Zhuang / Liu / Cheng Extended Finite Element Method

Tsinghua University Press Computational Mechanics Series
1. Auflage 2014
ISBN: 978-0-12-407856-7
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 286 Seiten

Extended Finite Element Method provides an introduction to the extended finite element method (XFEM), a novel computational method which has been proposed to solve complex crack propagation problems. The book helps readers understand the method and make effective use of the XFEM code and software plugins now available to model and simulate these complex problems. The book explores the governing equation behind XFEM, including level set method and enrichment shape function. The authors outline a new XFEM algorithm based on the continuum-based shell and consider numerous practical problems, including planar discontinuities, arbitrary crack propagation in shells and dynamic response in 3D composite materials. - Authored by an expert team from one of China's leading academic and research institutions - Offers complete coverage of XFEM, from fundamentals to applications, with numerous examples - Provides the understanding needed to effectively use the latest XFEM code and software tools to model and simulate dynamic crack problems

Autoren/Hrsg.

Zhuang, Zhuo

Liu, Zhanli

Cheng, Binbin

Liao, Jianhui

Leseproben

Chapter 1 Overview of Extended Finite Element Method
Abstract
The study of computational fracture mechanics is of great importance for both scientific research and engineering applications. Since being proposed in 1999, the extended finite element method (X-FEM) has become an efficient tool for solving crack arbitrary propagation problems. The basic idea and recent progress in the development of X-FEM are reviewed. The structure of this book is also given at the end of the chapter. Keywords
Computational fracture mechanicscrack propagationstrong and weak discontinuityextended finite element method Chapter Outline 1.1 Significance of Studying Computational Fracture Mechanics?1 1.2 Introduction to X-FEM?2 1.3 Research Status and Development of X-FEM?8 1.3.1 The Development of X-FEM Theory?8 1.3.2 Development of 3D X-FEM?10 1.4 Organization of this Book?11 Significance of Studying Computational Fracture Mechanics
Fracture is one of the most important failure modes. In various engineering fields, many catastrophic accidents have started from cracks or ends at crack propagation, such as the cracking of geologic structures and the collapse of engineering structures during earthquakes, damage of traffic vehicles during collisions, the instability crack propagation of pressure pipes, and the fracture of mechanical components. These accidents have caused great loss to people’s lives and economic property. However, usually it is very difficult to quantitatively provide the causes of crack initiation. So research on fracture mechanics, which is mainly focused on studying the propagation or arrest of initiated cracks, is of great theoretical importance and has broad application potential. Modern fracture mechanics has been booming and has been studied extensively in recent years; this is because it is already deeply rooted in the modern high-technology field and engineering applications. For example, large-scale computers facilitate the numerical simulation of complicated fracture processes, and new experimental techniques provided by modern physics, such as advanced scanning electron microscope (SEM) analysis, surface analysis, and high-speed photography, make it possible to study the fracture process from the micro-scale to the macro-scale. This understanding of the basic laws of fracture plays an important role in theoretically guiding the applications of fracture mechanics in engineering, such as the toughening of new materials, the development of biological and biomimetic materials, the seismic design of buildings and nuclear reactors, the reliability of microelectronic components, earthquake prediction in geomechanics, the exploration and storage of oil and gas, the new design of aerospace vehicles, etc. After integration with modern science and high-technology methods, fracture mechanics is taking on a new look. Cracks in reality are usually in three dimensions, and have complicated geometries and arbitrary propagation paths. For a long time, one of the difficult challenges of mechanics has been to study crack propagation along curved or kinked paths in three-dimensional structures. In these situations, the “straight crack” assumption in conventional fracture mechanics is no longer valid, so theoretical methods are very limited for this problem. Experiments are another important way to study the propagation of curved cracks, but most results are empirical and phenomenological, and mainly focus on planar cracks. In recent decades, numerical simulations have developed rapidly along with the development of computer technology. The new progress in computational mechanics methods, such as the finite element method, boundary element method, etc., provides the possibility of solving the propagation of curved cracks. Modeling crack propagation in three-dimensional solids and curved surfaces has become one of the hottest topics in computational mechanics. Computational fracture mechanics methods roughly include the finite element method with adaptive mesh (Miehe and Gürses, 2007), nodal force release method (Zhuang and O’Donoghue, 2000a, b), element cohesive model (Xu and Needleman, 1994), and embedded discontinuity model (Belytschko et al., 1988). All of these methods have some limitations when dealing with cracks with complicated geometries, such as when the crack path needs to be predefined, the crack must propagate along the element boundary, the computational cost is high, etc. In the last decades, the extended finite element method (X-FEM) proposed in the late 1990s has become one of the most efficient tools for numerical solution of complicated fracture problems. Introduction to X-FEM
One of the greatest contributions the scientists made to mankind in the twentieth century was the invention of the computer, which has greatly promoted the development of related industry and scientific research. Taking computational mechanics as an example, many new methods, such as the finite element method, finite difference, and finite volume methods have rapidly developed as the invention of computer. Thanks to these methods, a lot of traditional problems in mechanics can be simulated and analyzed numerically; more importantly, a number of engineering and scientific problems can be modeled and solved. As the development of modern information technology and computational science continues, simulation-based engineering and science has become helpful to scientists in exploring the mysteries of science, and provides an effective tool for the engineer to implement engineering innovations or product development with high reliability. The finite element method (FEM) is just one of the powerful tools of simulation-based engineering and science. Since the appearance of the first FEM paper in the mid-1950s, many papers and books on this issue have been published. Some successful experimental reports and a series of articles have made great contributions to the development of FEM. From the 1960s, with the emergence of finite element software and its rapid applications, FEM has had a huge impact on computer-aided engineering analysis. The appearance of numerous advanced software not only meets the requirement of simulation-based engineering and science, but also promotes further development of the finite element method itself. If we compare a finite element to a large tree, it is like the growth of several important branches, like hybrid elements, boundary elements, the meshless method, extended finite elements, etc., make this particular tree prosper. In analysis by the conventional finite element method, the physical model to be solved is divided into a series of elements connected in a certain arrangement, usually called the “mesh”. However, when there are some internal defects, like interfaces, cracks, voids, inclusions, etc. in the domain, it will create some difficulties in the meshing process. On one hand, the element boundary must coincide with the geometric edge of the defects, which will induce some distortion in the element; on the other hand, the mesh size will be dependent on the geometric size of the small defects, leading to a nonuniform mesh distribution in which the meshes around the defects are dense, while those far from defects are sparse. As we know, the smallest mesh size decides the critical stable time increment in explicit analysis. So the small elements around the defects will heavily increase the computational cost. Also, defects, like cracks, can only propagate along the element edge, and not flow along a natural arbitrary path. Aiming at solving these shortcomings by using the conventional FEM to solve crack or other defects with discontinuous interfaces, Belytschko and Moës proposed a new computational method called the “extended finite element method (X-FEM)” (Belytschko and Black, 1999; Moës et al., 1999), and made an important improvement to the foundation of conventional FEM. In the last 10 years, X-FEM has been constantly improved and developed, and has already become a powerful and promising method for dealing with complicated mechanics problems, like discontinuous field, localized deformation, fracture, and so on. It has been widely used in civil engineering, aviation and space, material science, etc. The core idea of X-FEM is to use a discontinuous function as the basis of a shape function to capture the jump of field variables (e.g., displacement) in the computational domain. So in the calculations, the description for the discontinuous field is totally mesh-independent. It is this advantage that makes it very suitable for dealing with fracture problems. Figure 1.1 is an example of a three-dimensional fracture simulated by X-FEM (Areias and Belytschko, 2005b), in which we find that the crack surface and front are independent of the mesh. Figure 1.2 demonstrates the process of transition crack growth under impact loading on the left lower side of a plane plate, in which we can investigate impact wave propagation in the plate and the stress singularity field at the crack tip location. In addition, it is very convenient to model the crack with complex geometries using X-FEM; one example of crack branching simulation is given in Figure 1.3 (Xu et al., 2013). X-FEM is not only used to simulate cracks, but also to simulate heterogeneous materials with voids and inclusions (Belytschko et al., 2003b;...