Concrete modelled using random elements

水泥生产约占全球二氧化碳排放量的5%，是所有人造材料中贡献最大的。尽管如此，研究表明，混凝土在建筑环境中的使用效率通常很低。该奖学金将通过一种新的钢筋混凝土结构分析方法来减少混凝土建筑对全球环境的影响，这种方法非常适合于生产具有显著减少材料消耗潜力的优化设计。新的分析方法将与实际施工过程一起考虑，建立在Orr博士之前在该领域的工作基础上，从而确保计算优化的形式可以实际建造，并在工业中采用研究。大多数现有的计算方法很难预测混凝土结构的真实行为，因为它们的基础数学假设被分析的结构在变形时保持连续，然而混凝土的一个基本特性是它会开裂（即它在变形时不保持连续）。与有限元方法相比，该奖学金将开发基于“周动力学”的混凝土无网格分析过程。术语“周动力学”（来自“近”和“力”）是由Silling博士创造的（另见支持声明），用于描述固体中的无网格分析方法。这种新方法没有假设一个连续的位移场，而是将固体材料建模为由微小力聚集在一起的颗粒的集合，其值是每个颗粒相对位置的函数。颗粒的位移遵循牛顿运动定律，并且非常适合于钢筋混凝土，因为：1)混凝土实际上是水泥和骨料颗粒的随机排列；2)破坏是由拉伸应变准则控制的，这是理想的，因为混凝土破坏的唯一真实方式是在张力下（日常设计情况下所有其他破坏模式都是拉伸破坏的结果），因此模型可以准确地预测行为，3)由于元件在张力下逐渐破坏，周动力方法自动模拟开裂行为，这是非常困难的传统模型。可以定义各种力-位移关系来模拟混凝土、钢筋和钢筋-混凝土粘结，这些关系共同定义了整体材料响应。该方法将材料建模为一个大量冗余的三维桁架，其中随机排列的颗粒通过不同长度的元素相互连接。虽然最佳的“元素密度”尚未确定（参见案例中的2.4.1节以获得支持），但概念验证工作已经使用了每立方米混凝土中数千万个颗粒和数亿个元素。从应用于这些元素的简单规则和属性，可以预测混凝土的所有复杂行为。单个元素的定义将通过实验室测试和计算分析来确定，同时使用历史和新的测试数据。至关重要的是，该模型已经在概念验证工作中被证明能够预测混凝土的开裂行为，克服了一个关键的计算挑战。优化程序，其中材料只放置在需要的地方，然后将与新的分析模型集成，以设计低碳混凝土结构。在Orr博士先前在这一领域的工作的基础上，还将考虑实际的施工方法。由这种优化过程产生的设计将具有非常规但完全可构建的几何形状（正如奥尔博士之前的工作所证明的那样）-使它们成为使用所提出的随机元素方法进行分析的理想选择。

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.