The incremental bulk modulus, Young's modulus and Poisson's ratio in nonlinear isotropic elasticity: Physically reasonable response

Scott, N. H. (2007) The incremental bulk modulus, Young's modulus and Poisson's ratio in nonlinear isotropic elasticity: Physically reasonable response. Mathematics and Mechanics of Solids, 12. pp. 526-542. ISSN 1081-2865

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Abstract

An incremental (or tangent) bulk modulus for finite isotropic elasticity is defined which compares an increment in hydrostatic pressure with the corresponding increment in relative volume. Its positivity provides a stringent criterion for physically reasonable response involving the second derivatives of the strain energy function. Also, an average (or secant) bulk modulus is defined by comparing the current stress with the relative volume change. The positivity of this bulk modulus provides a physically reasonable response criterion less stringent than the former. The concept of incremental bulk modulus is extended to anisotropic elasticity. For states of uniaxial tension an incremental Poisson's ratio and an incremental Young's modulus are similarly defined for nonlinear isotropic elasticity and have properties similar to those of the incremental bulk modulus. The incremental Poisson's ratios for the isotropic constraints of incompressibility, Bell, Ericksen, and constant area are considered. The incremental moduli are all evaluated for a specific example of the compressible neo-Hookean solid. Bounds on the ground state Lamé elastic moduli, assumed positive, are given which are sufficient to guarantee the positivity of the incremental bulk and Young's moduli for all strains. However, although the ground state Poisson's ratio is positive we find that the incremental Poisson's ratio becomes negative for large enough axial extensions.

Item Type:	Article
Additional Information:	mid:6311 dc:ueastatus:post-print formatted dc:ueahesastaffidentifier:0000757031438
Faculty \ School:	Faculty of Science Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Fluid and Solid Mechanics (former - to 2024)
Depositing User:	Vishal Gautam
Date Deposited:	01 Oct 2007
Last Modified:	28 Mar 2025 03:53
URI:	https://ueaeprints.uea.ac.uk/id/eprint/17000
DOI:	10.1177/1081286506064719

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