Multi-Scale Simulation of Stress Wave Propagation for Accurate Geometric Representation of Materials

这项研究将涉及进一步开发一种新的多尺度模拟代码（在同一模拟中使用不同的网格，精细和粗糙），模拟材料的行为，特别注意在材料系统和结构的快速机械激励（即振动）期间发生的波动现象（应力波）。该项目将重点关注模拟过程中的耦合力学（即细网格和粗网格如何相互作用），其中细网格将用于预计会出现损坏现象的材料区域，因此粗网格将无法准确模拟结构。然而，在同一模拟过程中，在材料沿着的大多数地方将使用粗网格，其中材料预计几乎没有变形，因此粗网格就足够了，这将显著缩短计算时间。本研究也将着重于NURBS的应用（在数值建模的研究领域中的一种众所周知的技术，用于确保模拟准确地建模形状），特别是用于复杂几何形状的建模，由于目前基于有限元的模拟难以准确表示结构的几何形状，研究的影响将是新的计算数学技术的发展，如上所述，与多尺度建模相关的许多典型问题源于耦合力学和材料几何形状的精确表示中的问题。所有将有限元模拟应用于其工作的工程公司（几乎每一个大型工程公司）都希望有方法来减少他们的模拟的计算时间，只要它不牺牲准确性，因此，精确模拟技术的发展，（这需要大量的时间）精确地耦合到一个粗糙的网格（这需要少得多的时间），可以应用于沿着一个结构不太感兴趣的领域，肯定会对该行业产生影响，只要实际结构的几何形状可以足够好地建模。一些公司已经在内部开发多尺度代码，但是在这项研究中开发的新技术的实施仍然会对这些求解器的成功产生很大的影响。目的和目标;1。推导出一种新的数学技术，用于在细网格和粗网格之间的边界处更精确地建模耦合力学，然后是当前的工业技术。然后将沿着材料沿着模拟应力波，并将计算机模拟的准确性与实验数据进行比较。2.应用NURBS的使用来更精确地为结构的几何体建模。由于多尺度框架的新奇，应用NURBS的新技术将需要在数学和计算上制定。将再次模拟应力波并与实验数据进行比较。该项目福尔斯属于EPSRC材料工程-金属和合金研究领域。该项目部分由劳斯莱斯资助，因此将与他们及其材料部门进行一些合作。在这个阶段，还没有决定罗尔斯·罗伊斯希望如何参与研究，我希望他们可以实验性地模拟一些航空航天级金属，我可以将我的结果与此进行比较。

This research will involve the further development of a novel code for multi-scale simulations (using different meshes in the same simulation, fine and coarse) that model the behaviour of materials, with particular attention to wave phenomena (stress waves) that occur during the rapid mechanical excitations (i.e. vibration) of materials systems and structures. The project will focus on the coupling mechanics (i.e. how a fine and coarse mesh interact with each other) during simulations, where fine meshing will be used on areas of a material where damage phenomena is expected, and therefore a coarse mesh will not accurately model the structure. However, a coarse mesh will be utilised in most places along the material during the same simulation, where the material is expected to have little deformity, whereby a coarse mesh is more than sufficient and this would significantly improve the computational time. The research will also focus on applications of NURBS (a well-known technique in the realm of research in numerical modelling, for ensuring that a simulation models a shape accurately) for modelling of complex geometries in particular, as the current finite element based simulations pose difficulties with accurate representation of a structures geometry.The impact of the research will be the development of new computational mathematical techniques for tackling many of the typical problems that are associated with multi-scale modelling, as mentioned, these problems stem from issues in the coupling mechanics and the accurate representation of a materials geometry. All engineering companies that apply finite element simulations to their work (nearly every large engineering company) wish for ways to reduce the computational time of their simulations as long as it does not sacrifice accuracy, therefore, the development of an accurate simulation technique where fine meshing (that takes a large amount of time) coupled accurately to a coarse mesh (that takes far less time) that can be applied to areas of less interest along a structure, would certainly have an impact on the industry, as long as the geometry of the actual structure can be modelled sufficiently well. Some companies will already be developing multi-scale code in-house, but the implementation of the new techniques that will be developed during this research will still have a large impact on the success of these solvers. Aims and objectives;1. Derive a novel mathematical technique for a more accurate modelling of coupling mechanics at the boundary between a fine and coarse mesh then the current industry techniques. A stress wave will then be simulated along a material and the accuracy of the computer simulation will be compared to experimental data. 2. Apply the use of NURBS to more accurately model the geometry of a structure. Due to the novelty of the multi-scale framework, a novel technique for applying NURBS will need to formulated both mathematically and computationally. A stress wave will again be modelled and compared to experimental data. This project falls within the EPSRC Materials Engineering - metals and alloys research area.This project is part-funded by Rolls-Royce and so there will be some collaboration with them and their materials department. At this stage it is not decided how involved Rolls-Royce wish to be in the research, I am hoping they can experimentally model some aerospace grade metal and I can compare my results against this.