  A thermomechanical, polar continuum formulation under finite strains is
proposed for anisotropic materials using a multiplicative decomposition of the
deformation gradient. First, the kinematics and conservation laws for three
dimensional, polar and non-polar continua are obtained. Next, these kinematics
are connected to their corresponding counterparts for surface continua based on
Kirchhoff-Love kinematics. Likewise, the conservation laws for Kirchhoff-Love
shells are derived from their three dimensional counterparts. From this, the
weak forms are obtained for three dimensional non-polar continua and
Kirchhoff-Love shells. These formulations are expressed in tensorial form so
that they can be used in both curvilinear and Cartesian coordinates. They can
be used to model anisotropic crystals and soft biological materials, and they
can be extended to other field equations, like Maxwell's equations to model
thermo-electro-magneto-mechanical materials.
