Theory and numerics of geometrically non-linear open system mechanics

The present contribution aims at deriving a general theoretical and numerical framework for open system thermodynamics. The balance equations for open systems di er from the classical balance equations by additional terms arising from possible local changes in mass. In contrast to existing formulations, these changes not only originate from additional mass sources or sinks but also from a possible in- or out ux of matter. Constitutive equations for the mass source and the mass ux are discussed for the particular model problem of bone remodelling in hard tissue mechanics. Particular emphasis is dedicated to the spatial discretization of the coupled system of the balance of mass and momentum. To this end we suggest a geometrically non-linear monolithic nite element based solution technique introducing the density and the deformation map as primary unknowns. It is supplemented by the consistent linearization of the governing equations. The resulting algorithm is validated qualitatively for classical examples from structural mechanics as well as for biomechanical applications with particular focus on the functional adaption of bones. It turns out that, owing to the additional incorporation of the mass ux, the proposed model is able to simulate size e ects typically encountered in microstructural materials such as openpored cellular solids, e.g. bones