Large-scale simulation of pneumatic and hydraulicfracture with a phase-field approach

计算断裂力学的主要挑战之一是预测和跟踪裂纹路径和破碎模式。事实上，除了对建模方面的高要求外，裂纹的复杂结构和不规则行为需要高度复杂的网格细化和离散化技术。这两个方面都使裂纹问题的数值模拟成为一项艰巨的任务，从而为断裂力学中高效可靠的模拟工具的发展提供了主要障碍。该项目的目标是通过开发一种新的断裂力学理论和方法框架来应对这一挑战，该框架特别允许对最近和即将到来的并行架构上的大规模问题进行数值模拟。为了实现这一目标，在建模方面，该框架将利用相场模型作为一种新的方法来表示裂纹界面。在离散化方法方面，我们将能够利用新技术，如基于NURBS的空间。这些离散化方法的一个重要方面是其上级稳定性相比，传统的拉格朗日方法。特别是在大变形的情况下，这是一个相当大的优点。然而，这种稳定性是有代价的，因为NURBS需要一致地处理较大的面片，这对开发有效的自适应技术提出了挑战。在这里，与补丁或轻量级的自适应性，我们将采用最近的发展相结合的灵活性，传统的细化技术与补丁的离散化视图，从而允许大规模并行架构的设计高效的方法。除了新的相场断裂的方法，我们也将扩展我们的新框架，以处理接触和摩擦效应沿着较大的内部裂纹界面。通过这种方式，我们的新框架将能够以一致的方式处理强非线性和非平滑效应。该项目将建立在工程，建模，计算科学，和高性能计算，以建立一个共同的基础，为发展非传统的有限元方法的大规模模拟的变化和一致的多，物理相场有限变形断裂模型。该项目产生的新框架将提供一些新的非标准计算工具，这些工具将沿着气动和水力压裂的模拟进行开发和测试。然而，由此产生的框架将以灵活的方式设计，这将允许其应用也超越水力压裂，从而从长远来看可能作为一类新的建模和仿真工具的基础。

One of the main challenges in computational fracture mechanics is to predict and track crack paths and fragmentation patterns. In fact, besides the high demands on the modeling side, the complicated structure and non-regular behavior of cracks requires highly sophisticated mesh refinement and discretization techniques. Both aspects turn the numerical simulation of crack problems into a difficult task, thereby providing a major obstacle for the development of efficient and reliable simulation tools in fracture mechanics. It is the goal of this project to address this challenge by developing a new theoretical and methodological framework for fracture mechanics, which will in particular allow for the numerical simulation of large-scale problems on recent and upcoming parallel architectures. In order to achieve this goal, on the modeling side, the framework will exploit phase-field models as a novel approaches for the representation of crack interfaces. On the side of the discretisation methods, we will be able to make use new technologies as NURBS based ansatz spaces. One important aspect of these discretisation methods is their superior stability properties when compared to traditional Lagrangian approaches. In particular in the context of large deformations, this is a considerable advantage. This stability, however, comes at a price, as NURBS require the consistent handling of larger patches which poses challenges when it comes to the development of efficient adaptive techniques. Here, with patchwise or lightweight adaptivity, we will employ recent developments combining the flexibility of traditional refinement techniques with a patchwise view on the discretisation, thereby allowing for the design of efficient approaches on massively parallel architectures. In addition to the new phase-field based approach for fracture we will also extend our new framework in order to deal with contact and frictional effects along the larger interior crack interfaces. In this way, our new framework will be capable of dealing with both, strongly non-linear as well as non-smooth effects, in a consistent manner.This project will build on complimentary expertise in engineering, modeling, computational science, and high performance computing in order to establish a common basis for the development of non-conventional finite element methods for large-scale simulations of variationally and thermodynamically consistent multi-physics phase-field fracture models undergoing finite deformations. The new framework emerging from this project will provide a number of new and non-standard computational tools, which will be developed and tested along the simulation of pneumatic and hydraulic fracturing. However, the resulting framework will be designed in a flexible way which will allow its application also beyond hydraulic fracturing, thereby on the long run possibly serving as the basis for a new class of modeling and simulation tools.