On the principle of complementary virtual work in the non-linear theory of elasticity

Bertóti, Edgár (2000) On the principle of complementary virtual work in the non-linear theory of elasticity. JOURNAL OF COMPUTATIONAL AND APPLIED MECHANICS, 1 (2). pp. 109-122. ISSN 1586-2070

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Abstract

A generalization of the principle of complementary virtual work in the current configuration is proposed by introducing the orthogonal rotation tensor as an independent variable. Applicability of the modified principle to (numerical) analysis of non-linear elasticity problems assumes the existence of an invertible constitutive relation between the Cauchy stress tensor and the left stretch tensor. It is shown that when transforming it into the reference configuration, the generalized principle of complementary virtual work is equivalent to Fraeijs de Veubeke's two-field dual-mixed principle, provided an appropriate constitutive equation between the Biot stress tensor and the right stretch tensor is taken into account. The independent equation system of non-linear elasticity in terms of stresses and rotations is derived, both in the current and reference configurations, using six independent first-order stress functions.

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