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

Sergia Colli1, Massimiliano Gei1, Davide Bigoni1,2
Department of Mechanical and Structural Engineering, University of Trento, Via Mesiano 77, I38123, Trento, Italy.
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.

Keywords

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

Cite This Article

Colli, S., Gei, M., Bigoni, D. (2009). A boundary element formulation for incremental nonlinear elastic deformation of compressible solids. CMES-Computer Modeling in Engineering & Sciences, 40(1), 29–62.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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