Microstructure Interpolation for Macroscopic Optimisation

Abstract

Recent advances in additive manufacturing now allow the physical construction of designs with features on the scale of tens of micrometres. It is impractical to design macroscopic objects with such feature sizes by hand, yet designs exploiting this new manufacturing ability can be produced through computational algorithms, such as with structural optimisation. While the computational ability of structural optimisation techniques is improving, the direct optimisation of a structure spanning two or more length scales is still dicult. Despite this, the new nescale manufacturing capability can be exploited using multiscale structural optimisation to nd the best high resolution design for a particular application.A multiscale design consists of microstructures which are repeatedly placed to create the design according to a macroscopic description. Previous work in multiscale optimisation has focused either on homogeneous microstructures that do not vary throughout the macroscopic design;analytically dened microstructures whose variation is well-known such as square lattices; or top-down multiscale design. In top-down multiscale design the macroscopic requirements at various locations prescribe the microstructural optimisation problems to be solved.We seek to solve some of the issues associated with top-down multiscale designs while allowing ii a wider space of microstructures than those that are analytically dened. We present a novel bottom-up method for multiscale structural optimisation over two length scales, which we call microstructure interpolation for macroscopic optimisation (MIMO). Shape interpolation, or morphing, between optimised microstructures produces a continuous set of microstructures that smoothly varies in both geometry and mechanical properties. The smooth set is used for macroscopic optimisation similar to the material distribution method (see Figure 1).The output of any multiscale optimisation method must be transformed into a single unied description before a physical product can be manufactured. This transformation requires smooth transitions between the various microstructures to be well dened; the smoothness is assumed but not enforced in many existing top-down methods. The MIMO approach trades the generality of existing multiscale methods for a stronger unied interpretation: while the space of allowed microstructures is diminished compared to existing top-down methods, the microstructures vary smoothly throughout the design. This smoothness makes it clear how the microstructures can be transitioned between neighbouring macroscopic elements ensuring connectedness in the unied two-scale design. The MIMO method is also straightforward to apply to problems where a functionally graded material is desired.In this thesis the MIMO method is developed and tested. We rstly perform shape interpolation between a number of elastically isotropic microstructures optimised for bulk modulus. They are parameterised by their volume fraction and vary in stiness. The interpolated microstructures have sm...