Analysis of three-dimensional micro-mechanical strain formulations for granular materials: Evaluation of accuracy

• Published in: International journal of solids and structures Vol. 47; no. 2; pp. 251 - 260
• Main Authors: Durán, O., Kruyt, N.P., Luding, S.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 15.01.2010; Elsevier
• Subjects: Cross-disciplinary physics: materials science; rheology; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Granular materials; Granular solids; Material form; Micromechanics; Physics; Rheology; Solid mechanics; Static elasticity (thermoelasticity...); Strain tensor; Structural and continuum mechanics; Micromechanics; Strain tensor; Granular materials; Continuum; Constitutive equation; Assembling; Stress tensor; Delaunay triangulation; Modelling; Discrete element method; Microstructure
• ISSN: 0020-7683; 1879-2146
• DOI: 10.1016/j.ijsolstr.2009.09.035

An important objective of recent research on micro-mechanics of granular materials is to develop macroscopic constitutive relations in terms of micro-mechanical quantities at inter-particle contacts. Although the micro-mechanical formulation of the stress tensor is well established, the corresponding formulation for the strain tensor has proven to be much more evasive, still being the subject of much discussion. In this paper, we study various micro-mechanical strain formulations for three-dimensional granular assemblies, following the work of Bagi in two dimensions ( Bagi, 2006). All of these formulations are either based on an equivalent continuum approach, or follow the best-fit approach. Their accuracy is evaluated by comparing their results, using data from Discrete Element Method simulations on periodic assemblies, to the macroscopic deformation. It is found that Bagi’s formulation ( Bagi, 1996), which is based on the Delaunay tessellation of space, is the most accurate. Furthermore, the best-fit formulation based on particle displacements only did unexpectedly well, in contrast to previously reported results for two-dimensional assemblies.