Download or read book A Nonlocal Operator Method for Quasi static and Dynamic Fracture Modeling written by Yongzheng Zhang and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Computational Methods Based on Peridynamics and Nonlocal Operators written by Timon Rabczuk and published by Springer Nature. This book was released on 2023-02-15 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of computational methods based on peridynamics and nonlocal operators and their application to challenging numerical problems which are difficult to deal with traditional methods such as the finite element method, material failure being “only” one of them. The authors have also developed a higher-order nonlocal operator approaches capable of solving higher-order partial differential equations on arbitrary domains in higher-dimensional space with ease. This book is of interest to those in academia and industry.

Download or read book Extended Finite Element and Meshfree Methods written by Timon Rabczuk and published by Academic Press. This book was released on 2019-11-13 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extended Finite Element and Meshfree Methods provides an overview of, and investigates, recent developments in extended finite elements with a focus on applications to material failure in statics and dynamics. This class of methods is ideally suited for applications, such as crack propagation, two-phase flow, fluid-structure-interaction, optimization and inverse analysis because they do not require any remeshing. These methods include the original extended finite element method, smoothed extended finite element method (XFEM), phantom node method, extended meshfree methods, numerical manifold method and extended isogeometric analysis. This book also addresses their implementation and provides small MATLAB codes on each sub-topic. Also discussed are the challenges and efficient algorithms for tracking the crack path which plays an important role for complex engineering applications. Explains all the important theory behind XFEM and meshfree methods Provides advice on how to implement XFEM for a range of practical purposes, along with helpful MATLAB codes Draws on the latest research to explore new topics, such as the applications of XFEM to shell formulations, and extended meshfree and extended isogeometric methods Introduces alternative modeling methods to help readers decide what is most appropriate for their work

Download or read book Advances in Applied Mechanics written by Daniel S. Balint and published by Academic Press. This book was released on 2020-10-23 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Applied Mechanics, Volume 53 in this ongoing series, highlights new advances in the field, with this new volume presenting interesting chapters on Phase field modelling of fracture, Advanced geometry representations and tools for microstructural and multiscale modelling, The material point method: the past and the future, From Experimental Modeling of Shotcrete to Large Scale Numerical Simulations of Tunneling, and Material point method after 25 years: theory, implementation, applications. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Advances in Applied Mechanics series

Download or read book Quasi static Non ordinary State based Peridynamics for the Modeling of 3D Fracture written by and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Dynamic Fracture written by K. Ravi-Chandar and published by Elsevier. This book was released on 2004-10-16 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book The Variational Approach to Fracture written by Blaise Bourdin and published by Springer Science & Business Media. This book was released on 2008-04-19 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Computational Methods in the Mechanics of Fracture written by Satya N. Atluri and published by North Holland. This book was released on 1986 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume not only covers the fundamental concepts of fracture mechanics, but also the computational methodologies necessary for practical engineering designs aimed at fracture control. It gives a concise summary of various fracture theories: linear elastic, elastic-plastic, and dynamic fracture mechanics of metals and composites. Novel numerical methods (finite element and boundary element) that enable the treatment of complicated engineering problems are emphasized. Examined are problems of linear elastic fracture of metallic and non-metallic composite materials, three-dimensional problems of surface flaws, elastic-plastic fracture, stable crack growth, and dynamic crack propagation. A comprehensive outline of the energetic approach and energy integrals on fracture mechanics is also given. Contents: Preface. Parts: I. Chapters: 1. Fracture: Mechanics or Art? (F. Erdogan). II. 2. Linear Elastic Fracture Mechanics (A.S. Kobayashi). 3. Elastic-Plastic Fracture (Quasi-Static) (S.N. Atluri and A.S. Kobayashi). 4. Dynamic Crack Propagation in Solids (L.B. Freund). 5. Energetic Approaches and Path-Independent Integrals in Fracture Mechanics (S.N. Atluri). III. 6.

Download or read book Potential Based Fracture Mechanics Using Cohesive Zone and Virtual Internal Bond Modeling written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Peridynamic Differential Operator for Numerical Analysis written by Erdogan Madenci and published by Springer. This book was released on 2019-01-17 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the peridynamic (PD) differential operator, which enables the nonlocal form of local differentiation. PD is a bridge between differentiation and integration. It provides the computational solution of complex field equations and evaluation of derivatives of smooth or scattered data in the presence of discontinuities. PD also serves as a natural filter to smooth noisy data and to recover missing data. This book starts with an overview of the PD concept, the derivation of the PD differential operator, its numerical implementation for the spatial and temporal derivatives, and the description of sources of error. The applications concern interpolation, regression, and smoothing of data, solutions to nonlinear ordinary differential equations, single- and multi-field partial differential equations and integro-differential equations. It describes the derivation of the weak form of PD Poisson’s and Navier’s equations for direct imposition of essential and natural boundary conditions. It also presents an alternative approach for the PD differential operator based on the least squares minimization. Peridynamic Differential Operator for Numerical Analysis is suitable for both advanced-level student and researchers, demonstrating how to construct solutions to all of the applications. Provided as supplementary material, solution algorithms for a set of selected applications are available for more details in the numerical implementation.

Download or read book Nonlinear and Dynamic Fracture Mechanics written by Nicholas Perrone and published by . This book was released on 1979 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Cohesive Modeling of Dynamic Fracture Rate Dependence and Intersonic Crack Motion written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Spacetime Damage based Cohesive Model for Elastodynamic Fracture with Dynamic Contact written by Reza Abedi and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamic material failure is important in a number of scientific and engineering applications and a variety of numerical methods for its modeling have been proposed. This thesis presents the formulation and implementation of an interfacial-damage, cohesive-fracture model, including contact and friction effects, for dynamic failure of brittle materials. The model is implemented within a spacetime discontinuous Galerkin (SDG) finite element method. An adaptive meshing procedure generates %When implemented on suitable spacetime grids that satisfy a special causality constraint to enable an efficient patch-by-patch, advancing-front solution scheme with O(N) computational complexity. Per-element balance properties, local adaptive operations, and the use of Riemann fluxes provide to the SDG method the extreme accuracy and efficiency required to solve multiscale fracture problems. A dimensional analysis of linear elastodynamics, with extensions to fracture models based on cohesive traction--separation laws, supports the formulation. The problem is formulated and analyzed using differential forms and the exterior calculus in spacetime. The analysis demonstrates that the velocity scalings implied by the spatial and temporal coordinate scalings and by the scalings of the material properties must be identical to obtain a self-similar scaling of an elastodynamic process. The use of differential forms reveals intrinsic structure and relations between the spacetime mechanics fields which are otherwise obscured by conventional tensorial analysis. For example, only four distinct scalings are required to define a scaled elastodynamic process when we work directly with forms, while eight are required when tensorial analysis is used. In the context of dynamic cohesive fracture, the analysis shows that, among the nondimensional variables, the ratio of the stress-loading scale to the cohesive strength is proportional to the ratio of the radius of the singularity-dominant zone from Linear Elastodynamic Fracture Mechanics (LEFM), to the cohesive-process-zone size. These ratios are, in turn, useful indicators of whether the small-scale-yielding caveat of LEFM is satisfied. A novel continuum formulation of the linear elastodynamic contact problem also supports the SDG finite element model. In contrast to previous contact models that invoke quasi-static contact conditions, the proposed model enforces dynamic contact conditions by prescribing momentum flux and compatibility conditions obtained from the local Riemann problems for bonded, separation, contact--stick, and contact--slip modes. This approach preserves the characteristic structure of the underlying equations at the contact interface, a property that is lacking in previous formulations. The fully-bonded and contact--stick conditions are identical, as expected, so the non-penetration and tangential slip constraints are treated exactly in the new continuum formulation. Furthermore, the direction of the tangential contact traction (friction) is shown to be continuous through transitions between contact--stick and contact-slip modes. These favorable properties, which improve the accuracy of and facilitate numerical implementations of the proposed model, are not obtained in many existing models which, for example, replace the non-penetration constraint with a large interfacial stiffness in the normal direction. %For example, the required continuity conditions are replaced with large penetration stiffness values in penalty methods. % Furthermore, it is shown that the relative tangential velocity in slip mode is aligned with the tangential traction that would have resulted under the stick mode. It is well documented that the determination of slip traction from slip velocity is discontinuous and poses several difficulties in numerical methods. The choice of stick tranction, on the otherhand, provides a continuous representation for the direction of slip traction. % The direction of slip traction is determined from the slip velocity in Coulomb law of friction. However, the discontinuous nature of this representation causes several difficulties in the numerical methods. It is shown that the orientation derived from a tangential traction that would have acted in stick mode eliminates the discontinuity. The transition between separation and contact modes retains its physically discontinuous character, and a regularization of this transition is introduced to facilitate and reduce the cost of numerical implementations. A discretization and numerical implementation within the adaptive SDG framework demonstrate the effectiveness of the new contact model in a numerical setting. A new two-scale cohesive fracture model replaces the usual traction-separation law with a damage model that represents mesoscale processes of void growth and coalescence. The evolution of a single damage parameter D, which represents the debonded area fraction on cohesive interfaces, is governed by an irreversible, time-delay evolution law characterized by a cohesive strength and a relaxation time that determines the maximum damage rate. Riemann fluxes for the fully-bonded condition are enforced in the undamaged area fraction (1-D) of the cohesive interface, while the Riemann fluxes for the contact--stick, contact--slip or separation conditions determine the fluxes in the debonded area fraction. These mesoscale Riemann values are averaged to derive macroscopic cohesive conditions. % The damage-based cohesive model is implemented within the adaptive SDG finite element framework to produce a numerical model that efficiently and accurately resolves the multi-scale response associated with dynamic fracture and transitions between contact, separation, stick and slip conditions in the event of crack closure. Beyond ensuring solution accuracy, the model uses the SDG scheme's adaptive meshing capabilities to freely nucleate and extend cohesive interfaces to capture solution-dependent crack paths. The SDG adaptive meshing aligns the boundaries of spacetime elements with crack-path trajectories having arbitrary position and orientation, and two adaptive error indicators ensure the accurate rendering of both the cohesive model and the bulk solution. Thus, the present model does not suffer the limited resolution and mesh-dependent effects encountered in most other numerical fracture models. Numerical results obtained with the proposed model demonstrate crack propagation, microcrack formation and crack branching phenomena.

Download or read book A3N2M Approximation Applications and Analysis of Nonlocal Nonlinear Models written by Tadele Mengesha and published by Springer Nature. This book was released on 2023-09-12 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects papers based on plenary and invited talks given at the 50th Barrett Memorial Lectures on Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models that was organized by the University of Tennessee, Knoxville and held virtually in May 2021. The three-day meeting brought together experts from the computational, scientific, engineering, and mathematical communities who work with nonlocal models. These proceedings collect contributions and give a survey of the state of the art in computational practices, mathematical analysis, applications of nonlocal models, and explorations of new application domains. The volume benefits from the mixture of contributions by computational scientists, mathematicians, and application specialists. The content is suitable for graduate students as well as specialists working with nonlocal models and covers topics on fractional PDEs, regularity theory for kinetic equations, approximation theory for fractional diffusion, analysis of nonlocal diffusion model as a bridge between local and fractional PDEs, and more.

Download or read book Peridynamic Modeling Numerical Techniques and Applications written by Erkan Oterkus and published by Elsevier. This book was released on 2021-04-29 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides readers with an incisive look at cutting-edge peridynamic modeling methods, numerical techniques, their applications, and potential future directions for the field. It starts with an introductory chapter authored by Stewart Silling, who originally developed peridynamics. It then looks at new concepts in the field, with chapters covering dual-horizon peridynamics, peridynamics for axisymmetric analysis, beam and plate models in peridynamics, coupled peridynamics and XFEM, peridynamics for dynamic fracture modeling, and more. From there, it segues into coverage of cutting-edge applications of peridynamics, exploring its biological applications, modeling at the nanoscale, peridynamics for composites delamination and damage in ceramics, and more, concluding with a chapter on the application of artificial intelligence and machine learning in peridynamics. Covers modeling methods, numerical techniques, applications, and future directions for the field Discusses techniques such as dual-horizon peridynamics, damage modeling using the phase-field approach, and contact analysis of rigid and deformable bodies with refined non-ordinary state-based peridynamics Looks at a range of different peridynamic applications such as ice modeling, fiber-reinforced composite modeling, modeling at nanoscale, and more

Download or read book Non Smooth Thermomechanics written by Michel Fremond and published by Springer Science & Business Media. This book was released on 2001-10-09 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on practical problems in mechanical engineering, here the author develops the fundamental concepts of non-smooth mechanics and introduces the necessary background material needed to deal with mechanics involving discontinuities and non-smooth constraints.

Download or read book Computational Methods for Fracture written by Timon Rabczuk and published by MDPI. This book was released on 2019-10-28 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.