Due to their low Young's Modulus, high strength and suitability for additive manufacturing, non-toxic beta-type titanium alloys are emerging as next-generation biomaterials. We present novel experimental results that demonstrate significant variation of Young's Modulus with direction for selective laser melted (SLM) biocom-patible Ti-24Nb-4Zr-8Sn (Ti2448). Grain orientation data for SLM-processed Ti2448 is measured using electron backscatter diffraction. By assuming the grain orientations are fixed relative to the axes of the SLM build ma-chine, the measured grain orientation data is used to generate a detailed microstructural finite element model of the polycrystalline SLM-processed material. The computational model provides excellent predictions of the anisotropic properties of SLM-processed Ti2448, indicating that preferential grain orientations that form during SLM processing of Ti2448 cause the experimentally measured variation of the Young's Modulus. The results show that computational models are able to accurately predict the anisotropic Young's Modulus of poly-crystalline materials, and, in the context of biocompatible Ti2448 show how to tailor the modulus of SLM components by choosing the build orientation.

We design an anisotropic, multiparametric family of optimised microstructures. The microstructures are parametrised by their Young’s moduli in the three axial directions. The family is smooth, in the sense that the features are similar enough for shape interpolation of the microstructures and interpolation of material properties. We demonstrate how the microstructure family can be used to provide functionally graded materials that match required material property gradients. The microstructure family could also be utilised for multi-scale design of macrosocpic structures with spatially varying microstructure.

We present a new approach to designing three-dimensional, physically realizable porous femoral implants with spatially varying microstructures and effective material properties. We optimize over a simplified design domain to reduce shear stress at the bone-prosthetic interface with a constraint on the bone resorption measured using strain energy. This combination of objective and constraint aims to reduce implant failure and allows a detailed study of the implant designs obtained with a range of microstructure sets and parameters. The microstructure sets are either specified directly or constructed using shape interpolation between a finite number of microstructures optimized for multifunctional characteristics. We demonstrate that designs using varying microstructures outperform designs with a homogeneous microstructure for this femoral implant problem. Further, the choice of microstructure set has an impact on the objective values achieved and on the optimized implant designs. A proof-of-concept metal prototype fabricated via selective laser melting (SLM) demonstrates the manufacturability of designs obtained with our approach.

We present a method for multiple length scale structural optimisation. We first optimise isotropic microstructures for maximum bulk modulus at five solid fractions. Shape interpolation between these optimised microstructures produces a continuous set that smoothly varies in both geometry and mechanical properties. This smooth set is used for macroscopic optimisation via the material distribution method. The approach is computationally efficient and the geometric smoothness makes it clear how the microstructures can be transitioned between neighbouring elements. Performance comparisons are made to traditional structural optimisation for some example compliance optimisation problems. The interpolated microstructure designs are most advantageous for two dimensional problems involving multiple loading cases. In these cases, intermediate densities are utilised to more effectively distribute the load. In three dimensions, the method would be useful for a number of applications where specific microstructural requirements, such as a connected pore space, are needed within a multiple-scale design.

We explore the efficacy of network optimisation theory for minimum cut to quantify the evolution of granular fabric and its functionality as a transmission medium in deforming dense granular media. Our focus here is on force transmission in a sheared assembly of polydisperse particles, in a biaxial compression test under constant confining pressure. The granular fabric is examined with respect to the material's force-bearing contact network over that regime when the material has reached its residual strength, and is deforming under a near constant volume in the presence of a fully developed shear band. The structural evolution of the fabric is quantitatively characterized using a representative weighted-directed network that is similarly evolving as the sample deforms. The edges or links, representing the interparticle contacts, are each weighted by the capacity of the contact to transmit force: a scalar that depends solely on the relative motion of the contacting grains. In the large strain failure regime, the minimum cut which represents the bottleneck in force transmission is found to lie in the persistent shear band. This study paves the way for the future analysis of flows and force transmission through an evolving contact network and, in turn, the characterisation of the relationship between the material's contact topology and its capacity to transmit forces through its contact network.