Academic literature on the topic 'Peridynamics Model'
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Journal articles on the topic "Peridynamics Model"
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Seleson, Pablo, Michael L. Parks, and Max Gunzburger. "Peridynamic State-Based Models and the Embedded-Atom Model." Communications in Computational Physics 15, no. 1 (January 2014): 179–205. http://dx.doi.org/10.4208/cicp.081211.300413a.
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AbstractWe investigate connections between nonlocal continuum models and molecular dynamics. A continuous upscaling of molecular dynamics models of the form of the embedded-atom model is presented, providing means for simulating molecular dynamics systems at greatly reduced cost. Results are presented for structured and structureless material models, supported by computational experiments. The nonlocal continuum models are shown to be instances of the state-based peridynamics theory. Connections relating multibody peridynamic models and upscaled nonlocal continuum models are derived.
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Shen, Feng, Qing Zhang, and Dan Huang. "Damage and Failure Process of Concrete Structure under Uniaxial Compression Based on Peridynamics Modeling." Mathematical Problems in Engineering 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/631074.
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Peridynamics is a nonlocal formulation of continuum mechanics, which uses integral formulation rather than the spatial partial differential equations. The peridynamic approach avoids using any spatial derivatives, which arise naturally in the classical local theory. It has shown effectiveness and advantage in solving discontinuous problems at both macro- and microscales. In this paper, the peridynamic theory is used to analyze damage and progressive failure of concrete structures. A nonlocal peridynamic model for concrete columns under uniaxial compression is developed. Numerical example illustrates that cracks in a peridynamic body of concrete form spontaneously. The result of the example clarifies the unique advantage of modeling damage accumulation and progressive failure of concrete based on peridynamic theory. This study provides a new promising alternative for analyzing complicated discontinuity problems. Finally, some open problems and future research trends in peridynamics are discussed.
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Liu, Shankun, Fei Han, Xiaoliang Deng, and Ye Lin. "Thermomechanical Peridynamic Modeling for Ductile Fracture." Materials 16, no. 11 (May 30, 2023): 4074. http://dx.doi.org/10.3390/ma16114074.
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In this paper, we propose a modeling method based on peridynamics for ductile fracture at high temperatures. We use a thermoelastic coupling model combining peridynamics and classical continuum mechanics to limit peridynamics calculations to the failure region of a given structure, thereby reducing computational costs. Additionally, we develop a plastic constitutive model of peridynamic bonds to capture the process of ductile fracture in the structure. Furthermore, we introduce an iterative algorithm for ductile-fracture calculations. We present several numerical examples illustrating the performance of our approach. More specifically, we simulated the fracture processes of a superalloy structure in 800 ℃ and 900 ℃ environments and compared the results with experimental data. Our comparisons show that the crack modes captured by the proposed model are similar to the experimental observations, verfying the validity of the proposed model.
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Mikeš, Karel, Milan Jirásek, Jan Zeman, Ondřej Rokoš, and Ron H. J. Peerlings. "LOCALIZATION ANALYSIS OF DAMAGE FOR ONE-DIMENSIONAL PERIDYNAMIC MODEL." Acta Polytechnica CTU Proceedings 30 (April 22, 2021): 47–52. http://dx.doi.org/10.14311/app.2021.30.0047.
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Peridynamics is a recently developed extension of continuum mechanics, which replaces the traditional concept of stress by force interactions between material points at a finite distance. The peridynamic continuum is thus intrinsically nonlocal. In this contribution, a bond-based peridynamic model with elastic-brittle interactions is considered and the critical strain is defined for each bond as a function of its length. Various forms of length functions are employed to achieve a variety of macroscopic responses. A detailed study of three different localization mechanisms is performed for a one-dimensional periodic unit cell. Furthermore, a convergence study of the adopted finite element discretization of the peridynamic model is provided and an effective event-driven numerical algorithm is described.
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Altenbach, Holm, Oleksiy Larin, Konstantin Naumenko, Olha Sukhanova, and Mathias Würkner. "Elastic plate under low velocity impact: Classical continuum mechanics vs peridynamics analysis." AIMS Materials Science 9, no. 5 (2022): 702–18. http://dx.doi.org/10.3934/matersci.2022043.
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<abstract><p>The aim of this paper is to compare the classical continuum mechanics and the peridynamic models in the structural analysis of a monolithic glass plate subjected to ball drop. Governing equations are recalled in order to highlight the differences and basic features of both approaches. In this study the behavior of glass is assumed to be linear-elastic and damage processes are ignored. The generalized Hooke's law is assumed within the classical theory, while the linear peridynamic solid constitutive model is applied within the peridynamic analysis. Mechanical models for the ball drop simulation are discussed in detail. An emphasis is placed on the discretization including finite element mesh, peridynamic node lattice and time stepping, as well as appropriate constraints and contact conditions in both finite element and non-local peridynamics models. Deflections of the plate after the ball drop are presented as functions of time and the results based on the finite element and peridynamic analysis are compared. Good agreements between the deflection values in selected points of the plate as well as deflection fields at several time points indicate, that the model assumptions for the non-local peridynamic analysis including the horizon size, the short-range force contact settings and the support conditions are well suited. The developed peridynamics models can be applied in the future to analyze damage patterns in glass plates.</p></abstract>
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Vazic, Bozo, Erkan Oterkus, and Selda Oterkus. "In-Plane and Out-of Plane Failure of an Ice Sheet using Peridynamics." Journal of Mechanics 36, no. 2 (January 17, 2020): 265–71. http://dx.doi.org/10.1017/jmech.2019.65.
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ABSTRACTWhen dealing with ice structure interaction modeling, such as designs for offshore structures/icebreakers or predicting ice cover’s bearing capacity for transportation, it is essential to determine the most important failure modes of ice. Structural properties, ice material properties, ice-structure interaction processes, and ice sheet geometries have significant effect on failure modes. In this paper two most frequently observed failure modes are studied; splitting failure mode for in-plane failure of finite ice sheet and out-of-plane failure of semi-infinite ice sheet. Peridynamic theory was used to determine the load necessary for inplane failure of a finite ice sheet. Moreover, the relationship between radial crack initiation load and measured out-of-plane failure load for a semi-infinite ice sheet is established. To achieve this, two peridynamic models are developed. First model is a 2 dimensional bond based peridynamic model of a plate with initial crack used for the in-plane case. Second model is based on a Mindlin plate resting on a Winkler elastic foundation formulation for out-of-plane case. Numerical results obtained using peridynamics are compared against experimental results and a good agreement between the two approaches is obtained confirming capability of peridynamics for predicting in-plane and out-of-plane failure of ice sheets.
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Karpenko, Olena, Selda Oterkus, and Erkan Oterkus. "An in-depth investigation of critical stretch based failure criterion in ordinary state-based peridynamics." International Journal of Fracture 226, no. 1 (October 2, 2020): 97–119. http://dx.doi.org/10.1007/s10704-020-00481-z.
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AbstractThis study presents an in-depth investigation of the critical stretch based failure criterion in ordinary state-based peridynamics for both static and dynamic conditions. Seven different cases are investigated to determine the effect of the failure parameter on peridynamic forces between material points and dilatation. Based on crack opening displacement (COD) results from both peridynamics and finite element analysis, it was found that one of the seven cases provides the best agreement between the two approaches. This particular case is further investigated by considering the influence of the discretisation and the horizon sizes on COD and crack propagation speeds. Moreover, PD predictions of COD for PMMA material is analysed with the theory of dynamic fracture mechanics and compared with the fracture experiments. It is shown that the peridynamic model can correctly model, simulate and predict the behaviour of the crack under different loading conditions. Furthermore, the presented PD models capture accurate fracture phenomena, specifically the crack path, branching angles and crack propagation speeds, which are in good agreement with experimental results.
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Ahadi, Aylin, Per Hansson, and Solveig Melin. "Simulating Nanoindentation of Thin Cu Films Using Molecular Dynamics and Peridynamics." Solid State Phenomena 258 (December 2016): 25–28. http://dx.doi.org/10.4028/www.scientific.net/ssp.258.25.
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Nanoindentation is a useful experimental method to characterize the micromechanical properties of materials. In this study molecular dynamics and peridynamics are used to simulate nanoindentation, with a spherical indenter targeting a thin single crystal Cu film, resting on an infinitely stiff substrate. The objective is to compare the results obtained from molecular dynamic simulations to those obtained using a peridynamic approach as regards the force-displacement curves and the deformation patterns after that the material parameters in the peridynamic model have been fitted to the force displacement curve from the molecular dynamic simulation.
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Vazic, Bozo, Erkan Oterkus, and Selda Oterkus. "Peridynamic Model for a Mindlin Plate Resting on a Winkler Elastic Foundation." Journal of Peridynamics and Nonlocal Modeling 2, no. 3 (January 10, 2020): 229–42. http://dx.doi.org/10.1007/s42102-019-00019-5.
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AbstractIn this study, a peridynamic model is presented for a Mindlin plate resting on a Winkler elastic foundation. In order to achieve static and quasi-static loading conditions, direct solution of the peridynamic equations is utilised by directly assigning inertia terms to zero rather than using widely adapted adaptive dynamic relaxation approach. The formulation is verified by comparing against a finite element solution for transverse loading condition without considering damage and comparing against a previous study for pure bending of a Mindlin plate with a central crack made of polymethyl methacrylate material having negligibly small elastic foundation stiffness. Finally, the fracture behaviour of a pre-cracked Mindlin plate rested on a Winkler foundation subjected to transverse loading representing a floating ice floe interacting with sloping structures. Similar fracture patterns observed in field observations were successfully captured by peridynamics.
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Shen, Feng, Zihan Chen, Jia Zheng, and Qing Zhang. "Numerical Simulation of Failure Behavior of Reinforced Concrete Shear Walls by a Micropolar Peridynamic Model." Materials 16, no. 8 (April 18, 2023): 3199. http://dx.doi.org/10.3390/ma16083199.
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A reinforced concrete shear wall is an important building structure. Once damage occurs, it not only causes great losses to various properties but also seriously endangers people’s lives. It is difficult to achieve an accurate description of the damage process using the traditional numerical calculation method, which is based on the continuous medium theory. Its bottleneck lies in the crack-induced discontinuity, whereas the adopted numerical analysis method has the continuity requirement. The peridynamic theory can solve discontinuity problems and analyze material damage processes during crack expansion. In this paper, the quasi-static failure and impact failure of shear walls are simulated by improved micropolar peridynamics, which provides the whole process of microdefect growth, damage accumulation, crack initiation, and propagation. The peridynamic predictions are in good match with the current experiment observations, filling the gap of shear wall failure behavior in existing research.
Dissertations / Theses on the topic "Peridynamics Model"
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Van, Der Merwe Carel Wagener. "A peridynamic model for sleeved hydraulic fracture." Thesis, Stellenbosch : Stellenbosch University, 2014. http://hdl.handle.net/10019.1/95993.
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Thesis (MEng)--Stellenbosch University, 2014.ENGLISH ABSTRACT: Current numerical methods in the eld of hydraulic fracturing are based mainly on continuum methods, such as the Finite Element Method (FEM) and the Boundary Element Method (BEM). These methods are governed by Linear Elastic Fracture Mechanics (LEFM) criteria, which su er from the inherent aw of a non-physical stress representation at the fracture tip. In response to this, a non-local method is proposed, namely the peridynamic theory, to model sleeved hydraulic fracture. A 2D implicit quasi-static ordinary state based peridynamic formulation is implemented on various benchmark problems, to verify the ability to capture constitutive behaviour in a linear elastic solid, as well as, the quanti cation of adverse e ects on the accuracy of the displacement solution, due to the nature of the non-local theory. Benchmark tests consist of a plate in tension, where convergence to the classical displacement solution, non-uniform re nement and varying cell sizes are tested, as well as, a thick walled cylinder with internal pressure, where three di erent loading techniques are tested. The most accurate loading technique is applied to the sleeved fracture model, in order to simulate fracture initiation and propagation. This model is then veri ed and validated by using the Rummel & Winter hydraulic fracturing model and experimental results, respectively. Displacement error minimisation methods are implemented and as a result, the displacement solutions for a plate in tension converges to the analytical solution, while the thick walled cylinder solutions su er from inaccuracies due to an applied load on an irregularly discretized region. The fracture initiation test captures the fracture tip behaviour of the Rummel & Winter model and the fracture propagation test show good correlation with experimental results. This research shows that the peridynamic approach to sleeved hydraulic fracture can yield a realistic representation of fracture initiation and propagation, however, further research is needed in the area of a pressure load application on a solid using the peridynamic approach.
AFRIKAANSE OPSOMMING: Huidige numeriese metodes in die veld van hidrouliese breking is hoofsaaklik gebaseer op kontinuum metodes, soos die Eindige Element Metode (EEM) en die Rand Element Metode (REM). Hierdie metodes word beheer deur Linie^ere Elastiese Breukmeganika (LEB) kriteria, wat ly aan die inherente gebrek van 'n nie- siese voorstelling van die spanning by die fraktuur punt. Om hierdie probleme aan te spreek, word 'n nie-lokale metode voorgestel, naamlik die peridinamiese teorie, om gehulsde hidrouliese breking te modelleer. 'n 2D implisiete kwasi-statiese ordin^ere toestand gebaseerde peridinamika formulering word ge mplimenteer op verskeie norm probleme, om te veri eer of dit oor die vermo e beskik om die konstitutiewe gedrag van 'n linie^ere elastiese soliede materiaal te modeleer, asook die kwanti sering van nadelige e ekte op die verplasings oplossing as gevolg van die natuur van die nie-lokale teorie. Normtoetse bestaan uit 'n plaat in trek spanning, waar konvergensie na die klassieke verplasings oplossing, nie-uniforme verfyning en vari^eerende sel groottes getoets word, asook 'n dikwandige silinder onder interne druk, waar drie verskillende belasting aanwendingstegnieke getoets word. Die mees akkurate belasting aanwendingstegniek word dan gebruik in die gehulsde hidrouliese breking model, om fraktuur aanvangs en uitbreiding na te boots. Die model word dan geveri- eer deur die Rummel & Winter hidrouliese breking model en eksperimentele resultate, onderskeidelik. Fout minimering metodes word toegepas en as 'n resultaat, konvergeer die verplasing oplossing vir die plaat na die analitiese oplossing, terwyl die oplossing van die dikwandige silinder onakuraathede toon as gevolg van 'n toegepaste belasting op 'n onre elmatig gediskretiseerde gebied. Die modellering van die fraktuur inisi ering by die fraktuur punt, stem goed ooreen met die Rummel en Winter voorspelling en die fraktuur uitbreiding stem goed ooreen met eksperimentele resultate. Hierdie navorsing toon dat die peridinamiese benadering tot gehulsde hidrouliese breking wel die fraktuur inisi ering en uitbreiding realisties kan modelleer, maar nog navorsing word wel benodig in die area waar 'n druk belasting op 'n peridinamiese soliede model toegepas word.
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Birkey, Justin. "Development of Visual EMU, a graphical user interface for the peridynamic EMU code." Thesis, Manhattan, Kan. : Kansas State University, 2007. http://hdl.handle.net/2097/466.
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Glaws, Andrew Taylor. "Finite Element Simulations of Two Dimensional Peridynamic Models." Thesis, Virginia Tech, 2014. http://hdl.handle.net/10919/48121.
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This thesis explores the science of solid mechanics via the theory of peridynamics. Peridynamics has several key advantages over the classical theory of elasticity. The most notable of which is the ease with which fractures in the the material are handled. The goal here is to study the two theories and how they relate for problems in which the classical method is known to work well. While it is known that state-based peridynamic models agree with classical elasticity as the horizon radius vanishes, similar results for bond-based models have yet to be developed. In this study, we use numerical simulations to investigate the behavior of bond-based peridynamic models under this limit for a number of cases where analytic solutions of the classical elasticity problem are known. To carry out this study, the integral-based peridynamic model is solved using the finite element method in two dimensions and compared against solutions using the classical approach.Master of Science
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Bai, Ruqing. "Numerical modeling of isotropic and composites structures using a shell-based peridynamic method." Thesis, Compiègne, 2019. http://www.theses.fr/2019COMP2482.
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Le travail de thèse porte sur de nouveaux compléments et améliorations pour la théorie de la péridynamique concernant la modélisation numérique de structures minces telles que les poutres et les plaques, les composites isotropes et multicouches soumis à un chargement dynamique. Nos développements ont principalement porté sur l'exploration des possibilités offertes par la méthode péridynamique, largement appliquée dans divers domaines de l'ingénierie où des discontinuités fortes ou faibles peuvent se produire, telles que des fissures. La procédure de généralisation de la méthode Peridynamics pour la modélisation des structures de poutres de Timoshenko et des structures de plaques de Reissner-Mindlin avec une large plage de rapport épaisseur sur longueur allant de structures épaisses à très minces est indiquée. Et un impact avec une faible vitesse simplifié basé sur le modèle péridynamique développé pour la poutre de Timoshenko et la plaque de Reissner-Mindlin a été proposé en utilisant une procédure de contact spécifique pour l'estimation « naturelle » de la charge d'impact. L’originalité de la méthode actuelle réside dans l’introduction avec deux techniques permettant de réduire le problème de blocage par cisaillement qui se pose dans les structures à poutres et à plaques minces, à savoir la méthode d’intégration réduite (ou sélective) et la formulation mixte. Le modèle péridynamique résultant pour les structures de poutre de Timoshenko et les structures de plaque de Reissner-Mindlin est efficace et ne souffre d'aucun phénomène de verrouillage par cisaillement. En outre, la procédure de généralisation de la méthode péridynamique pour la modélisation de structures composites minces renforcées par des fibres est introduite. L’approche péridynamique pour la modélisation d’une couche est d’abord validée en quasi-statique, ce qui inclut des problèmes de prévision de la propagation de fissures soumis à des conditions de chargement mécaniques. La méthode péridynamique a ensuite été étendue à l’analyse de structures composites minces renforcées par des fibres utilisant la théorie fondamentale d’une couche. Enfin, plusieurs applications impliquant des structures composites minces renforcées par des fibres et des résultats numériques ont été validées par comparaison à la solution FEM obtenue à l'aide d'un logiciel commercial ou à des solutions de référence de la littérature. Dans toutes les applications, Péridynamics montre que les résultats correspondent parfaitement aux solutions de référence, ce qui prouve son potentiel d’efficacité, en particulier pour la simulation de chemins de fissures dans les structures isotropes et compositesThis thesis introduces some new complements and improvments for the Bond-Based Peridynamics theory concerning the numerical modeling of thin structures such as beams and plates, isotropic and multilayer composites subjected to dynamic loading. Our developments have been focused mainly on exploring the possibilities offered by the Peridynamic method, which has been widely applied in various engineering domains where strong or weak discontinuities may occur such as cracks or heterogeneous media. The generalization procedure of the Peridynamics method for the modeling of Timoshenko beam structures and Reissner-Mindlin plate structures respectively with a wide range of thickness to length ratio starting from thick structures to very thin structures is given. And A simplified low velocity impact based on the developed Peridynamic model for Timoshenko beam and ReissnerMindlin plate has been proposed by using a specific contact procedure for the estimation of the impact load. The originality of the present method was the introduction for the first time of two techniques for the alleviation of the shear locking problem which arises in thin beam and plate structures, namely the reduced (or selective) integration method and mixed formulation. The resulting Peridynamic model for Timoshenko beam structures and Reissner-Mindlin plate structures is efficient and does not suffer from any shear locking phenomenon. Besides, the generalization procedure of Peridynamic method for the modeling of fiber-reinforced thin composite structures is introduced. The Peridynamic approach for the modeling of a lamina is firstly validated in the quasi-statics including a crack propagation prediction problems subjected to mechanical loading conditions and then the Peridynamic method was further extended to analyze fiber-reinforced thin composite structures using the fundamental lamina theory. Finally, several applications involving fiber-reinforced thin composite structures and numerical results were validated by comparison to the FEM solution obtained using commercial software or to reference solutions from the literature. In all applications, the Peridynamics shows that results are matching perfectly the reference solutions, which proves its efficiency potentiality especially for crack paths simulation in isotropic and composite structures
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Deepu, S. P. "Non-Local Continuum Models for Damage in Solids and Delamination of Composites." Thesis, 2017. http://etd.iisc.ac.in/handle/2005/4206.
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The focus of the thesis is on developing new damage models for brittle materials and using these to study delamination of composite structures. Chapter 1 gives an introductory literature review in order to motivate the work undertaken in the chapters to follow. Chapter 2 deals with a new micropolar damage model for delamination in composites. By combining phase field theory and peridynamics, Chapter 3 develops a new formalism to study damage in brittle materials under dynamic loading. Chapter 4 exploits and extends this idea for modelling delamination of composites. An extended chapter-wise summary of the contributions in the thesis is provided below.
In Chapter 2, a micropolar cohesive damage model for delamination of composites is proposed. The main idea is to embed micropolarity, which brings in an added layer of kinematics through the micro-rotation degrees of freedom within a continuum model to account for the micro-structural effects during delamination. The resulting cohesive model, described through a modified traction separation law, includes micro-rotational jumps in addition to displacement jumps across the interface. The incorporation of micro-rotation requires the model to be supplemented with physically relevant material length scale parameters, whose effects during delamination in modes I and II are brought forth using numerical simulations appropriately supported by experimental evidences.
In Chapter 3, we attempt at reformulating the phase field theory within the framework of peridynamics (PD) to arrive at a non-local continuum damage model. This obtains a better criterion for bond breaking in PD, marking a departure from the inherently ad-hoc bond-stretch-based or bond-energy-based conditions and thus allowing the model to simulate fragmentation which a phase field model cannot by itself accomplish. Moreover, posed within the PD setup, the integral equation for the phase field eases the smoothness restrictions on the field variable. Taking advantages of both the worlds, the scheme thus offers a better computational approach to problems involving cracks or discontinuities. Starting with Hamilton’s principle, an equation of the Ginzburg-Landau type with dissipative correction is arrived at as a model for the phase field evolution. A constitutive correspondence route is followed to incorporate
classical constitutive relations within our PD model. Numerical simulations of dynamic crack propagation (including branching) and the Kalthoff-Winkler experiment are also provided. To demonstrate the natural ability of the model to prevent interpenetration, a mode II delamination simulation is presented. A brief discussion on the convergence of PD equations to classical theory is provided in the Appendix B.
In Chapter 4, we extend and exploit the phase field based PD damage model, developed in Chapter 3, for studying delamination of composites. Utilizing the phase field augmented PD framework, our idea is to model the interfacial cohesive damage through degradation functions and the fracture or fragmentation through the critical energy release rate. Our model eliminates the conventional traction-separation law (TSL) that is known to result in the popular cohesive zone model (CZM). In the process, the approach potentially addresses some limitations of the existing techniques, which make use of an empirical interaction among different modes of loading (e.g. mode I, mode II etc.). By regarding delamination under different loading conditions as problems that differ only in their boundary conditions, our approach provides for a more general scheme for tracking delamination. Our proposal thus accords no special treatment to the different modes and can handle general spatial locations of weaker interface layers. With no special crack tracking algorithms or additional ad-hoc criteria for crack propagation, considerable computational simplicity also accrues. The approach can tackle cases where cracks may propagate even in the bulk material body. The new bond breaking criterion that we employ replaces the ad-hocism inherent in bond-stretch-based or bond-energy-based conditions. Using numerical simulations on mode I (double cantilever beam test), mode II (end loaded split and end notched flexure tests) and mixed mode (fixed ratio mixed mode test) delamination cases, the model is validated against relevant experimental observations. Simulations on modified mixed mode bending test and multiple layer delamination test are also presented.
The thesis is wound up in Chapter 5 with a summary of accomplished research and some suggestions for future research.
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Rahaman, Md Masiur. "Dynamic Flow Rules in Continuum Visco-plasticity and Damage Models for Poly-crystalline Solids." Thesis, 2017. http://etd.iisc.ac.in/handle/2005/4240.
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Modelling highly non-linear, strongly temperature- and rate-dependent visco-plastic behaviour of poly-crystalline solids (e.g., metals and metallic alloys) is one of the most challenging topics of contemporary research interest, mainly owing to the increasing use of metallic structures in engineering applications. Numerous classical models have been developed to model the visco-plastic behaviour of poly-crystalline solids. However, limitations of classical visco-plasticity models have been realized mainly in two cases: in problems at the scale of mesoscopic length (typically in the range of a tenth of a micron to a few tens of micron) or lower, and in impact problems under high-strain loading with varying temperature. As a remedy of the first case, several length scale dependent non-local visco-plasticity models have been developed in the last few decades. Unfortunately, a rationally grounded continuum model with the capability of reproducing visco-plastic response in accord with the experimental observations under high strain-rates and varying temperatures remains elusive and attempts in this direction are often mired in controversies. With the understanding of metal visco-plasticity as a macroscopic manifestation of the underlying dislocation motion, there are attempts to develop phenomenological as well as physics-based continuum models that could be applied across different regimes of temperature and strain rate. Yet, none of these continuum visco-plasticity models accurately capture the experimentally observed oscillations in the stress-strain response of metals (e.g. molybdenum, tantalum etc.) under high strain rates and such phenomena are sometimes even dismissed as mere experimental artefacts. The question arises as to whether the existing models have consistently overlooked any important mechanism related to dislocation motion which could be very important at high strain-rate loading and possibly responsible for oscillations in the stress-strain response.
In the search for an answer to this question, one observes that the existing macro-scale continuum visco-plasticity models do not account for the effects of dislocation inertia which is identified in this thesis as a dominating factor in the visco-plastic response under high strain rates. Incorporating the effect of dislocation inertia in the continuum response, a visco-plasticity model is developed. Here the ow rule is derived based on an additional balance law, the micro-force balance, for the forces arising from (and maintaining) the plastic flow. The micro-force balance together with the classical momentum balance equations thus describes the visco-plastic response of isotropic poly-crystalline materials. The model is thermodynamically consistent as the constitutive relations for the fluxes are determined on satisfying the laws of thermodynamics. The model includes consistent derivation of temperature evolution, thus replaces the empirical route.
Partial differential equations (PDEs) describing the visco-plastic behaviour in the present model is highly non-linear and solving them requires the employment of numerical techniques. Had the interest been limited only to problems with nicely behaved continuous field variables, the finite element method (FEM) could have been a natural choice for solving the governing PDEs. Keeping in mind the limitations of the FEM in discretizing such large deformation problems and in handling discontinuities, a smooth particle hydrodynamics (SPH) formulation for the micro-inertia driven visco-plasticity model is undertaken in this thesis. The visco-plasticity model is then exploited to simulate ductile damage by suitably coupling the discretized SPH equations with an existing damage model. The current scheme does not necessitate the introduction of a yield or damage surface in evolving the plastic strain/ damage parameters and thus the numerical implementation avoids a computationally intensive return mapping. Our current approach therefore provides for an efficient numerical route to simulating impact dynamics problems.
However, implementation of the SPH equations demands some additional terms such as artificial viscosity to arrive at a numerically stable solution. Using such stabilizing terms is however bereft of a rational or physical basis. The choice of artificial viscosity parameters is ad-hoc -an inappropriate choice leading to unphysical solutions. In order to circumvent this, the micro-inertia driven visco-plasticity model is reformulated using peri dynamics (PD), a more efficacious scheme to treat shock waves/discontinuities within a continuum model. Remarkably, the PD model naturally accounts for the localization residual terms in the local balances for internal energy and entropy, originally conceived of by Edelen and co-workers nearly half a century ago as a source of non-local interaction.
Exploiting the present model, we also explore the determination of conservation laws based on a variational formulation for dissipative visco-plastic solids wherein the system variables are appropriately augmented with those describing the time-reversed dynamics. This in turn enables us to undertake symmetry analyses on the resulting Lagrangian to assess, for instance, material resistance to crack propagation. Specifically, our results confirm that materials with higher rate sensitivity tend to offer higher resistance to fracture. Moreover, it is found that the kinetic energy of the inertial forces contributes to increased plastic flow thereby reducing the available free energy for crack propagation. This part of the work potentially opens a model-based route to the design of micro-defect structures for optimal fracture resistance.
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Pelech, Petr. "Peridynamické a nelokální modely v mechanice kontinua pevných látek." Master's thesis, 2016. http://www.nusl.cz/ntk/nusl-352762.
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In this work we study peridynamics, a non-local model in continuum me- chanics introduced by Silling (2000). The non-locality is reflected in the fact that points at finite distance exert a force upon each other. If, however, these points are more distant than a characteristic length called horizon, it is customary to assume that they do not interact. We compare peridynamics with elasticity, especially in the limit of small horizon. We restrict ourselves, concerning this vanishing non-locality, to variational formulation of time- independent processes. We compute a Γ-limit for homogeneous and isotropic solid in linear peridynamics. In some cases this Γ-limit coincides with linear elasticity and the Poisson ratio is equal to 1 4. We conclude by clarifying why in some situation the computed Γ-limit can differ from the linear elasticity. 1
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Roy, Pranesh. "Non-classical continuum models for solids using peridynamics and gauge theory." Thesis, 2018. https://etd.iisc.ac.in/handle/2005/4847.
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This thesis focuses on three areas of nonclassical continuum mechanics of solids. In the first part, we develop a few peridynamics (PD) models and solution strategies for discretized PD equations in the context of the mechanics of solids and structures. A strategy for removal of zero energy modes in PD correspondence models is presented in the second part of this thesis and a way of modelling solid continua with defects is outlined drawing upon analogies from gauge theory. In the last part, exploring conformal gauge symmetries in elastic solids, we show how several electromechanical and magnetomechanical phenomena can emerge solely from local conformal symmetry considerations of the Lagrangian.
We start with formulating a PD theory for thick linear elastic shells to model fracture and fragmentation in these structures. Effects of shear deformation and coupling between surface wryness with in-plane stress resultants and surface strain with moment resultants are considered. A few numerical simulations on thick plate, thick cylindrical shell and quasi-static fracture propagation on thick cylindrical shell are presented. Next, a reduced dimensional PD theory is developed for axisymmetric structures. Apart from reduction of computational burden, it eliminates stress singularity near the axis of symmetry due to the nonlocality in PD. We furnish a few numerical simulations on Taylor impact test with copper and steel specimens and compared them with experimental observations. After that, inelastic response of ceramics is investigated using phase field based PD theory to eliminate some of the limitations of Deshpande-Evans (DE) ceramics constitutive model. A macroscopic PD phase field based integro-differential damage evolution rule is used replacing DE crack growth law which removes possible mesh dependent solutions. We numerically solve a spherical cavity expansion problem using dimensional reduction and demonstrate evolution of damage and plastic fronts. Next, a general procedure for solving discretized PD continuum and atomic systems is presented using Hamilton-Jacobi theory and time-dependent perturbation techniques. Here, approximate analytical solutions of positions and momenta are obtained as functions of initial conditions and time with which separate analysis for each initial condition can be eliminated resulting in saving in computational time. A few simulations on linear discretized PD problems are furnished to demonstrate the efficacy of our method. We also solved graphene sheets under tension and shear loading using simplified Tersoff potential for given initial conditions. After that, flexoelectricity – an electromechanical coupling phenomenon is modeled in PD to investigate nanoscale fracture propagation in dielectrics. An analytical solution is presented for an infinite 3D body considering bond based case. Incorporating damage through phase field theory, we present a few numerical simulations on damage propagation in a flexoelectric plate.
In the second part of the thesis, we develop a sub-horizon based PD theory to eliminate zero-energy and other unphysical deformation modes from the correspondence framework of non-ordinary state based PD which requires only a minor alteration of the conventional PD correspondence equations and little additional computational demand. With this, one may study convergence of the solutions for a fixed horizon size with increasing particle density and obtain meaningful nonlocal solutions. We also outlined a way to model defective continua in this framework drawing upon analogies from a translation invariant gauge theory of solids.
In the last part, a conformal gauge theory of solids is laid out. We note that, if the pulled back metric of the current configuration (right Cauchy-Green tensor) is scaled with a constant, the volumetric part of Lagrange density changes but the isochoric part remains invariant. However, under a position dependent scaling, isochoric part loses its invariance. In order to restore invariance of the isochoric part, we introduce a 1-form compensating field and modify the definition of derivative to a gauge covariant one (minimal replacement). Noting close connection with Weyl geometry, we impose Weyl condition through the Lagrangian and for the evolution of 1-form, a minimal coupling is constructed. We obtain Euler-Lagrange equations from Hamilton’s principle and noticed a close similarity with flexoelectricity governing equations interpreting the exact part of 1-form with electric field and the anti-exact part with the polarization vector. Next, piezoelectricity and electrostriction phenomena are modeled through contraction of Weyl condition in various manners. We also modeled magnetomechanical phenomena applying Hodge decomposition theorem on the 1-form which leads to curl of a pseudo-vector field and a vector field. Identifying the pseudo-vector field with the magnetic potential and vector part with magnetization, flexomagnetism, piezomagnetism and magnetostriction phenomena are modeled.
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Pathrikar, Anil. "Nonlocal continuum models for plasticity and damage." Thesis, 2021. https://etd.iisc.ac.in/handle/2005/5719.
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Nonlocal interactions of material points play a vital role in modelling certain important aspects of inelastic phenomena such as plasticity and damage in solids. For plasticity problems, nonlocal interactions allow characterizations of size-dependence and energetic hardening. In the case of damage, nonlocality describes energetically favourable conditions for propagation as well as branching of cracks. The nonlocal description of inelastic phenomenon introduces certain internal length scales representative of the material micro-structure. A geometric perspective of the kinematics of inelastic deformation induces certain interesting attributes in the form of a non-trivial metric, curvature, etc. to the mathematical model. Towards realizing a unified and rational modelling setup, it is important to trace the geometric origins of the kinematics underlying nonlocal interactions.
The first part of the thesis dwells on modelling of visco-plasticity and damage in metals by introducing gradients of plasticity and damage variables to capture the size-dependent plastic response and the nonlocal aspects of damage. We also try to account for dislocation inertia affecting the yield strength at high strain rates. In addition, the nonlocal flow rule also encapsulates energetic hardening. We describe temperature evolution, which is thermodynamically consistent and accounts for the heat dissipated. The coupled visco-plastic damage model is numerically implemented through peridynamics (PD) and validated via the simulations of adiabatic shear band propagation and shear plugging failure. The nonlocal terms can be accorded a geometric meaning using the concepts of gauge theory and differential geometry. We therefore focus on a geometric characterization of brittle damage via the gauge theory of solids. The local configurational changes in the manifold are captured using a non-trivial affine connection, called gauge connection. The resulting manifold is equipped with the gauge covariant quantities like gauge torsion and gauge curvature. Consequently, this theory serves as a natural device to model different aspects such as stiffness degradation, tension-compression asymmetry and microscopic inertia. The model is again numerically implemented using PD, and validated through the simulations of dynamic fracture instabilities and dynamic crack propagation. Similar to damage, the geometric underpinnings of plastic deformation are unveiled using ideas from differential geometry, e.g. the postulate that a plastically deforming body is a Riemannian manifold endowed with a metric structure and a non-trivial connection. The geometric approach provides a rational means of modelling several important features of plastic deformation, e.g. the free energy of defects, yielding and energetic hardening; and results into a nonlocal flow rule. The model is validated through the numerical simulations of homogeneous visco-plastic deformation and Taylor impact test.
The brittle damage in materials undergoing small deformation typically correspond to small strain. The symmetry principles of gauge theory are also used to obtain a brittle damage model in the linearized setting that is invariant with respect to local or inhomogeneous transformations. The efficacy of the model is established through PD based quasi-static simulations and investigation of blast-induced fracture in rocks.
The applied loads causing deformation may be of thermomechanical origin, rather than being purely mechanical. In the second part of thesis, brittle damage modelling under thermomechanical loading is undertaken. The deformation due to thermal and mechanical loads is coupled via Duhamel's postulate. The heat equation considers radiative and conductive heat transfer, temperature fluctuations due to thermomechanical effect and local temperature rise at crack tip. PD reformulation of this model involves a scalar entropy flux to incorporate nonlocal thermal interactions. The correspondence relations for entropy flux and other PD states, are derivable through energy and entropy equivalence. Numerical simulations include transient heat flow in a silica tile and its coupled thermomechanical analysis, and the temperature change study in Kalthoff's problem.
The damage mechanism of certain materials like ceramics is sensitive to the rate of applied loading. The third part of the thesis develops a damage model for ceramics based on micro-mechanical considerations to account for its strain rate dependent behavior. PD is used to reformulate the equations in the integro-differential form, considering the discontinuities and fragmentation at high strain rates. Numerical studies include spherical cavity expansion problem, impact induced damage in a ceramic target and a composite ceramic target.
Books on the topic "Peridynamics Model"
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Gerstle, Walter. Introduction to practical peridynamics: Computational solid mechanics without stress and strain. New Jersey: World Scientific, 2016.
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Handbook of Peridynamic Modeling. Taylor & Francis Group, 2016.
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T, Foster John, Florin Bobaru, Philippe H. Geubelle, and Stewart A. Silling. Handbook of Peridynamic Modeling. Taylor & Francis Group, 2016.
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Peridynamic Theory And Its Applications. Springer-Verlag New York Inc., 2013.
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Madenci, Erdogan, and Erkan Oterkus. Peridynamic Theory and Its Applications. Springer, 2013.
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Madenci, Erdogan, and Erkan Oterkus. Peridynamic Theory and Its Applications. Springer New York, 2016.
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Madenci, Erdogan, and Erkan Oterkus. Peridynamic Theory and Its Applications. Springer London, Limited, 2013.
Find full textBook chapters on the topic "Peridynamics Model"
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Ganzenmüller, Georg C., Stefan Hiermaier, and Michael May. "Improvements to the Prototype Micro-brittle Model of Peridynamics." In Lecture Notes in Computational Science and Engineering, 163–83. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06898-5_9.
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Rabczuk, Timon, Huilong Ren, and Xiaoying Zhuang. "Nonlocal Operator Method for Dynamic Brittle Fracture Based on an Explicit Phase Field Model." In Computational Methods Based on Peridynamics and Nonlocal Operators, 243–69. Cham: Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-20906-2_9.
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Lyu, Yao, Jinglu Zhang, Ari Sarafopoulos, Jian Chang, Shihui Guo, and Jian Jun Zhang. "Integral-Based Material Point Method and Peridynamics Model for Animating Elastoplastic Material." In Transactions on Computational Science XXXVII, 91–108. Berlin, Heidelberg: Springer Berlin Heidelberg, 2020. http://dx.doi.org/10.1007/978-3-662-61983-4_6.
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Wang, Hong. "Peridynamics and Nonlocal Diffusion Models: Fast Numerical Methods." In Handbook of Nonlocal Continuum Mechanics for Materials and Structures, 1–23. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-22977-5_35-1.
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Wang, Hong. "Peridynamics and Nonlocal Diffusion Models: Fast Numerical Methods." In Handbook of Nonlocal Continuum Mechanics for Materials and Structures, 1331–52. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-319-58729-5_35.
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Du, Qiang, and Xiaochuan Tian. "Robust Discretization of Nonlocal Models Related to Peridynamics." In Lecture Notes in Computational Science and Engineering, 97–113. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06898-5_6.
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Zhang, Shangyuan, and Yufeng Nie. "Peridynamic Damage Model Based on Absolute Bond Elongation." In Computational Science – ICCS 2022, 637–50. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-08751-6_46.
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Freimanis, Andris, and Ainārs Paeglītis. "Modal Analysis of Healthy and Cracked Isotropic Plates in Peridynamics." In Topics in Modal Analysis & Testing, Volume 9, 359–61. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74700-2_41.
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Galvanetto, U., F. Scabbia, and M. Zaccariotto. "Accurate numerical integration in 3D meshless peridynamic models." In Current Perspectives and New Directions in Mechanics, Modelling and Design of Structural Systems, 457–63. London: CRC Press, 2022. http://dx.doi.org/10.1201/9781003348443-75.
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Galvanetto, U., F. Scabbia, and M. Zaccariotto. "Accurate numerical integration in 3D meshless peridynamic models." In Current Perspectives and New Directions in Mechanics, Modelling and Design of Structural Systems, 161–62. London: CRC Press, 2022. http://dx.doi.org/10.1201/9781003348450-75.
Full textConference papers on the topic "Peridynamics Model"
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Littlewood, David J. "Simulation of Dynamic Fracture Using Peridynamics, Finite Element Modeling, and Contact." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-40621.
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Peridynamics is a nonlocal extension of classical solid mechanics that allows for the modeling of bodies in which discontinuities occur spontaneously. Because the peridynamic expression for the balance of linear momentum does not contain spatial derivatives and is instead based on an integral equation, it is well suited for modeling phenomena involving spatial discontinuities such as crack formation and fracture. In this study, both peridynamics and classical finite element analysis are applied to simulate material response under dynamic blast loading conditions. A combined approach is utilized in which the portion of the simulation modeled with peridynamics interacts with the finite element portion of the model via a contact algorithm. The peridynamic portion of the analysis utilizes an elastic-plastic constitutive model with linear hardening. The peridynamic interface to the constitutive model is based on the calculation of an approximate deformation gradient, requiring the suppression of possible zero-energy modes. The classical finite element portion of the model utilizes a Johnson-Cook constitutive model. Simulation results are validated by direct comparison to expanding tube experiments. The coupled modeling approach successfully captures material response at the surface of the tube and the emerging fracture pattern.
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Kulkarni, Shank S., Alireza Tabarraei, and Xiaonan Wang. "Study of Spurious Wave Reflection at the Interface of Peridynamics and Finite Element Regions." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-86129.
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Peridynamics ability to model crack as a material response removes deficiencies associated with using classical continuum-based methods in modeling discontinuities. Due to its nonlocal formulation, however, peridynamics is computationally more expensive than the classical continuum-based numerical methods such as finite element method. To reduce the computational cost, peridynamics can be coupled with finite element method. In this method, peridynamics is used only in critical areas such as the vicinity of crack tip and finite element method is used everywhere else. The main issue associated with such coupling methods is the spurious wave reflections occurring at the interface of peridynamics and finite elements. High frequency waves traveling from peridynamics to finite element spuriously reflect back at the interface and the amplitude of transmitted waves also alter. In this paper, we take an analytical approach to study this phenomenon of spurious reflections. We study the impact of factors such as horizon size of peridynamic formulation, discretization, and change in mesh size on the amplitude of spuriously reflected waves. Finally, we present a method to reduce these spurious reflections by using Arlequin method.
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Kulkarni, Shank S., Alireza Tabarraei, and Xiaonan Wang. "Modeling the Creep Damage of P91 Steel Using Peridynamics." In ASME 2019 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/imece2019-10069.
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Abstract Creep is an important failure mechanism of metal components working at a high temperature. To ensure the structural integrity and safety of systems working at high temperature it is essential to predict failure due to creep. Classical continuum based damage models are used widely for modeling creep damage. A more recently developed non-local mechanics formulation called peridynamics has displayed better performance in modeling damage with respect to classical local mechanics methods. In this paper, the peridynamic formulation is extended to model creep in metals. We have chosen Liu-Murakami creep model for developing a peridynamic formulation for modeling creep. The proposed formulation is validated by simulating creep tests for P91 steel and comparing the results with experimental data from the literature.
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Littlewood, David J. "A Nonlocal Approach to Modeling Crack Nucleation in AA 7075-T651." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-64236.
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A critical stage in microstructurally small fatigue crack growth in AA 7075-T651 is the nucleation of cracks originating in constituent particles into the matrix material. Previous work has focused on a geometric approach to modeling microstructurally small fatigue crack growth in which damage metrics derived from an elastic-viscoplastic constitutive model are used to predict the nucleation event [1, 2]. While a geometric approach based on classical finite elements was successful in explicitly modeling the polycrystalline grain structure, singularities at the crack tip necessitated the use of a nonlocal sampling approach to remove mesh size dependence. This study is an initial investigation of the peridynamic formulation of continuum mechanics as an alternative approach to modeling microstructurally small fatigue crack growth. Peridynamics, a nonlocal extension of continuum mechanics, is based on an integral formulation that remains valid in the presence of material discontinuities. To capture accurately the material response at the grain scale, a crystal elastic-viscoplastic constitutive model is adapted for use in non-ordinary state-based peridynamics through the use of a regularized deformation gradient. The peridynamic approach is demonstrated on a baseline model consisting of a hard elastic inclusion in a single crystal. Coupling the elastic-viscoplastic material model with peridynamics successfully facilitates the modeling of plastic deformation and damage accumulation in the vicinity of the particle inclusion. Lattice orientation is shown to have a strong influence on material response.
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Ha, Youn D., and Florin Bobaru. "Dynamic Brittle Fracture Captured With Peridynamics." In ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-65515.
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The bond-based peridynamic model is able to capture many of the essential characteristics of dynamic brittle fracture observed in experiments: crack branching, crack-path instability, asymmetries of crack paths, successive branching, secondary cracking at right angles from existing crack surfaces, etc. In this paper we investigate the influence of the stress waves on the crack branching angle and the velocity profile. We observe that crack branching in peridynamics evolves as the phenomenology proposed by the experimental evidence [1]: when a crack reaches a critical stage (macroscopically identified by its stress intensity factor) it splits into two or more branches, each propagating with the same speed as the parent crack, but with a much reduced process zone.
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A., Aguiar, and Seitenfuss A. "A LINEARLY ELASTIC CONSTITUTIVE MODEL IN PERIDYNAMICS." In Innovative technologies In science and education. DSTU-Print, 2019. http://dx.doi.org/10.23947/itno.2019.386-392.
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Vasenkov, Alex V. "Stent Fracture Predictions With Peridynamics." In 2018 Design of Medical Devices Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/dmd2018-6866.
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Currently, stent therapy constitutes to over 95% of all endovascular interventions. The biological and clinical complications of stent therapy can now be well controlled with modern techniques and procedures. However, the mechanical failure of stent remains an important clinical problem [1]. While there is a consensus that such failure usually proceeds through mechanical fracture activation due to fatigue, the mechanisms of fracture activation are not well understood. The virtual analysis of fracture is typically conducted using the Finite Element Method (FEM) model regulated by the externally applied criteria of fracture nucleation. Typically, the FEM model must deal with ambiguity of derivatives of displacement at discontinuities and should contain requirements on mesh size to resolve material damage. In this study, we pursue an alternative approach, called peridynamics, to depict the mechanism of fracture activation. Peridynamic damage model does not require special criteria to guide crack or damage growth and naturally accounts for surface roughness that can highly influence fatigue life of stent.
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Bhattacharya, Debdeep, Patrick Diehl, and Robert P. Lipton. "Peridynamics for Quasistatic Fracture Modeling." In ASME 2021 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/imece2021-70793.
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Abstract Fracture involves interaction across large and small length scales. With the application of enough stress or strain to a brittle material, atomistic scale bonds will break, leading to fracture of the macroscopic specimen. From the perspective of mechanics fracture should appear as an emergent phenomena generated by a continuum field theory eliminating the need for a supplemental kinetic relation describing crack growth. We develop a new fast method for modeling quasi-static fracture using peridynamics. We apply fixed point theory and model stable crack evolution for hard and soft loading. For soft loading we recover unstable fracture. For hard loading we recover stable crack growth. We show existence of quasistatic fracture solutions in the neighborhood of stable critical points for appropriately defined energies. The numerical method uses an analytic stiffness matrix for fast numerical implementation. A rigorous mathematical analysis shows that the method converges for load paths associated with soft and hard loading. For soft loading the crack becomes unstable shortly after the stress at the tip of the pre-crack reaches the material strength.
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Ren, Baihua, and Jun Song. "Peridynamic Simulation of Particles Impact and Interfacial Bonding in Cold Spray Process." In ITSC2021, edited by F. Azarmi, X. Chen, J. Cizek, C. Cojocaru, B. Jodoin, H. Koivuluoto, Y. C. Lau, et al. ASM International, 2021. http://dx.doi.org/10.31399/asm.cp.itsc2021p0396.
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Abstract Recently, cold spray (CS) technology has attracted extensive interest as an alternative to thermal spray methods to build a coating, which uses high kinetic energy solid particles to impact and adhere to the substrate. To date, numerous numerical studies have been carried out to investigate the deposition processes and associated mechanisms during multiple particle impact in CS. However, in the commonly used numerical techniques, the individual powder particles are often treated separately from one another, thus fail to properly consider the adhesion mechanisms during deposition. In this study, we propose a new numerical approach on base of peridynamics (PD), which incorporates interfacial interactions as a part of constitutive model to capture deformation, bonding and rebound of impacting particles in one unified framework. Two models are proposed to characterize the adhesive contacts: a) a long-range Lenard-Johns type potential that reproduce the mode I fracture energy by suitable calibrations, and b) a force - stretch relation of interface directly derived from the bulk materials mode I fracture simulations. The particle deformation behavior modeled by the peridynamic method compares well with the benchmark finite element method results, which indicates the applicability of the peridynamic model for CS simulation. Furthermore, it is shown that the adhesive contact models can accurately describe interfacial bonding between the powder particles and substrate.
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Zhang, J. "An extended ordinary state-based peridynamics model for ductile fracture analysis." In Aerospace Science and Engineering. Materials Research Forum LLC, 2023. http://dx.doi.org/10.21741/9781644902677-43.
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Abstract. The present research establishes a two-step strategy to incorporate classical elastoplastic constitutive model into ordinary state-based peridynamics (OSB-PD) for ductile fracture analysis. Three length levels are notified, respectively, bond level, material particle level and bulk level. The unified Bodner-Partom theory is incorporated into the OSB-PD framework to define the bond-wise relationship between deformation state and force state. Particle-wise variables indicating plastic deformation state are extracted from connecting bonds to establish the unified ductile damage model at particle level. The damage indicator in turn exerts effects on the following plastic deformation. At present study, the collaboration among PD and unified theories amplifies the theoretical unity of PD in defining material behaviors. Simulations under quasi-static and impact loading conditions are carried out to demonstrate the effectiveness of the present model in reproducing ductile fractures at bulk level.
Reports on the topic "Peridynamics Model"
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Mitchell, John Anthony. A nonlocal, ordinary, state-based plasticity model for peridynamics. Office of Scientific and Technical Information (OSTI), May 2011. http://dx.doi.org/10.2172/1018475.
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Mitchell, John Anthony. A non-local, ordinary-state-based viscoelasticity model for peridynamics. Office of Scientific and Technical Information (OSTI), October 2011. http://dx.doi.org/10.2172/1029821.
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Silling, Stewart Andrew, and Abe Askari. Peridynamic model for fatigue cracking. Office of Scientific and Technical Information (OSTI), October 2014. http://dx.doi.org/10.2172/1160289.
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D'Elia, Marta, Stewart Silling, Yue Yu, and Huaiqian You. A data-driven peridynamic continuum model for upscaling molecular dynamics. Office of Scientific and Technical Information (OSTI), August 2021. http://dx.doi.org/10.2172/1821529.
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Silling, Stewart A. Stability of Peridynamic Correspondence Material Models and Their Particle Discretizations. Office of Scientific and Technical Information (OSTI), July 2016. http://dx.doi.org/10.2172/1457611.
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D'Elia, Marta, and Yue Yu. On the prescription of boundary conditions for nonlocal Poisson's and peridynamics models. Office of Scientific and Technical Information (OSTI), June 2021. http://dx.doi.org/10.2172/1817978.
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D'Elia, Marta, Stewart Silling, Huaiqian You, Yue Yu, and Muge Fermen-Coker. Peridynamic Model for Single-Layer Graphene Obtained from Coarse Grained Bond Forces. Office of Scientific and Technical Information (OSTI), September 2021. http://dx.doi.org/10.2172/1819404.
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Vogler, Tracy, and Christopher James Lammi. A Nonlocal Peridynamic Plasticity Model for the Dynamic Flow and Fracture of Concrete. Office of Scientific and Technical Information (OSTI), October 2014. http://dx.doi.org/10.2172/1159446.
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