Small Indentations of Rubber Blocks: Effect of Size and Shape of Block and of Lateral Compression

Abstract

Abstract Many gaskets and seals consist of a long rubber strip or thin-walled ring, placed on a flat rigid surface and indented by a flat-ended rigid indenter. We have examined their resistance to small indentations by FEA. They are treated as infinitely-long elastic blocks of rectangular cross-section, resting on a rigid frictionless base. The indentation stiffness is calculated for various ratios of indenter tip width to block width and to block thickness, using two restraint conditions on the outer surfaces: frictionless walls (zero outwards displacement), as for a gasket placed in a recess; or stress-free, as for a gasket with no lateral restraint. For an infinitely-wide and infinitely-thick block, the theoretical resistance to indentation is zero. For comparison, the indentation stiffness is calculated for cylindrical rubber blocks of varied radius and thickness, indented by a flat-ended cylindrical indenter. In this case the result for an infinitely-large block is finite. A second study treats indentation of a rubber block, pre-compressed in the surface plane. Biot showed that the indentation stiffness of a half-space becomes zero at a critical compression, about 33% for equi-biaxial compression and 44 % for plane strain compression, for both a neo-Hookean and a Mooney-Rivlin elastic solid. FEA calculations were made of the indentation stiffness of neo-Hookean blocks of various sizes, pre-compressed to various degrees. The results are compared with Biot's result. In an Appendix, the critical degree of compression is calculated for a more realistic strain energy function than either the neo-Hookean or the Mooney-Rivlin approximation.