### Abstract

We compute the large-body and the small-particle Gamma-limit of a family of energies for nematic elastomers. We work under the assumption of small deformations (linearized kinematics) and consider both compressible and incompressible materials. In the large-body asymptotics, even if we describe the local orientation of the liquid crystal molecules according to the model of perfect order (Frank theory), we prove that we obtain a fully biaxial nematic texture (that of the de Gennes theory) as a by-product of the relaxation phenomenon connected to Gamma-convergence. In the case of small particles, we show that formation of new microstructure is not possible, and we describe the map of minimizers of the Gamma-limit as the phase diagram of the mechanical model.

Original language | English |
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Pages (from-to) | 2354-2383 |

Number of pages | 30 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 43 |

Issue number | 5 |

DOIs | |

Publication status | Published - Nov 21 2011 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Analysis
- Computational Mathematics
- Applied Mathematics