Shear driven planar Couette and Taylor-like instabilities for a class of compressible isotropic elastic solids

• Published in: Zeitschrift für angewandte Mathematik und Physik Vol. 61; no. 3; pp. 537 - 554
• Main Authors: Fosdick, Roger, Foti, Pilade, Fraddosio, Aguinaldo, Marzano, Salvatore
• Format: Journal Article
• Language: English
• Published: Basel SP Birkhäuser Verlag Basel 01.06.2010
• Subjects: Engineering; Mathematical Methods in Physics; Theoretical and Applied Mechanics; Bifurcation; Non-linear elasticity; 74G60; 74B20; Material instabilities; 74B15
• ISSN: 0044-2275; 1420-9039
• DOI: 10.1007/s00033-009-0020-4

We study the possibility for an isotropic elastic body to support forms of instability induced by shear stress states which are reminiscent of the planar Couette and the Taylor–Couette patterns observed in the flow of viscous fluids. Here, we investigate the emergence of bifurcating periodic deformations for an infinitely long compressible elastic block confined between and attached to parallel plates which are subject to a relative shear displacement. We specialize our analysis by considering a generalized form of the Blatz–Ko strain energy function and show through numerical representative examples that planar Couette modes are always preferred with respect to the twisting Taylor–Couette modes. Finally, we introduce a suitably restricted form of the strong ellipticity condition for the incremental elasticity tensor and discuss its significance in this bifurcation problem.