Generalized Finite Element Methods For Three Dimensional Crack Growth Simulations

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Generalized Finite Element Methods For Three Dimensional Crack Growth Simulations

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Author : Jeronymo P. Pereira
language : en
Publisher:
Release Date : 2010

Generalized Finite Element Methods For Three Dimensional Crack Growth Simulations written by Jeronymo P. Pereira and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.

Three-dimensional (3-D) crack growth analysis is crucial for the assessment of structures such as aircrafts, rockets, engines and pressure vessels, which are subjected to extreme loading conditions. The analysis of 3-D arbitrary crack growth using the standard Finite Element Method (FEM) encounters several difficulties. The singularities at crack fronts require strongly refined finite element meshes that must fit the discontinuity surfaces while keeping the aspect ratio of the elements within acceptable bounds. Fully automatic generation of meshes in complex 3-D geometries satisfying these requirements is a daunting task. Partition-of-unity methods, such as the Generalized FEM (GFEM), are promising candidates to surmount the shortcomings of the standard FEM in crack growth simulations. These methods allow the representation of discontinuities and singularities in the solution via geometrical descriptions of crack surfaces, that are independent of the volume mesh, coupled with suitable enrichment functions. As a result, volume meshes need not fit crack surfaces. This work proposes an hp-version of the GFEM (hp-GFEM) for crack growth simulations. This method provides enough flexibility to build high-order discretizations for crack growth simulations. At each crack growth step, high-order approximations on locally refined meshes are automatically created in complex 3-D domains while preserving the aspect ratio of elements, regardless of crack geometry. The hp-GFEM uses explicit surface meshes composed of triangles to represent non-planar 3-D crack surfaces. By design, the proposed methodology allows the crack surface to be arbitrarily located within the GFEM mesh. To track the crack surface evolution, the proposed methodology considers an extension of the Face Offsetting Method (FOM). Based on the hp-GFEM solution, the FOM provides geometrically feasible crack front descriptions by updating the vertex positions and checking for self-intersections of the edges. The hp-GFEM with FOM allows the simulation of arbitrary crack growth independent of the volume mesh. Numerical simulations using the hp-GFEM coupled with the FOM are corroborated by experimental data and experimental observations. As an alternative to large-scale crack growth simulations, this work combines the proposed hp-GFEM with the generalized finite element method with global-local enrichment functions (GFEMgl). The proposed method allows crack growth simulations with arbitrary path in industrial level complexity problems while keeping the global mesh unchanged. Furthermore, this method allows crack growth simulations without solving the entire problem from scratch at each crack growth step. The GFEMgl for crack growth explores solutions from previous crack growth steps, hierarchical property of the enrichment functions as well as static condensation of the global-local degrees of freedom to expedite the solution process. Numerical examples demonstrate the robustness, efficiency and accuracy of the proposed GFEMgl for crack growth simulations.

Three Dimensional Simulation Of Arbitrary Crack Growth

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Author : Brett Richard Davis
language : en
Publisher:
Release Date : 2014

Three Dimensional Simulation Of Arbitrary Crack Growth written by Brett Richard Davis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.

A finite-element-based simulation technique is developed in Chapter 1 to predict arbitrary shape evolution of 3-D, geometrically explicit cracks under stable growth conditions. Point-by-point extensions along a crack front are predicted using a new, energy-based growth formulation that relies on a first-order expansion of the energy release rate. The key term in this expansion is the variation of energy release rate, made readily available via the virtual crack extension (VCE) method. The variation of energy release rate acts as an influence function relating changes in applied load to geometry changes along the crack front. The crack-growth formulation is incorporated into an incremental-iterative solution procedure that continually updates the crack configuration by re-meshing. The numerical technique allows crack shapes to evolve according to energy-based mechanics, while reducing the effects of computational artifacts, e.g. mesh bias. Chapter 1 offers three simulations of mode I, planar crack growth as proof-of-concept of the new technique. To extend the simulation approach to more general crack growth situations, Chapter 2 presents a new implementation for decomposing 3-D mixed-mode energy release rates using the VCE method. The technique uses a symmetric/anti-symmetric approach to decompose local crack-front displacements that are substituted into the global VCE energy release rate form. The subsequent expansion leads to the mixedmode energy release rate expressions. As a result of the expansion, previously unaddressed modal-interaction coupling terms are found to impact the mixed-mode energy release rates. Five numerical examples are presented as verification of the implementation. This development expands the VCE method's advantages over similar procedures when simulating arbitrary crack growth. The energy-based growth formulation and accompanying simulation technique is generalized in Chapter 3 to predict arbitrary, mixed-mode, non-planar crack evolution. The implementation uses a novel basis-function approach to generate a crack extension expression, rather than relying on the local, point-by-point approach described in Chapter 1. The basis-function expression dampens the effect of numerical noise on crack growth predictions that could otherwise produce unstable simulation results. Two simulations are presented to demonstrate the technique's ability to capture both general non-planar behavior, as well as local mixed-mode phenomena, e.g. "factory-roof" formation, along the crack front.

Development Of Domain Integral And Generalized Finite Element Methods For Three Dimensional Analysis Of Near Surface Cracking In Flexible Pavements

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Author : Hasan Ozer
language : en
Publisher:
Release Date : 2011

Development Of Domain Integral And Generalized Finite Element Methods For Three Dimensional Analysis Of Near Surface Cracking In Flexible Pavements written by Hasan Ozer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.

Layered elastic theories and finite element method are among the most familiar and practiced mechanistic approaches. These approaches succeed to a certain extent in the analysis of classical bottom-up fatigue cracking of relatively thin flexible pavements, where tensile stresses and strains govern the behavior at the asphalt layer. However, elastic theories are incapable of predicting other pavement distresses, including near-surface cracking. Similarly, finite element method, which is equipped with fracture and continuum mechanics theories, also poses a significant challenge to the analysis of the near-surface cracking problem, where crack initiation and propagation planes are not easily predictable. Hence, the main objective of this study is to identify the effect of loading tire contact stresses on developing near-surface cracking potential. A numerical approach is chosen to analyze the problem, taking into account considering nonuniform tire-pavement contact stresses and multi-axial stress states in the proximity of tires. This study highlights the impact of novel computational methods, such as the Generalized Finite Element Method (GFEM), on the discovery and understanding of cracking mechanisms in pavements. GFEM allows for realistic modeling of complex phenomena that control fracture initiation and propagation. In this study, GFEM is adapted to analyze relatively thick flexible pavement structures to predict near-surface cracking. The three-dimensional (3-D) and highly multi-axial nature of the problem is successfully captured by this method, which is ideally designed for 3-D fracture problems for complex geometries and mixed loading conditions. This study proposes a high-order domain integral method for the computation of the crack front parameters such as energy release rate and stress intensity factors (SIFs). The method provides an approximation of the energy release rate function as a linear combination of Legendre polynomials. As a result, extracted functions are smoothly varying, which is crucial to obtain accurate crack propagation paths in 3-D for elastic or inelastic materials. Crack front directionality is captured by the proposed formulations and implementation using an energy release rate-based approach. The study also applies for the first time the domain integral techniques to pavement fracture problems utilizing the asphalt concrete viscoelastic characteristics. The GFEM, equipped with the tools developed in this study, is used as a computational platform to analyze near-surface cracking in relatively thick flexible pavement structures. Three-dimensional models of typical pavement structures are developed to analyze near-surface cracking and make predictions for potential critical locations for crack initiation and growth. Two potential scenarios become evident for crack growth in the vicinity of tires: Shear crack under compression and tensile crack. It is observed from the analysis that shear crack growth is the dominant mode of crack development due to loading in the proximity of tires, while tensile crack growth appears to develop within the pavement.

Meshfree Methods For Partial Differential Equations Ix

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Author : Michael Griebel
language : en
Publisher: Springer
Release Date : 2019-06-19

Meshfree Methods For Partial Differential Equations Ix written by Michael Griebel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-19 with Mathematics categories.

This volume collects selected papers presented at the Ninth International Workshop on Meshfree Methods held in Bonn, Germany in September 2017. They address various aspects of this very active research field and cover topics from applied mathematics, physics and engineering. The numerical treatment of partial differential equations with meshfree discretization techniques has been a very active research area in recent years. While the fundamental theory of meshfree methods has been developed and considerable advances of the various methods have been made, many challenges in the mathematical analysis and practical implementation of meshfree methods remain. This symposium aims to promote collaboration among engineers, mathematicians, and computer scientists and industrial researchers to address the development, mathematical analysis, and application of meshfree and particle methods especially to multiscale phenomena. It continues the 2-year-cycled Workshops on Meshfree Methods for Partial Differential Equations.

Extended Finite Element Method For Crack Propagation

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Author : Sylvie Pommier
language : en
Publisher: John Wiley & Sons
Release Date : 2013-03-04

Extended Finite Element Method For Crack Propagation written by Sylvie Pommier and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-04 with Technology & Engineering categories.

Novel techniques for modeling 3D cracks and their evolution in solids are presented. Cracks are modeled in terms of signed distance functions (level sets). Stress, strain and displacement field are determined using the extended finite elements method (X-FEM). Non-linear constitutive behavior for the crack tip region are developed within this framework to account for non-linear effect in crack propagation. Applications for static or dynamics case are provided.

Three Dimensional Finite Element Analysis Of Cyclic Fatigue Crack Growth Of Multiple Surface Flaws

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Author : Corneliu Manu
language : en
Publisher:
Release Date : 1980

Three Dimensional Finite Element Analysis Of Cyclic Fatigue Crack Growth Of Multiple Surface Flaws written by Corneliu Manu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Finite element method categories.

Advances In Crack Growth Modeling

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Author : M.H. Aliabadi
language : en
Publisher: Trans Tech Publications Ltd
Release Date : 2013-07-15

Advances In Crack Growth Modeling written by M.H. Aliabadi and has been published by Trans Tech Publications Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-15 with Technology & Engineering categories.

Volume is indexed by Thomson Reuters BCI (WoS). Crack growth is a complex phenomenon and difficult to model without assumed simplifications. In recent years, there has been an increasing realization that advanced computational methods such as the Finite Element Method, the Boundary Element Method and Mesh Free Methods can be used to simulate crack growth in complex structural parts. This special issue contains original papers written by active researchers in the field of computational fracture mechanics. The aim is to inform those in the fracture mechanics community who might not be at the forefront of computational research of the recent developments and techniques available and the wide range of applications for which solutions are now possible.

Three Dimensional Analysis Of Crack Growth

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Author : Yaoming Mi
language : en
Publisher: Computational Mechanics
Release Date : 1996

Three Dimensional Analysis Of Crack Growth written by Yaoming Mi and has been published by Computational Mechanics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Nature categories.

Three Dimensional Finite Element Simulation Of Fatigue Crack Growth And Closure

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Author : Stephen G. Cupschalk
language : en
Publisher:
Release Date : 1987

Three Dimensional Finite Element Simulation Of Fatigue Crack Growth And Closure written by Stephen G. Cupschalk and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Stress corresion categories.

Advanced Three Dimensional Simulations And Cohesive Modeling Of Fatigue Crack Growth

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Author : Ani Ural
language : en
Publisher:
Release Date : 2004

Advanced Three Dimensional Simulations And Cohesive Modeling Of Fatigue Crack Growth written by Ani Ural and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.