A procedure for obtaining a lower bound estimate of the critical load for arbitrary incompressible hyperelastic solids is presented. By considering a lower bound estimate for the Hadamard functional based on the Korn inequality, we establish sufficient conditions for the infinitesimal stability of a distorted configuration. We then determine an optimal lower bound estimate of the critical load in a monotonic loading process and specialize our procedure to the case of homogeneous deformations of incompressible, hyperelastic bodies. We apply our procedure to some representative dead-load boundary value problems for Mooney–Rivlin elastic solids and discuss its effectiveness and handiness for applications by comparing our results to other estimates.

A lower bound estimate of the critical load in bifurcation analysis for incompressible elastic solids / Fosdick, R.; Foti, Pilade; Fraddosio, Aguinaldo; Marzano, Salvatore; Piccioni, Mario Daniele. - In: MATHEMATICS AND MECHANICS OF SOLIDS. - ISSN 1081-2865. - 20:1(2014), pp. 53-79. [10.1177/1081286514543599]

A lower bound estimate of the critical load in bifurcation analysis for incompressible elastic solids

FOTI, Pilade;FRADDOSIO, Aguinaldo;MARZANO, Salvatore;PICCIONI, Mario Daniele
2014-01-01

Abstract

A procedure for obtaining a lower bound estimate of the critical load for arbitrary incompressible hyperelastic solids is presented. By considering a lower bound estimate for the Hadamard functional based on the Korn inequality, we establish sufficient conditions for the infinitesimal stability of a distorted configuration. We then determine an optimal lower bound estimate of the critical load in a monotonic loading process and specialize our procedure to the case of homogeneous deformations of incompressible, hyperelastic bodies. We apply our procedure to some representative dead-load boundary value problems for Mooney–Rivlin elastic solids and discuss its effectiveness and handiness for applications by comparing our results to other estimates.
2014
A lower bound estimate of the critical load in bifurcation analysis for incompressible elastic solids / Fosdick, R.; Foti, Pilade; Fraddosio, Aguinaldo; Marzano, Salvatore; Piccioni, Mario Daniele. - In: MATHEMATICS AND MECHANICS OF SOLIDS. - ISSN 1081-2865. - 20:1(2014), pp. 53-79. [10.1177/1081286514543599]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/60177
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