Constitutive modeling of three-dimensional monoatomic linear elastic multilattices

While simple lattices realize only the seven holohedral crystal classes, multilattices can realize all 32 crystal classes in three dimensions. For classical linear elasticity, from the constitutive point of view, the multilattice structure necessitates dependence of the energy apart from the strain tensor on the shift vectors as well. We give a generic expression of the energy for ( n + 1) monoatomic multilattices for all 32 crystal classes. We then focus on monoatomic 2-lattices and give the appropriate expression for the energy for all 29 types. The [Formula: see text] and [Formula: see text] phases of quartz can be viewed as realizations of a 3-lattice; we lay down expressions for the energy for both its phases. Our framework is valid for the geometrically and materially linear regime.