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Author: Víctor Eduardo Cardoso Nungaray
Publisher:
ISBN:
Category :
Languages : en
Pages : 120
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Book Description
This thesis presents a proposal to simulate mechanics and dynamics of brittle fracture. A variational formulation is used to describe Lagrangian mechanics, by minimizing the difference between potential and kinetic energy of the system, obtaining a pair of partial differential equations; the solution of these equations corresponds to the displacement field and damage phase-field respectively. Such an equations are coupled in the sense that the damage field is used in the first equation and the displacement field is used in the second one. In this work we propose a numerical method based on control volumes to solve the differential equations, extending the formulation to support the separation of control volumes, processing these volumes as discrete entities. This treatment results in accurate calculations of stress field and the nucleation of new internal fractures that can be propagated through domain creating multiple bifurcations. To integrate equations inside control volumes we introduce a family of polynomial splines that we refer as homeostatic splines, since its derivatives are null at vertices with a smooth function variation between adjacent volumes. Furthermore, we propose a shape function with trigonometric components for dynamic analysis, allowing bigger time steps that with traditional approaches. Finally, we perform ten numerical experiments to show the effectiveness of the method and to compare our results with those published by other authors.
Author: Víctor Eduardo Cardoso Nungaray
Publisher:
ISBN:
Category :
Languages : en
Pages : 120
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Book Description
This thesis presents a proposal to simulate mechanics and dynamics of brittle fracture. A variational formulation is used to describe Lagrangian mechanics, by minimizing the difference between potential and kinetic energy of the system, obtaining a pair of partial differential equations; the solution of these equations corresponds to the displacement field and damage phase-field respectively. Such an equations are coupled in the sense that the damage field is used in the first equation and the displacement field is used in the second one. In this work we propose a numerical method based on control volumes to solve the differential equations, extending the formulation to support the separation of control volumes, processing these volumes as discrete entities. This treatment results in accurate calculations of stress field and the nucleation of new internal fractures that can be propagated through domain creating multiple bifurcations. To integrate equations inside control volumes we introduce a family of polynomial splines that we refer as homeostatic splines, since its derivatives are null at vertices with a smooth function variation between adjacent volumes. Furthermore, we propose a shape function with trigonometric components for dynamic analysis, allowing bigger time steps that with traditional approaches. Finally, we perform ten numerical experiments to show the effectiveness of the method and to compare our results with those published by other authors.
Author: Blaise Bourdin
Publisher: Springer Science & Business Media
ISBN: 1402063954
Category : Technology & Engineering
Languages : en
Pages : 173
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Book Description
Presenting original results from both theoretical and numerical viewpoints, this text offers a detailed discussion of the variational approach to brittle fracture. This approach views crack growth as the result of a competition between bulk and surface energy, treating crack evolution from its initiation all the way to the failure of a sample. The authors model crack initiation, crack path, and crack extension for arbitrary geometries and loads.
Author: Gianpietro Del Piero
Publisher: Springer Science & Business Media
ISBN: 9400772262
Category : Science
Languages : en
Pages : 89
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Book Description
This book exposes a number of mathematical models for fracture of growing difficulty. All models are treated in a unified way, based on incremental energy minimization. They differ from each other by the assumptions made on the inelastic part of the total energy, here called the "cohesive energy". Each model describes a specific aspect of material response, and particular care is devoted to underline the correspondence of each model to the experiments. The content of the book is a re-elaboration of the lectures delivered at the First Sperlonga Summer School on Mechanics and Engineering Sciences in September 2011. In the year and a half elapsed after the course, the material has been revised and enriched with new and partially unpublished results. Significant additions have been introduced in the occasion of the course "The variational approach to fracture and other inelastic phenomena", delivered at SISSA, Trieste, in March 2013. The Notes reflect a research line carried on by the writer over the years, addressed to a comprehensive description of the many aspects of the phenomenon of fracture, and to its relations with other phenomena, such as the formation of microstructure and the changes in the material’s strength induced by plasticity and damage. Reprinted from the Journal of Elasticity, volume 112, issue 1, 2013.
Author: Bin Li
Publisher:
ISBN:
Category :
Languages : en
Pages : 113
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Book Description
Fracture mechanics of brittle materials has focused on bulk materials with isotropic surface energy. In this situation different physical principles for crack path selection are very similar or even equivalent. The situation is radically different when considering crack propagation in brittle materials with anisotropic surface energy. Such materials are important in applications involving single crystals, extruded polymers, or geological and organic materials. When this anisotropy is strong, the phenomenology of crack propagation becomes very rich, with forbidden crack propagation directions or complex sawtooth crack patterns. Thus, this situation interrogates fundamental issues in fracture mechanics, including the principles behind the selection of crack direction. Similarly, tearing of brittle thin elastic sheets, ubiquitous in nature, technology and daily life, challenges our understanding of fracture. Since tearing typically involves large geometric nonlinearity, it is not clear whether the stress intensity factors are meaningful or if and how they determine crack propagation. Geometry, together with the interplay between stretching and bending deformation, leads to complex behaviors, restricting analytical approximate solutions to very simplified settings and specific parameter regimes. In both situations, a rich and nontrivial experimental record has been successfully understood in terms of simple energetic models. However, general modeling approaches to either fracture in the presence of strong surface energy anisotropy or to tearing, capable of exploring new physics, have been lacking. The success of energetic simple models suggests that variational theories of brittle fracture may provide a unifying and general framework capable of dealing with the more general situations considered here. To address fracture in materials with strongly anisotropic surface energy, we propose a variational phase-field model resorting to the extended Cahn-Hilliard framework proposed in the context of crystal growth. Previous phase-field models for anisotropic fracture were formulated in a framework only allowing for weak anisotropy. We implement numerically our higher-order phase-field model with smooth local maximum entropy approximants in a direct Galerkin method. The numerical results exhibit all the features of strongly anisotropic fracture, and reproduce strikingly well recent experimental observations. To explore tearing of thin films, we develop a geometrically exact model and a computational framework coupling elasticity (stretching and bending), fracture, and adhesion to a substrate. We numerically implement the model with subdivision surface finite elements. Our simulations qualitatively and quantitatively reproduced the crack patterns observed in tearing experiments. Finally, we examine how shell geometry affects fracture. As suggested by previous results and our own phase-field simulations, shell shape dramatically affects crack evolution and the effective toughness of the shell structure. To gain insight and eventually develop new concepts for optimizing the design of thin shell structures, we derive the configurational force conjugate to crack extension for Koiter's linear thin shell theory. We identify the conservative contribution to this force through an Eshelby tensor, as well as non-conservative contributions arising from curvature.
Author: Andrea Braides
Publisher: Springer Science & Business Media
ISBN: 9783540647713
Category : Mathematics
Languages : en
Pages : 176
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Book Description
Functionals involving both volume and surface energies have a number of applications ranging from Computer Vision to Fracture Mechanics. In order to tackle numerical and dynamical problems linked to such functionals many approximations by functionals defined on smooth functions have been proposed (using high-order singular perturbations, finite-difference or non-local energies, etc.) The purpose of this book is to present a global approach to these approximations using the theory of gamma-convergence and of special functions of bounded variation. The book is directed to PhD students and researchers in calculus of variations, interested in approximation problems with possible applications.
Author: Saili Yang
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Fracture simulation in solid mechanics still faces many challenges. Various numerical methods have been developed in this area. Some of the popular methods include virtual crack closure, extended methods, damage mechanics based methods, phase-field methods and cohesive zone methods. In practice, these methods encounter one or more than one of the following difficulties: (1) inability initiate a crack; (2) instability associated with material softening; (3) complex crack tracking processes with crack propagation; (4) complicated fracture parameters without clear physical interpretations. Even though the meshfree methods can avoid any mesh related issues, they also possess other issues such like imposing essential boundary conditions and numerical integration. In this work, a conforming reproducing kernel finite volume method (RKFM) is derived based on a global weak form. In this method, the essential boundary conditions can be directly enforced with collocation. The variational consistency conditions (for Galerkin exactness) have been examined, with associated numerical patch tests and convergence rate tests performed. It is found that the method can converge optimally with low-order quadrature, in contrast to conventional Galerkin meshfree methods. The comparison of using conforming and nonconforming cells is also made, where it is found the conforming condition is essential for convergence. In addition, the method has been extended to elastodynamics, where a one dimensional wave problem is used as a benchmark with good agreement with the analytical solution. The cohesive zone model (CZM), in which the fracture parameters possess clear physical meanings, is then implemented with RKFM. The cohesive traction in CZM can be treated as natural boundary conditions applied on the cracked cell surface. The crack separation is explicitly defined as a displacement jump using the reproducing kernel approximation. A cell conforming kernel is proposed under this framework for expediency. This approach is distinctly different from other CZM based methods where cohesive elements are inserted dynamically. The classical branching problem is tested for verification of this method in capturing the ability to capture dynamic branching, and provide results that are insensitive to the resolution of the discretization. This method has been also used to simulate a single edge notched specimen test for validation, which shows great consistency with the experimental results. A phase-field approach is further developed under the RKPM framework, where the hyperbolic version is considered for efficient explicit dynamics. In this process, a regularized strain energy is proposed as the driving force for phase-field updates. The dynamic crack branching problem is also tested with this method, where the method is shown to be effective, and also provides solutions insensitive to refinement. A discontinuous RKFM formulation is also given to enhance the stability when using a cell-conforming kernel. In this formulation, a discontinuous RK approximation is proposed. Different numerical traces are tested to alleviate the discontinuity across cells. An averaged numerical trace is shown to be effective in stabilizing the simulation with a nonuniform discretization. The implementation of CZM is not influenced in this discontinuous formulation. The discontinuous RK approximation and the CZM implementation are also applied in reproducing kernel particle methods (RKPM). In this investigation, quasi-linear RK approximation is found to be inconsistent with a singular kernel when using a direct nodal integration. A discontinuous stabilized conforming nodal integration method is given to deal with this issue. This method can also be combined with CZM and shows effectiveness in predicting the crack branching problem. Both the RKFM-CZM and RKFM-phase-field methods are applied to simulate the fracture process in a high performance concrete, where the numerical results are compared with the experimental results with good agreement obtained.
Author: Timon Rabczuk
Publisher: MDPI
ISBN: 3039216864
Category : Technology & Engineering
Languages : en
Pages : 406
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Book Description
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.
Author: Francesco dell'Isola
Publisher: Springer Science & Business Media
ISBN: 3709109833
Category : Technology & Engineering
Languages : en
Pages : 363
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Book Description
F. dell'Isola, L. Placidi: Variational principles are a powerful tool also for formulating field theories. - F. dell'Isola, P. Seppecher, A. Madeo: Beyond Euler-Cauchy Continua. The structure of contact actions in N-th gradient generalized continua: a generalization of the Cauchy tetrahedron argument. - B. Bourdin, G.A. Francfort: Fracture. - S. Gavrilyuk: Multiphase flow modeling via Hamilton's principle. - V. L. Berdichevsky: Introduction to stochastic variational problems. - A. Carcaterra: New concepts in damping generation and control: theoretical formulation and industrial applications. - F. dell'Isola, P. Seppecher, A. Madeo: Fluid shock wave generation at solid-material discontinuity surfaces in porous media. Variational methods give an efficient and elegant way to formulate and solve mathematical problems that are of interest to scientists and engineers. In this book three fundamental aspects of the variational formulation of mechanics will be presented: physical, mathematical and applicative ones. The first aspect concerns the investigation of the nature of real physical problems with the aim of finding the best variational formulation suitable to those problems. The second aspect is the study of the well-posedeness of those mathematical problems which need to be solved in order to draw previsions from the formulated models. And the third aspect is related to the direct application of variational analysis to solve real engineering problems.
Author: K. Ravi-Chandar
Publisher: Elsevier
ISBN: 0080472559
Category : Science
Languages : en
Pages : 265
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Book Description
Dynamic fracture in solids has attracted much attention for over a century from engineers as well as physicists due both to its technological interest and to inherent scientific curiosity. Rapidly applied loads are encountered in a number of technical applications. In some cases such loads might be applied deliberately, as for example in problems of blasting, mining, and comminution or fragmentation; in other cases, such dynamic loads might arise from accidental conditions. Regardless of the origin of the rapid loading, it is necessary to understand the mechanisms and mechanics of fracture under dynamic loading conditions in order to design suitable procedures for assessing the susceptibility to fracture. Quite apart from its repercussions in the area of structural integrity, fundamental scientific curiosity has continued to play a large role in engendering interest in dynamic fracture problems In-depth coverage of the mechanics, experimental methods, practical applications Summary of material response of different materials Discussion of unresolved issues in dynamic fracture
Author: Jia-Liang Le
Publisher: Oxford University Press
ISBN: 0192846248
Category : Brittleness
Languages : en
Pages : 332
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Book Description
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.
