Concurrent Multiscale Modelling for Structural Integrity

一个目标是解决围绕变形、断裂和损伤现象的多尺度表现问题，这些现象动态地改变了航空发动机内组成的复杂组件内的多重接触。在数学上，关键的挑战来自这样一个事实，即高度动态事件通常使用有限元素（在空间上）和有限差分（在时间上）离散化来模拟，因此在相同长度尺度的相同模型中进行细化会引入已知和可量化的数值误差。因此，随着计算能力的提高，在整个域的有限部分中出现质量守恒和能量耗散问题的机会出现了，可以通过以下方式考虑：*探索与有限元模拟兼容的新算法，以在不牺牲精度的情况下降低计算成本*通过误差估计器评估计算的准确性*确定进一步子离散化所需的子域的大小。同时考虑对材料异质性和结构的需求*同时进行从较高到较低长度尺度的场映射*计算较低长度尺度下材料的响应并将其返回到以上尺度的域部分这些质量守恒的能量耗散问题，其中大约5-10%的域将需要细化，以“鸟击”的现实场景为例。这个非常小的区域包含高频应力波，而区域的其余部分则以弹性方式起作用。像鸟击这样的能量耗散冲击事件就是这类问题的一个例子，并且是燃气涡轮发动机的突出问题。众所周知，相同尺度下的细化方法会导致不同尺寸的有限元产生杂散波和应力波的滤波。因此，在应用中获得的非常局部的塑性应变，如上述，为研究多尺度模拟提供了强大的动力，因为人们希望更好地理解单元不具有弹性行为的部分域的行为。该项目属于EPSRC ASiMoV（复杂多体组件的大规模计算），其中包括来自剑桥大学，布里斯托尔大学，华威大学和EPCC（爱丁堡）的合作者。在工业上，该项目与劳斯莱斯公司密切相关，该财团的主要目标是在高性能计算机上对燃气涡轮发动机进行大规模的热-机械-电磁模拟。

One aims to address the problem of multiscale manifestations of phenomena surrounding deformation, fracture and damage that dynamically change the multiplicity of contacts within the complex assemblies comprised within an aerospace engine. Mathematically, the key challenge arises from the fact that highly dynamic events are commonly simulated using Finite Elements (in space) and Finite Differences (in time) discretisation, whereby refinement within the same model at the same length scale introduces numerical errors that are known and quantifiable. Hence, an opportunity arises, with increasing computational power, for the mass-conserving and energy dissipative problems in limited portions of the overall domain, to be considered by the following:* Exploration of novel algorithms that are compatible with finite element simulations to reduce computational cost without sacrificing accuracy* Assessing the accuracy of the computation via error estimators* Determining the size of the sub-domain needed for further sub-discretisation, whilst considering the need for material heterogeneities and structure * Conducting the mapping of fields from higher to lower length scales concurrently* Computing the response of materials at the lower length scales and returning them back to the portions of the domain at the scales aboveThese mass-conserving energy dissipative problems, where roughly 5-10% of the domain will require refinement are exemplified by the real-life scenario of "birdstrike". This very small area contains the high frequency stress waves, whereas the rest of the domain acts in an elastic manner. Energy dissipative impact events such as birdstrike are an example of these kinds of problems and are prominent issues for gas turbineengines. It is well known that refinement methods at the same scale that lead to different sized finite elements can produce spurious waves and the filtering of stress waves. Therefore, the very localised plastic strain obtained in applications, like the above, provide strong motivation for the study of multiscale simulations as one looks to better understand the behaviour in portion of the domain where elements do not behave elastically.This project falls within the EPSRC ASiMoV (Large scale computation of complex multi-body assemblies), of which involves collaborators from the University of Cambridge, Bristol University, University of Warwick and EPCC (Edinburgh). Industrially, the project is closely tied to Rolls Royce plc, where the consortium's key aim is to run large scale thermo-mechanical-electromagnetic simulations of gas turbine engines on high performance computers.