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

Abstract:

http://www.springerlink.com/content/wx185g5301300521/fulltext.pdf

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.