Application of an anisotropic growth and remodelling formulation to computational structural design

Abstract

A classical structural optimisation problem consists of a problem-specific objective function which has to be minimised in consideration of particular constraints with respect to design and state variables. In this contribution we adopt a conceptually different approach for the design of a structure which is not based on a classical optimisation technique. Instead, we establish a constitutive micro-sphere-framework in combination with an energy-driven anisotropic microstructural growth formulation, which was originally proposed for the simulation of adaptation and remodelling phenomena in hard biological tissues such as bones.The goal of this contribution is to investigate this anisotropic growth formulation with a special emphasis on its application to structural design problems. To this end, four illustrative three-dimensional benchmark-type boundary value problems are discussed and compared qualitatively with the results obtained by classical structural optimisation strategies. The simulation results capture the densification effects and clearly identify the main load bearing regions. It turns out, that even though making use of this conceptually different growth formulation as compared to the procedures used in a classical structural optimisation context, we identify qualitatively very similar structures or rather regions of densification. Moreover, in contrast to common structural optimisation strategies, which mostly aim to optimise merely the size, shape or topology, our formulation also contains the improvement of the material itself, which—apart from the structural improvement—results in the generation of problem-specific local material anisotropy and textured evolution.