by S. Rudykh, K. Bhattacharya and G. deBotton, Proc. R. Soc. A 470: 20130618.
Stability of anisotropic magnetorheological elastomers in finite deformations: A micromechanical approach
Stephan Rudykh and Katia Bertoldi
Journal of the Mechanics and Physics of Solids 61 (2013) 949–967
Macroscopic instabilities of fiber reinforced composites undergoing large deformations are studied. Analytical predictions for the onset of instability are determined by application of a new variational estimate for the behavior of hyperelastic composites. The resulting, closed-form expressions, are compared with corresponding predictions of finite element simulations. The simulations are performed with 3-D models of periodic composites with hexagonal unit cell subjected to compression along the fibers as well as to non-aligned compression. Throughout, the analytical predictions for the failures of neo-Hookean and Gent composites are in agreement with the numerical simulations.
It is found that the critical stretch ratio for Gent composites is close to the one determined for neo-Hookean composites with similar volume fractions and contrasts between the phases properties.
During non-aligned compression the fibers rotate and hence, for some loading directions, the compression along the fibers never reaches the level at which loss of stability may occur.