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2010•Engineering MechanicsRequires access

ON CONSTITUTIVE EQUATIONS OF ISOTROPIC NON-LINEAR ELASTIC MEDIUM

Huang Zhi-zhong

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Abstract

By means of tensor function,conjugate variables of stress and strain,the different constitutive equations of isotropic non-linear elastic medium and the relations between different equation forms are studied.The constitutive equations of non-linear Green elastic medium in terms of tensor invariables and scalar invariables are deduced.It is proved that the equations are complete and irreducible.Finally the constitutive equations are applied to rubber materials as an illustration of engineering practice.

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What this paper is about

By means of tensor function,conjugate variables of stress and strain,the different constitutive equations of isotropic non-linear elastic medium and the relations between different equation forms are studied.The constitutive equations of non-linear Green elastic medium in terms of tensor invariables and scalar invariables are deduced.It is proved that the equations are complete and irreducible.Finally the constitutive equations are applied to rubber materials as an illustration of engineering practice.

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Available abstract

By means of tensor function,conjugate variables of stress and strain,the different constitutive equations of isotropic non-linear elastic medium and the relations between different equation forms are studied.The constitutive equations of non-linear Green elastic medium in terms of tensor invariables and scalar invariables are deduced.It is proved that the equations are complete and irreducible.Finally the constitutive equations are applied to rubber materials as an illustration of engineering practice.

Key concepts: Cauchy elastic material, Constitutive equation, Isotropy, Cauchy stress tensor, Levy–Mises equations, Scalar (mathematics), Linear elasticity, Mathematical analysis

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