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[J]. Networks and Heterogeneous Media, 2007, 2(2): 279-311. doi: 10.3934/nhm.2007.2.279
Abstract
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.
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