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.
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