Vol. 7, No. 5, 2012

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ISSN: 1559-3959
New invariants in the mechanics of deformable solids

Viktor V. Kuznetsov and Stanislav V. Levyakov

Vol. 7 (2012), No. 5, 461–467
Abstract

A system of invariants of symmetric three-dimensional tensors of second order is proposed in a new form. The system contains three classical invariants of a tensor and three new invariants which depend on the components of two or three tensors. The system proposed allows one to express the strain energy density of a linear elastic anisotropic body and virtual work done by internal stresses in terms of the invariants for any constitutive law of the material. Application of the invariants to the derivation of the tetrahedron finite element of anisotropic solids is discussed.

Keywords
tensors, invariants, anisotropic material, strain, stress, tetrahedral finite element
Milestones
Received: 20 January 2012
Accepted: 7 May 2012
Published: 15 November 2012
Authors
Viktor V. Kuznetsov
Department of Engineering Mathematics
Novosibirsk State Technical University
Novosibirsk, 630092
Russia
Stanislav V. Levyakov
Dapartment of Engineering Mathematics
Novosibirsk State Technical University
Novosibirsk, 630092
Russia