Unusual field-coupled nonlinear continuum mechanics of smart materials

A set of anisotropic constitutive relations is developed using nonlinear continuum mechanics to model chemical and field-coupled material behavior in a relatively broad range of smart materials. A Landau-based free energy function is formulated and numerically implemented to elucidate how finite deformation and crystal anisotropy affect field-coupled deformation and how deformation affects microstructure evolution. Rotationally invariant order parameters are introduced within the Landau energy function to illustrate how field-coupled mechanics occurs without introducing explicit phenomenological parameters. Spontaneous deformation due to scalar, vector, and tensor order parameters is quantified. It is shown that both the scalar and vector order parameters induce hydrostatic deformation, while the second-order tensor order parameter induces a range of different anisotropic spontaneous deformation states. Numerical simulations are given, which illustrate unusual field-coupled microstructure evolution for a select number of active materials in comparison with data in the literature. The materials simulated range from chemically responsive glassy polymer networks, soft polydomain liquid crystal elastomers, to tetragonal phase ferroelectric materials. The results illustrate that finite deformation continuum mechanics can be useful in modeling many unusual field-coupled, anisotropic constitutive relations without introducing explicit coupling parameters.