A structural optimisation viewpoint on growth phenomena

Evolutionary solid bodies undergoing changes of mass, of properties, and of shapes are considered in models of growth and adaptation and similarily in structural optimisation. A fundamental separation of different growth phenomena and a subsequent parametrisation using independent design variables for the amount of substance as well as for molar mass and molar volume facilitates an efficient formulation of the design space. Thus, the effects of design variations, i.e. change of amount of substance, on the variations of the structural response, i.e. the deformation in physical space, can be clearly described. Overall, a novel treatment of growth processes based on an evolution of the amount of substance is outlined. The parallelism of variations in physical and design space are highlighted and compared with the multiplicative decomposition of the deformation gradient into a growth and an elastic part incorporating an incompatible intermediate configuration. This drawback is overcome by a compatible manifold based on material points modelling the amount of substance outside of any geometrical space.