Ellipticity of gradient poroelasticity
Victor A. Eremeyev
Abstract
We discuss the ellipticity properties of an enhanced model of poroelastic continua called dilatational strain gradient elasticity. Within the theory there exists a deformation energy density given as a function of strains and gradient of dilatation. We show that the equilibrium equations are elliptic in the sense of Douglis–Nirenberg. These conditions are more general than the ordinary and strong ellipticity but keep almost all necessary properties of equilibrium equations. In particular, the loss of the ellipticity could be considered as a criterion of a strain localization or material instability.
Topics & Concepts
PoromechanicsElasticity (physics)Mathematical analysisStrain energy density functionInstabilityClassical mechanicsFinite strain theoryMathematicsPhysicsMechanicsMaterials scienceThermodynamicsPorous mediumComposite materialPorosityFinite element methodNonlocal and gradient elasticity in micro/nano structuresThermoelastic and Magnetoelastic PhenomenaElasticity and Material Modeling