Analytical and numerical solutions for the onset of cavitation in rubber under general loading conditions

O. LOPEZ-PAMIES; T. NAKAMURA; M. I. IDIART

Vancouver

Congreso; ASME 2010 International Mechanical Engineering Congress & Exposition; 2010

American Society of Mechanical Engineers

Physical evidence has shown that sufficiently large tensile loads can induce the suddenappearance of internal cavities in elastomeric solids. The occurrence of such instabilities, commonly referred to as cavitation, can be attributed to the growth of pre-existing defects into finite sizes. Because of its close connection with material failure initiation, the phenomenon of cavitation has received much attention from the materials and mechanics communities. Cavitation has also been a subject of interest in the mathematical community because its modeling has prompted the development of techniques to deal with a broad class of non-convex variational problems. While in recent years considerable progress has been made via energy minimization methods to establish existence results, fundamental problems regarding the quantitative prediction of the occurrence of cavitation in real elastomeric materials remain largely unresolved.In this work, we concern ourselves with studying the effect of loading triaxiality on the onset ofcavitation in rubber. Specifically, we derive analytical — by means of a new iterated homogenization method — and numerical — by means of the finite element method — results for the onset of cavitation in a Neo-Hookean solid when subjected to arbitrary 3D loading conditions. In this connection, it should be emphasized that the vast majority of cavitation studies to date have been almost exclusively limited to hydrostatic loading conditions, presumably because of the simpler tractability of this relevant but overly restricted case. However, the occurrence of cavitation is expected to depend very intricately on the triaxiality of the applied loading conditions, not just on the hydrostatic component.