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On the admissibility of an isotropic, smooth elastic continuum

Ostoja-Starzewski M.

Archives of Mechanics

2005

Vol. 57, nr 4

345--355

Many studies of elasticity of inhomogeneous materials - in both elastostatics and elastodynamics - assume the existence of locally isotropic, smooth stiffness tensor fields. We investigate the correctness of such a model in the simplest setup of anti-plane classical elasticity. We work with the concept of mesoscale (or apparent) moduli for a finite-size window placed in such a material, in accordance with the Hill condition for the Hooke law. The limit from mesoscale down to infinitesimal windows is admissible within the model of an assumed smooth, locally isotropic continuum. However, this limit is not admissible from the standpoint of a microstructure, and, in order to set up an inhomogeneous elastic medium, one must introduce its anisotropy. A separate argument against the local isotropy stems from the representation of a correlation function of a wide-sense stationary and isotropic random field, whose realizations are smooth stiffness tensor fields.

An energy-based yield criterion for solids of cubic elasticity and orthotropic limit state

Kowalczyk K., Ostrowska-Maciejewska J., Pęcherski R. B.

Archives of Mechanics

2003

Vol. 55, nr 5-6

431-448

The aim of the paper is to formulate a particular case of the J. Rychlewski yield condition for anisotropic linear elastic solids with Hooke's law and the limit tensor representing elastic range in the Mises yield condition under the assumption that different symmetry of elasticity tensors and the limit tensor appears. The elasticity tensor C is assumed to have cubic symmetry. The yield condition is based on the concept of stored elastic energy density, the theory of proper elastic states and energy orthogonal stress states developed by J. Rychlewski [1-3]. Three possible specifications of energy-based yield condition for cubic crystals are considered: the criterion based on the total distortion energy, the criterion based on the energy accumulated in the three proper states pertinent to cubic symmetry and the energy based criterion for cubic symmetry in elastic range and orthotropic symmetry in the limit state. Physical motivation, comparison with available experimental results and possible applications in mechanics of anisotropic solids as well as in nanomechanics are discussed.