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Contact problems for a finitely deformed incompressible elastic halfspace

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Abstract

This paper examines the class of problems related to the interaction between a finitely deformed incompressible elastic halfspace and contacting elements that include smooth, flat rigid indenters with elliptical and circular shapes and a thick plate of infinite extent. The contact between the finitely deformed elastic halfspace and the contacting elements is assumed to be bilateral. The interaction between both the rigid circular indenter and the finitely deformed halfspace is induced by a Mindlin force that acts at the interior of the halfspace regions and by exterior loads. Similar considerations apply for the contact between the flexible plate of infinite extent and the finitely deformed elastic halfspace. The theory of small deformations superposed on large deformations proposed by Green et al. (Proc R Soc Ser A 211:128–155, 1952) is used as the basis for the formulation of the problem, and results of potential theory and integral transform techniques are used to develop the analytical results. In particular, explicit results are presented for the displacement of the rigid elliptical indenter and the maximum deflection of the flexible plate induced by the Mindlin forces, when the finitely deformed halfspace region has a strain energy function of the Mooney–Rivlin form.

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  1. William Scott Professor and James McGill Professor, Department of Civil Engineering and Applied Mechanics, McGill University, 817 Sherbrooke Street West, Montreal, QC, H3A 0C3, Canada

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Communicated by Angela Madeo and Francois Nicot.

Dedicated to Professor Felix Darve on the occasion of his retirement.

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Selvadurai, A.P.S. Contact problems for a finitely deformed incompressible elastic halfspace. Continuum Mech. Thermodyn. 27, 287–304 (2015). https://doi.org/10.1007/s00161-014-0376-3

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