June  2007, 2(2): 279-311. doi: 10.3934/nhm.2007.2.279

Ideally soft nematic elastomers

1. 

Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy

Received  March 2006 Revised  January 2007 Published  March 2007

The paper examines a class of energies $W$ of nematic elastomers that exhibit ideally soft behavior. These are generalizations of the neo-classical energy function proposed by Bladon, Terentjev & Warner [7]. The effective energy (quasiconvexification) of $W$ is calculated for a large subclass of considered energies. Within the subclass, the rank 1 convex, quasiconvex, and polyconvex envelopes coincide and reduce to the largest function below $W$ that satisfies the Baker–Ericksen inequalities. Compressible cases are included. The effective energy displays three regimes: one fluid-like, one partially fluid-like and one hard, as established by DeSimone & Dolzmann [20] for the energy function of Bladon, Terentjev & Warner. Ideally soft deformation modes are shown to arise.
Citation: M. Silhavý. Ideally soft nematic elastomers. Networks and Heterogeneous Media, 2007, 2 (2) : 279-311. doi: 10.3934/nhm.2007.2.279
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