Strain and stress concentrations in elastomers at finite deformations: effects of strain-induced crystallization, filler reinforcement, and deformation rate

Abstract

Strain and stress concentrations are studied for elastomers at finite deformations. Effects of strain-induced crystallization, filler reinforcement and deformation rate are also investigated, and micromechanical descriptions are provided for the observed results. A simple problem is subjected to finite element simulations to show the results evidently. Material parameters are obtained from experimental tests conducted on standard tensile samples of filled and unfilled natural rubber (NR) as well as styrene–butadiene rubber (SBR) as crystallizing and non-crystallizing rubbers, respectively. In all simulations, the strain concentration factor \(K_E\) is shown to decrease monotonically where the reduction is more apparent as the filler content increases. At enough large stretches, \(K_E\) is higher for filled NRs compared to the unfilled NR which is not the case for SBR. The stress concentration factor \(K_S\) rises sharply by deformation of the samples. At large stretches, in the case of SBR, filler reinforcement only shifts the maximum value of \(K_S\) to a lower level of strain, while in the case of NR, it reduces \(K_S\) significantly. It is concluded that \(K_S\) can rise from its theoretical value remarkably which should be noticed in design purposes particularly for crystallizing elastomers. Furthermore, the effect of deformation rate is investigated employing a visco-hyperelastic constitutive law along with an associated VUMAT in ABAQUS/Explicit. It is observed that, at high deformation rates, \(K_E\) decreases. Despite the reduction in strain concentration, \(K_S\) would be higher which is not desired in design of mechanical parts.