This book describes the basics and developments of the new XFEM approach to fracture analysis of composite structures and materials. It provides state of the art techniques and algorithms for fracture analysis of structures including numeric examples at the end of each chapter as well as an accompanying website which will include MATLAB resources, executables, data files, and simulation procedures of XFEM. The first reference text for the extended finite element method (XFEM) for fracture analysis of structures and materials Includes theory and applications, with worked numerical problems and solutions, and MATLAB examples on an accompanying website with further XFEM resources Provides a comprehensive overview of this new area of research, including a review of Fracture Mechanics, basic through to advanced XFEM theory, as well as current problems and applications Includes a chapter on the future developments in the field, new research areas and possible future applications of the method

An overview of the virtual crack closure technique is presented. The approach used is discussed, the history summarized, and insight into its applications provided. Equations for two-dimensional quadrilateral elements with linear and quadratic shape functions are given. Formula for applying the technique in conjuction with three-dimensional solid elements as well as plate/shell elements are also provided. Necessary modifications for the use of the method with geometrically nonlinear finite element analysis and corrections required for elements at the crack tip with different lengths and widths are discussed. The problems associated with cracks or delaminations propagating between different materials are mentioned briefly, as well as a strategy to minimize these problems. Due to an increased interest in using a fracture mechanics based approach to assess the damage tolerance of composite structures in the design phase and during certification, the engineering problems selected as examples and given as references focus on the application of the technique to components made of composite materials.

Damage Modeling of Composite Structures: Strength, Fracture, and Finite Element Analysis provides readers with a fundamental overview of the mechanics of composite materials, along with an outline of an array of modeling and numerical techniques used to analyze damage, failure mechanisms and safety tolerance. Strength prediction and finite element analysis of laminated composite structures are both covered, as are modeling techniques for delaminated composites under compression and shear. Viscoelastic cohesive/friction coupled model and finite element analysis for delamination analysis of composites under shear and for laminates under low-velocity impact are all covered at length. A concluding chapter discusses multiscale damage models and finite element analysis of composite structures. Integrates intralaminar damage and interlaminar delamination under different load patterns, covering intralaminar damage constitutive models, failure criteria, damage evolution laws, and virtual crack closure techniques Discusses numerical techniques for progressive failure analysis and modeling, as well as numerical convergence and mesh sensitivity, thus allowing for more accurate modeling Features models and methods that can be seamlessly extended to analyze failure mechanisms and safety tolerance of composites under more complex loads, and in more extreme environments Demonstrates applications of damage models and numerical methods

Introduces the theory and applications of the extended finite element method (XFEM) in the linear and nonlinear problems of continua, structures and geomechanics Explores the concept of partition of unity, various enrichment functions, and fundamentals of XFEM formulation. Covers numerous applications of XFEM including fracture mechanics, large deformation, plasticity, multiphase flow, hydraulic fracturing and contact problems Accompanied by a website hosting source code and examples

Nonlinear Mechanics for Composite Heterogeneous Structures applies both classical and multi-scale finite element analysis to the non-linear, failure response of composite structures. These traditional and modern computational approaches are holistically presented, providing insight into a range of non-linear structural analysis problems. The classical methods include geometric and material non-linearity, plasticity, damage and contact mechanics. The cutting-edge formulations include cohesive zone models, the Extended Finite Element Method (XFEM), multi-scale computational homogenization, localization of damage, neural networks and data-driven techniques. This presentation is simple but efficient, enabling the reader to understand, select and apply appropriate methods through programming code or commercial finite element software. The book is suitable for undergraduate studies as a final year textbook and for MSc and PhD studies in structural, mechanical, aerospace engineering and material science, among others. Professionals in these fields will also be strongly benefited. An accompanying website provides MATLAB codes for two-dimensional finite element problems with contact, multi-scale (FE2) and non-linear XFEM analysis, data-driven and machine learning simulations.

This book offers a collection of 17 scientific papers about the computational modeling of fracture. Some of the manuscripts propose new computational methods and/or how to improve existing cutting edge methods for fracture. These contributions can be classified into two categories: 1. Methods which treat the crack as strong discontinuity such as peridynamics, scaled boundary elements or specific versions of the smoothed finite element methods applied to fracture and 2. Continuous approaches to fracture based on, for instance, phase field models or continuum damage mechanics. On the other hand, the book also offers a wide range of applications where state-of-the-art techniques are employed to solve challenging engineering problems such as fractures in rock, glass, concrete. Also, larger systems such as fracture in subway stations due to fire, arch dams, or concrete decks are studied.

Many modern engineering structures are composed of brittle heterogenous, or quasibrittle, materials. These include concrete, composites, tough ceramics, rocks, cold asphalt mixtures, and many brittle materials at the microscale. Understanding the failure behavior of these materials is of paramount importance for improving the resilience and sustainability of various engineering structures including civil infrastructure, aircraft, ships, military armors, and microelectronic devices. Designed for graduate and upper-level undergraduate university courses, this textbook provides a comprehensive treatment of quasibrittle fracture mechanics. It includes a concise but rigorous examination of linear elastic fracture mechanics, which is the foundation of all fracture mechanics. It also covers the fundamental concepts of nonlinear fracture mechanics, and introduces more advanced concepts such as triaxial stress state in the fracture process zone, nonlocal continuum models, and discrete computational models. Finally, the book features extensive discussion of the various practical applications of quasibrittle fracture mechanics across different structures and engineering disciplines, and throughout includes exercises and problems for students to test their understanding.