Stress integration and mesh refinement for large deformation in geomechanics

TLDR

Large‑deformation analyses of hardening materials rely on stress integration schemes, with the total‑Lagrangian, updated‑Lagrangian, and arbitrary Lagrangian–Eulerian methods commonly used, each having multiple integration variants. The study proposes an operator‑split ALE method that incorporates a novel mesh‑refinement strategy. The method re‑analyses the domain with linear elasticity using prescribed boundary displacements to generate a refined mesh for the second ALE step, and compares the performance of TL, UL, and ALE on classic geotechnical benchmarks. The operator‑split ALE scheme is objective, and its repeated elastic analysis yields a more efficient mesh refinement than conventional mesh generation, applicable to arbitrary dimensions and topologies. © 2005 John Wiley & Sons, Ltd.

Abstract

Abstract This paper first discusses alternative stress integration schemes in numerical solutions to large‐ deformation problems in hardening materials. Three common numerical methods, i.e. the total‐Lagrangian (TL), the updated‐Lagrangian (UL) and the arbitrary Lagrangian–Eulerian (ALE) methods, are discussed. The UL and the ALE methods are further complicated with three different stress integration schemes. The objectivity of these schemes is discussed. The ALE method presented in this paper is based on the operator‐split technique where the analysis is carried out in two steps; an UL step followed by an Eulerian step. This paper also introduces a new method for mesh refinement in the ALE method. Using the known displacements at domain boundaries and material interfaces as prescribed displacements, the problem is re‐analysed by assuming linear elasticity and the deformed mesh resulting from such an analysis is then used as the new mesh in the second step of the ALE method. It is shown that this repeated elastic analysis is actually more efficient than mesh generation and it can be used for general cases regardless of problem dimension and problem topology. The relative performance of the TL, UL and ALE methods is investigated through the analyses of some classic geotechnical problems. Copyright © 2005 John Wiley & Sons, Ltd.