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Multiscale Simulation Of Failure Based On Space Time Finite Element Method And Non Ordinary State Based Peridynamics
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Book Synopsis Multiscale Simulation of Failure Based on Space-time Finite Element Method and Non-ordinary State-based Peridynamics by : Shogo Wada
Download or read book Multiscale Simulation of Failure Based on Space-time Finite Element Method and Non-ordinary State-based Peridynamics written by Shogo Wada and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineering materials such as rubbers are widely used in industrial applications and are often exposed to cyclic stress and strain conditions while in service. To ensure safety and reliability, quantifying the effect of loads on the life is an important but challenging task, due to the combination of geometric/material nonlinearities and loading conditions for extended time durations. In this work, a novel simulation-based approach based on space-time finite element method (FEM) is presented with a goal to capture fatigue failure in rubbery material subjected to cyclic loads and dynamic fracture in general elastic solids. It is established by integrating the time discontinuous Galerkin (TDG) formulation with either nonlinear material constitutive laws or peridynamics models. In the first implementation, nonlinear space-time FEM framework is established and integrated with a continuum damage mechanics (CDM) model to account for the damage evolution due to cyclic loading. CDM parameters for synthetic rubber are calibrated based on fatigue experiment. The nonlinear system in space-time FEM is solved using Newton’s method in which the system Jacobian is approximated with a finite difference approach. The developed approach is then employed to solve a set of benchmark problems involving fracture and low cycle fatigue in rubber. Additional tests on notched rubber sheet specimen are carried out to validate the simulation predictions. The simulation predictions yield good agreement with the tests. In addition, it is shown that responses to fatigue load with 106 cycles can be captured using the proposed approach. In the second case, a multiscale method that couples the space-time FEM based on the time discontinuous Galerkin method with non-ordinary state-based peridynamics (NOPD) is developed for dynamic fracture simulation. A concurrent coupling scheme is presented for the coupling, in which the whole domain is discretized by finite elements, and a local domain of interest is simulated with NOPD. The space-time FEM approach allows flexible choice of time step size and this makes the computation more effective. As a meshfree method, NOPD is introduced as a fine scale representation to capture the initiation and propagation of the crack. Through coupling to space-time FEM, NOPD simulation domain moves with the propagating crack front, leading to an adaptive multiscale simulation scheme. The robustness of this methodology is demonstrated through examples of a linear elastic material, in which comparisons are made to the full scale NOPD simulation. In summary, the proposed space-time approach introduces the key capability to establish approximations in the temporal domain, thus enabling prediction of nonlinear responses that are strongly time-dependent. This is demonstrated in two cases in this dissertation: the first involves fatigue failure prediction at extended time scale, and the second deals with dynamic fracture at small time scale. Based on the implementation and results, it is concluded the established space-time FEM framework is both efficient and accurate, and overcomes the critical limit of the traditional FEM approach using semi-discrete time integration schemes. The presented framework is ideal for many engineering problems featured by a multitude of temporal scales.
Book Synopsis Peridynamic Theory and Its Applications by : Erdogan Madenci
Download or read book Peridynamic Theory and Its Applications written by Erdogan Madenci and published by Springer Science & Business Media. This book was released on 2013-10-21 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the peridynamic theory, which provides the capability for improved modeling of progressive failure in materials and structures, and paves the way for addressing multi-physics and multi-scale problems. The book provides students and researchers with a theoretical and practical knowledge of the peridynamic theory and the skills required to analyze engineering problems. The text may be used in courses such as Multi-physics and Multi-scale Analysis, Nonlocal Computational Mechanics, and Computational Damage Prediction. Sample algorithms for the solution of benchmark problems are available so that the reader can modify these algorithms, and develop their own solution algorithms for specific problems. Students and researchers will find this book an essential and invaluable reference on the topic.
Book Synopsis Handbook of Peridynamic Modeling by : Florin Bobaru
Download or read book Handbook of Peridynamic Modeling written by Florin Bobaru and published by CRC Press. This book was released on 2016-11-03 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook covers the peridynamic modeling of failure and damage. Peridynamics is a reformulation of continuum mechanics based on integration of interactions rather than spatial differentiation of displacements. The book extends the classical theory of continuum mechanics to allow unguided modeling of crack propagation/fracture in brittle, quasi-brittle, and ductile materials; autonomous transition from continuous damage/fragmentation to fracture; modeling of long-range forces within a continuous body; and multiscale coupling in a consistent mathematical framework.
Book Synopsis Peridynamic Differential Operator for Numerical Analysis by : Erdogan Madenci
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.
Book Synopsis Dynamic Fracture by : K. Ravi-Chandar
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
Book Synopsis Nonlocal Modeling, Analysis, and Computation by : Qiang Du
Download or read book Nonlocal Modeling, Analysis, and Computation written by Qiang Du and published by SIAM. This book was released on 2019-03-20 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas. Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics. A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to local partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives for as well as bridges to existing models. The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on traditional models, analytical techniques, and algorithms.
Book Synopsis Extended Finite Element Method by : Amir R. Khoei
Download or read book Extended Finite Element Method written by Amir R. Khoei and published by John Wiley & Sons. This book was released on 2015-02-23 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Proceedings of the 17th International Conference on New Trends in Fatigue and Fracture by : Ricardo R. Ambriz
Download or read book Proceedings of the 17th International Conference on New Trends in Fatigue and Fracture written by Ricardo R. Ambriz and published by Springer. This book was released on 2017-11-17 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings of one of the major conferences in fatigue, fracture and structural integrity (NT2F). The papers are organized and divided in five different themes: fatigue and fracture mechanics of structures and advanced materials; fatigue and fracture in pressure vessels and pipelines: mechanical behavior and structural integrity of welded, bonded and bolted joints; residual stress and environmental effects on the fatigue behavior; and simulation methods, analytical and computation models in fatigue and fracture.
Book Synopsis Algorithms for Fast Simulations of Space-time Adaptive Finite Element Methods by : Marcin Skotniczny
Download or read book Algorithms for Fast Simulations of Space-time Adaptive Finite Element Methods written by Marcin Skotniczny and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advances in Applied Mechanics written by and published by Elsevier. This book was released on 2007-04-04 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: The major developments in the fields of fluid and solid mechanics are scattered throughout an array of technical journals, often making it difficult to find what the real advances are, especially for a researcher new to the field or an individual interested in discovering the state-of-the-art in connection with applications. The Advances in Applied Mechanics book series draws together recent significant advances in various topics in applied mechanics. Published since 1948, Advances in Applied Mechanics aims to provide authoritative review articles on topics in the mechanical sciences, primarily of interest to scientists and engineers working in the various branches of mechanics, but also of interest to the many who use the results of investigations in mechanics in various application areas such as aerospace, chemical, civil, environmental, mechanical and nuclear engineering. Advances in Applied Mechanics continues to be a publication of high visibility and impact. Review articles are provided by active, leading scientists in the field by invitation of the editors. Many of the articles published have become classics within their fields. Volume 41 in the series contains articles on topological fluid mechanics, electrospinning, vortex dynamics and self-assembly. Covers all fields of the mechanical sciences Highlights classical and modern areas of mechanics that are ready for review Provides comprehensive coverage of the field in question
Author :National Aeronautics and Space Adm Nasa Publisher :Independently Published ISBN 13 :9781794083608 Total Pages :42 pages Book Rating :4.0/5 (836 download)
Book Synopsis A Procedure for Modeling Structural Component/Attachment Failure Using Transient Finite Element Analysis by : National Aeronautics and Space Adm Nasa
Download or read book A Procedure for Modeling Structural Component/Attachment Failure Using Transient Finite Element Analysis written by National Aeronautics and Space Adm Nasa and published by Independently Published. This book was released on 2019-01-14 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: Structures often comprise smaller substructures that are connected to each other or attached to the ground by a set of finite connections. Under static loading one or more of these connections may exceed allowable limits and be deemed to fail. Of particular interest is the structural response when a connection is severed (failed) while the structure is under static load. A transient failure analysis procedure was developed by which it is possible to examine the dynamic effects that result from introducing a discrete failure while a structure is under static load. The failure is introduced by replacing a connection load history by a time-dependent load set that removes the connection load at the time of failure. The subsequent transient response is examined to determine the importance of the dynamic effects by comparing the structural response with the appropriate allowables. Additionally, this procedure utilizes a standard finite element transient analysis that is readily available in most commercial software, permitting the study of dynamic failures without the need to purchase software specifically for this purpose. The procedure is developed and explained, demonstrated on a simple cantilever box example, and finally demonstrated on a real-world example, the American Airlines Flight 587 (AA587) vertical tail plane (VTP). NASA/CR-2007-214540 Lovejoy, Andrew E. and Jegley, Dawn C. (Technical Monitor) Langley Research Center
Book Synopsis Error Analysis of a Space-time Finite Element Method for Solving PDES on Evolving Surfaces by : Maxim A. Olshanskii
Download or read book Error Analysis of a Space-time Finite Element Method for Solving PDES on Evolving Surfaces written by Maxim A. Olshanskii and published by . This book was released on 2013 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Peridynamic Theory for Progressive Failure Prediction in Homogeneous and Heterogeneous Materials by :
Download or read book Peridynamic Theory for Progressive Failure Prediction in Homogeneous and Heterogeneous Materials written by and published by . This book was released on 2008 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical continuum theory is not capable of predicting failure without an external crack growth criteria and treats the interface having zero thickness. Alternatively, a nonlocal continuum theory referred to as peridynamic theory eliminates these shortcomings by utilizing formulation that uses displacements, rather than derivatives of displacements, and including material failure in its constitutive relations through the response functions. This study presents a new response function as part of the peridynamic theory to include thermal loading. Furthermore, an efficient numerical algorithm is presented for solution of peridynamic equations. Solution method relies on the discretization of peridynamic equations at collocation points resulting in a set of ordinary differential equations with respect to time. These differential equations are then integrated using explicit methods. In order to improve numerical efficiency of the computations, spatial partitioning is introduced through uniform grids as arrays of linked lists. Furthermore, the domain of interest is divided into subunits each of which is assigned to a specific processor to utilize parallel processing using OpenMP. In order to obtain the static solutions, the adaptive dynamic relaxation method is developed for the solution of peridynamic equations. Furthermore, an approach to couple peridynamic theory and finite element analysis is introduced to take advantage of their salient features. The regions in which failure is expected are modeled using peridynamics while the remaining regions are modeled utilizing finite element method. Finally, the present solution method is utilized for damage prediction of many problems subjected to mechanical, thermal and buckling loads.
Book Synopsis A Spacetime Discontinous Galerkin Finite-element Method for Elastodynamic Analysis by : Lin Yin
Download or read book A Spacetime Discontinous Galerkin Finite-element Method for Elastodynamic Analysis written by Lin Yin and published by . This book was released on 2002 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Numerical Study on Continuous Space-time Finite Element Methods for Dynamic Signorini Problems by :
Download or read book A Numerical Study on Continuous Space-time Finite Element Methods for Dynamic Signorini Problems written by and published by . This book was released on 2015 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Adaptive Space-time Finite Element Methods for Optimization Problems Governed by Nonlinear Parabolic Systems by : Dominik Meidner
Download or read book Adaptive Space-time Finite Element Methods for Optimization Problems Governed by Nonlinear Parabolic Systems written by Dominik Meidner and published by . This book was released on 2008 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quasibrittle Fracture Mechanics and Size Effect by : Jia-Liang Le
Download or read book Quasibrittle Fracture Mechanics and Size Effect written by Jia-Liang Le and published by Oxford University Press. This book was released on 2021-11-19 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
