], [10], and arbitrary Lagrangian-Eulerian (ALE) methods [11]− [15]. These methods were originally developed in the 1960s and 1970s, mostly for applications in computational physics, and often involve sophisticated non-standard algorithms; see [16] for an overview.…”

Contribution to the Non-Lagrangian Formulation of Geotechnical and Geomechanical Processes

“…Concerning the modeling of geotechnical and geomechanical processes, several non-Lagrangian approaches are documented in the literature. These may be classified into SALE formulations using direct approximation of the convective terms [121,122,146], SALE formulations using first-order [14,16,19,20,61] and secondorder advection algorithms [102,151], and Eulerian formulations using advection algorithms. The order of the advection algorithm refers to the maximum accuracy with which the spatial distribution of the solution variable is approximated.…”

Homogeneous equilibrium model for geomechanical multi-material flow with compressible constituents

“…The ALE formulation [104,6,26] introduces a reference domain which may move in space at an arbitrary velocity w generally different from the material velocity v. For w = v the ALE formulation reduces to the Lagrangian formulation, and for w = 0 the Eulerian formulation is obtained. The Eulerian formulation of the set of equations (58) can be written in compact form [26,30] ∂q ∂t methods apply a Lagrange-remap strategy [6,26,27]. Conceptually, (83) is split into two sets of equations which are solved sequentially: Fig.…”

“…The research presented in this paper addresses multi-material flow situations encountered in geomechanics and geotechnical engineering. Examples are natural hazards like landslides [18,19], avalanches and debris flows [20,21,22], liquefaction-induced soil failure [23,24], and elementary installation processes like digging, injection, mixing, displacement, or penetration [25,26,27,28,29]. Schematic views are shown in Fig.…”