2002/03/19 by I. Goldhirsch, C. Goldenberg
Engineering · Materials Science · Physics and Astronomy · #Geotechnical and Geomechanical Engineering #Nonlocal and gradient elasticity in micro/nano structures #Rock Mechanics and Modeling #cond-mat.dis-nn #cond-mat.mtrl-sci #cond-mat.stat-mech
paper · pdf · doi:10.1140/epje/i2002-10073-5
published as European Physical Journal E 9, 245 (2002) · 6 pages, 5 figures, LaTeX2e with svjour.cls and svepj.clo, submitted to EPJ E, minor error corrected in v2
arxiv created 2002/03/19 · openalex publication_date 2002/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The modeling of the elastic properties of disordered or nanoscale solids requires the foundations of the theory of elasticity to be revisited, as one explores scales at which this theory may no longer hold. The only cases for which microscopically based derivations of elasticity are documented are (nearly) uniformly strained lattices. A microscopic approach to elasticity is proposed. As a first step, microscopically exact expressions for the displacement, strain and stress fields are derived. Conditions under which linear elastic constitutive relations hold are studied theoretically and numerically. It turns out that standard continuum elasticity is not self-evident, and applies only above certain spatial scales, which depend on details of the considered system and boundary conditions. Possible relevance to granular materials is briefly discussed.