  Molecular photo-switches as, e.g., azobenzene molecules allow, when embedded
into a polymeric matrix, for photo-active polymer compounds responding
mechanically when exposed to light of certain wavelength. Photo-mechanics, i.e.
light-matter interaction in photo-active polymers holds great promise for,
e.g., remote and contact-free activation of photo-driven actuators. In a series
of earlier contributions, Oates et al. developed a successful continuum
formulation for the coupled electric, electronic and mechanical problem
capturing azobenzene polymer compounds, thereby mainly focussing on
geometrically linearized kinematics. Building on that formulation, we here
explore the variational setting of a geometrically exact continuum framework
based on Dirichlet's and Hamilton's principle as well as, noteworthy,
Hamilton's equations. Thereby, when treating the dissipative case, we resort to
incremental versions of the various variational problems via suited
incorporation of a dissipation potential. In particular, the Hamiltonian
setting of geometrically exact photo-mechanics is up to now largely
under-explored even for the energetic case, arguably since the corresponding
Lagrangian is degenerate in Dirac's sense. Moreover, in general, the
Hamiltonian setting of dissipative dynamical systems is a matter of ongoing
debate per se. In this contribution, by advocating a novel incremental version
of the Hamiltonian setting exemplified for the dissipative case of
photo-mechanics, we aim to also unify the variational approach to dissipative
dynamical systems. Taken together, the variational setting of a geometrically
exact continuum framework of photo-mechanics paves the way for forthcoming
theoretical and numerical analyses.
