Deformation and stability of compressible rubber O-rings

Abstract

BackgroundIn rubber elastic models it is generally assumed that the bulk modulus is infinite, resulting in a material that does not change its volume and a pressure that cannot be evaluated from the material model.MethodsWe have developed a general procedure that incorporates a finite bulk modulus. Using the developed framework accurate results can be obtained without the need for special finite elements. It gives the correct results even in the limit of infinite bulk modulus.ResultsIt was shown that material compressibility causes additional stresses mostly associated with an additional hydrostatic pressure. It was also demonstrated that once a bulk modulus is included in the constitutive model, stability analyses of rubber-like materials subject to large deformation become numerically stable and accurate. Hence, it is essential to use compressibility with neo-Hookean solids for accurate stress and lifing predictions. The role of twist in the formation of stress-strain states in rubber O-rings has been evaluated. Such a twist causes elastic instabilities resulting in highly deformed O-ring shapes. Numerical analysis using compressible material models predicted the stable deformed states that O-ring do not remain circular. The ring is buckled and reaches a “chair” –type non-planar shape just beyond inside-out twist.ConclusionsThe results indicate that elastic material volume change causes additional stresses mostly associated with an additional hydrostatic pressure. Simulations using various rubber elastic models showed that allowing volume changes allows accurate stress state prediction, reduces numerical difficulties and improves the numerical stability.