Cement manufacture accounts for about 5% of global carbon dioxide emissions, the single largest contribution of any man-made material. Despite this, research has shown that concrete is generally inefficiently used in the built environment. This fellowship will look to reduce the global environmental impact of concrete construction through a new method for the analysis of reinforced concrete structures that is well suited to producing the optimised designs that have the potential to significantly reduce material consumption. The new analysis method will be considered alongside practical construction processes, building on previous work by Dr Orr in this field, thus ensuring that the computationally optimised form can actually be built, and the research adopted, in industry. Most existing computational methods poorly predict the real behaviour of concrete structures, because their underlying mathematics assumes that the structure being analysed remains continuous as it deforms, yet a fundamental property of concrete is that it cracks (i.e. it does not remain continuous as it deforms). In contrast to finite element methods, this fellowship will develop a meshfree analysis process for concrete based on 'peridynamics'. The term 'peridynamic' (from 'near' and 'force') was coined by Dr Silling (see also statements of support) to describe meshfree analysis methods in solids. This new approach does not presume a continuous displacement field and instead models solid materials as a collection of particles held together by tiny forces, the value of which is a function of each particle's relative position. Displacement of a particle follows Newton's laws of motion, and is well suited to reinforced concrete since: 1) concrete really is a random arrangement of cement and aggregate particles; 2) failure is governed by tensile strain criteria, which is ideal as the only real way that concrete fails is in tension (all other failure modes in everyday design situations are a consequence of tensile failure) and the model can therefore accurately predict behaviour, and 3) since the elements fail progressively in tension, the peridynamic approach automatically models cracking behaviour, which is extremely difficult to model conventionally. A variety of force-displacement relationships can be defined to model the concrete, the reinforcement, and the reinforcement-concrete bond that together define the overall material response. The approach models the material as a massively redundant three-dimensional truss in which the randomly arranged particles are interconnected by elements of varying length. Although an optimal 'element density' has not yet been determined (see Section 2.4.1 in the case for support) proof of concept work has used tens of millions of particles and hundreds of millions of elements per cubic metre of concrete. From the simple rules and properties applied to these elements, all the complex behaviour of concrete can be predicted. Individual element definitions will be determined by laboratory tests and computational analysis, with both historic and new test data utilised. Crucially, the model has been shown in proof-of-concept work to be able to predict the cracking behaviour of concrete, overcoming a key computational challenge. Optimisation routines, in which material is placed only where it is needed, will then be integrated with the new analysis model to design low-carbon concrete structures. Consideration of the practical construction methods will also be given, building on previous work in this area by Dr Orr. The designs that result from such optimisation processes will have unconventional but completely buildable geometries (as evidenced in Dr Orr's previous work) - making them ideal for analysis using the proposed random elements approach.