Stress gradient continuum theory

Samuel Forest (1) , Karam Sab (2)

1 CDM - Centre des Matériaux
2 msa - Matériaux et Structures Architecturés

A stress gradient continuum theory is presented that fundamentally differs from the well-established strain gradient model. It is based on the assumption that the deviatoric part of the gradient of the Cauchy stress tensor can contribute to the free energy density of solid materials. It requires the introduction of so-called micro-displacement degrees of freedom in addition to the usual displacement components. An isotropic linear elasticity theory is worked out for two-dimensional stress gradient media. The analytical solution of a simple boundary value problem illustrates the essential differences between stress and strain gradient models. (C)2011 Elsevier Ltd. All rights reserved.

Mots clés: Strain gradient; Strain gradient elasticity; Stress gradient; Stress gradient elasticity; Micromorphic continuum; Size effect

Domaines: Mécanique [physics.med-ph]

Samuel Forest, Karam Sab. Stress gradient continuum theory. Mechanics Research Communications, 2012, 40, pp.16-25. ⟨10.1016/j.mechrescom.2011.12.002⟩. ⟨hal-00697585⟩