Considerations on incompressibility in linear elasticity

Federico, Salvatore and Grillo,, Alfio and Wittum, G. (2009) Considerations on incompressibility in linear elasticity. Il nuovo cimento C, 32 (1). pp. 81-87. ISSN 1826-9885

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The classical way to treat incompressible linear elastic materials is to use the inverse constitutive relationship (strain as a function of the stress), based on the compliance tensor, in place of the direct constitutive equation (stress as a function of strain), based on the elasticity (stiffness) tensor. This is because the elasticity tensor is affected by a diverging bulk modulus, requiring in order to allow the material to sustain any hydrostatic load, and is therefore not defined. In this work we show that there is a part of the elasticity tensor that can be saved also for incompressible materials, by filtering the components that deal with hydrostatic loads. The procedure is based on the treatment of incompressibility by means of the constant of isochoric motion, i.e. of conservation of volume, and fourth-order tensor algebra.

Item Type: Article
Uncontrolled Keywords: General theory of continuum mechanics of solids ; Static elasticity
Subjects: 600 Tecnologia - Scienze applicate > 620 Ingegneria e attivita' affini > 621 Fisica applicata; Ingegneria meccanica
Depositing User: Marina Spanti
Date Deposited: 24 Mar 2020 16:18
Last Modified: 24 Mar 2020 16:18

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