New invariants in the mechanics of deformable solids

Kuznetsov, Viktor; Levyakov, Stanislav

doi:10.2140/jomms.2012.7.461

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New invariants in the mechanics of deformable solids

Viktor V. Kuznetsov and Stanislav V. Levyakov

Vol. 7 (2012), No. 5, 461–467

DOI: 10.2140/jomms.2012.7.461

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

Vol. 7, No. 5, 2012

Viktor V. Kuznetsov and Stanislav V. Levyakov

Abstract

Keywords

Milestones

Authors