On the microscopic foundations of elasticity.

摘要: The modeling of the elastic properties disordered or nanoscale solids requires foundations theory elasticity to be revisited, as one explores scales at which this may no longer hold. only cases for microscopically based derivations are documented (nearly) uniformly strained lattices. A microscopic approach is proposed. As a first step, exact expressions displacement, strain and stress fields derived. Conditions under linear constitutive relations hold studied theoretically numerically. It turns out that standard continuum not self-evident, applies above certain spatial scales, depend on details considered system boundary conditions. Possible relevance granular materials briefly discussed.