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Molecular photo-switches as, e.g., azobenzene molecules allow, when embeddedinto a polymeric matrix, for photo-active polymer compounds respondingmechanically 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 seriesof earlier contributions, Oates et al. developed a successful continuumformulation for the coupled electric, electronic and mechanical problemcapturing azobenzene polymer compounds, thereby mainly focussing ongeometrically linearized kinematics. Building on that formulation, we hereexplore the variational setting of a geometrically exact continuum frameworkbased on Dirichlet's and Hamilton's principle as well as, noteworthy,Hamilton's equations. Thereby, when treating the dissipative case, we resort toincremental versions of the various variational problems via suitedincorporation of a dissipation potential. In particular, the Hamiltoniansetting of geometrically exact photo-mechanics is up to now largelyunder-explored even for the energetic case, arguably since the correspondingLagrangian is degenerate in Dirac's sense. Moreover, in general, theHamiltonian setting of dissipative dynamical systems is a matter of ongoingdebate per se. In this contribution, by advocating a novel incremental versionof the Hamiltonian setting exemplified for the dissipative case ofphoto-mechanics, we aim to also unify the variational approach to dissipativedynamical systems. Taken together, the variational setting of a geometricallyexact continuum framework of photo-mechanics paves the way for forthcomingtheoretical and numerical analyses.

A Geometrically Exact Continuum Framework for Light-Matter Interaction in Photo-Active Polymers I. Variational Setting