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
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
Part I of this SpringerBrief presents the problem of a crack between two dissimilar isotropic materials and describes the mathematical background. A fracture criterion is discussed and Methods for calculating fracture parameters such as stress intensity factors using the finite element method and three post-processors are considered. Actual test data and both deterministic and statistical failure curves are presented.In Part II of the book, similar descriptions are given for delaminations in composite laminates. The mathematical treatment of this type of damage including the first term of the asymptotic expansion of the stress and displacement fields is considered. Numerical post-processors for determining stress intensity factors for these cases are reviewed. Two examples of specific laminates are presented: one with a failure curve and the other with a failure surface. Finally, beam specimens used for testing such failures are discussed.
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
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.
Composite Laminated: Theories and Their Applications presents the latest methods for analyzing composite laminates and their applications. The title introduces the most important analytical methods in use today, focusing on fracture, damage, multi-physics and sensitivity analysis. Alongside these methods, it presents original research carried out over two decades on laminated composite structures and gives detailed coverage of laminate theories, analytic solutions and finite element models. Specific chapters cover An introduction to composites, Elasticity, Shear, State space theory, Layerwise theories, The extended layerwise method, Fracture and damage mechanics, Multi-physical fracture problems, Analytical methods of stiffened sandwich structures, Progressive failure analysis, and more. This volume offers a comprehensive guide to the state-of-the-art in the analysis and applications of composite laminates, which play a critical role in all types of engineering, from aerospace to subsea structures, including in medical prosthetics, circuit boards and sports equipment. - Presents a guide to the analysis and application of advanced composite materials - Gives detailed exposition of plate/shell theories and their implementation in finite element code architecture - Considers the robustness, effectiveness and applications aspects of laminated plate/shell methods - Gives hands-on experience of code architecture, providing composite analysis software which can be plugged in to commercial applications - Presents experimental research alongside methods, laminate theories, analytic solutions, and finite element models
Multi-scale modelling of composites is a very relevant topic in composites science. This is illustrated by the numerous sessions in the recent European and International Conferences on Composite Materials, but also by the fast developments in multi-scale modelling software tools, developed by large industrial players such as Siemens (Virtual Material Characterization toolkit and MultiMechanics virtual testing software), MSC/e-Xstream (Digimat software), Simulia (micromechanics plug-in in Abaqus), HyperSizer (Multi-scale design of composites), Altair (Altair Multiscale Designer) This book is intended to be an ideal reference on the latest advances in multi-scale modelling of fibre-reinforced polymer composites, that is accessible for both (young) researchers and end users of modelling software. We target three main groups: This book aims at a complete introduction and overview of the state-of-the-art in multi-scale modelling of composites in three axes: • ranging from prediction of homogenized elastic properties to nonlinear material behaviour • ranging from geometrical models for random packing of unidirectional fibres over meso-scale geometries for textile composites to orientation tensors for short fibre composites • ranging from damage modelling of unidirectionally reinforced composites over textile composites to short fibre-reinforced composites The book covers the three most important scales in multi-scale modelling of composites: (i) micro-scale, (ii) meso-scale and (iii) macro-scale. The nano-scale and related atomistic and molecular modelling approaches are deliberately excluded, since the book wants to focus on continuum mechanics and there are already a lot of dedicated books about polymer nanocomposites. A strong focus is put on physics-based damage modelling, in the sense that the chapters devote attention to modelling the different damage mechanisms (matrix cracking, fibre/matrix debonding, delamination, fibre fracture,...) in such a way that the underlying physics of the initiation and growth of these damage modes is respected. The book also gives room to not only discuss the finite element based approaches for multi-scale modelling, but also much faster methods that are popular in industrial software, such as Mean Field Homogenization methods (based on Mori-Tanaka and Eshelby solutions) and variational methods (shear lag theory and more advanced theories). Since the book targets a wide audience, the focus is put on the most common numerical approaches that are used in multi-scale modelling. Very specialized numerical methods like peridynamics modelling, Material Point Method, eXtended Finite Element Method (XFEM), isogeometric analysis, SPH (Smoothed Particle Hydrodynamics),... are excluded. Outline of the book The book is divided in three large parts, well balanced with each a similar number of chapters:
