Open Access

ARTICLE

A boundary element formulation for incremental nonlinear elastic deformation of compressible solids

Sergia Colli¹, Massimiliano Gei¹, Davide Bigoni^1,2
1 Department of Mechanical and Structural Engineering, University of Trento, Via Mesiano 77, I38123, Trento, Italy.
2 Corresponding author, Tel. +39 0461 882507; Fax: +39 0461 882599; Web-site: http://www.ing.unitn.it/∼bigoni; E-mail: bigoni@ing.unitn.it.

Computer Modeling in Engineering & Sciences 2009, 40(1), 29-62. https://doi.org/10.3970/cmes.2009.040.029

Abstract

Incremental plane strain deformations superimposed upon a uniformly stressed and deformed nonlinear elastic (compressible) body are treated by developing {\it ad hoc} boundary integral equations that, discretized, lead to a novel boundary element technique. The approach is a generalization to compressible elasticity of results obtained by Brun, Capuani, and Bigoni (2003, Comput. Methods Appl. Mech. Engrg. 192, 2461-2479), and is based on a Green's function here obtained through the plane-wave expansion method. New expressions for Green's tractions are determined, where singular terms are solved in closed form, a feature permitting the development of a optimized numerical code. An application of the presented formulation, namely, bifurcation of a compressible Mooney-Rivlin rectangular block, highlights the strengths of the approach.

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Keywords

Green's function, boundary integral equations, shear bands, bifurcation, instability.

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