New elastic behaviour arising from the unusual constitutive relation of nematic solids

Abstract

We sketch the unusual linear and non-linear constitutive relations for solids with an internal, orientational degree-of-freedom. Nematic elastomers are a realisation of such materials and are shown to obey the theorem of Golubovic and Lubensky (Phys. Rev. Lett. 63, 1082, 1989) which predicts that some of their shape changes must occur at zero energy cost. Examples are given of remarkable linear and non-linear elastic response: soft distortions, spontaneous shape change and elastic instabilities. The underlying symmetry arguments of GL are elaborated upon. The continuum elasticity mechanism for zero energy response of Olmsted (J. Phys. II Fr. 4, 2215, 1994) is extended to give a continuum explanation of semi-soft elastic response, that is where a small energy cost is required in real systems for the soft modes of ideal elastomers. The non-ideality and thermomechanical history required for semi-soft responses are explained. Experimental semi-soft stress–strain curves are compared with the theoretical relations.