Journal articles: '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.

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Lu, Wei, Mingyang Li, Bozo Vazic, Selda Oterkus, Erkan Oterkus, and Qing Wang. "Peridynamic Modelling of Fracture in Polycrystalline Ice." Journal of Mechanics 36, no. 2 (February 21, 2020): 223–34. http://dx.doi.org/10.1017/jmech.2019.61.

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ABSTRACTIn this study, a peridynamic material model for a polycrystalline ice is utilised to investigate its fracture behaviour under dynamic loading condition. First, the material model was validated by considering a single grain, double grains and polycrystalline structure under tension loading condition. Peridynamic results are compared against finite element analysis results without allowing failure. After validating the material model, dynamic analysis of a polycrystalline ice material with two pre-existing cracks under tension loading is performed by considering weak and strong grain boundaries with respect to grain interiors. Numerical results show that the effect of microstructure is significant for weak grain boundaries. On the other hand, for strong grain boundaries, the effect of microstructure is insignificant. The evaluated results have demonstrated that peridynamics can be a very good alternative numerical tool for fracture analysis of polycrystalline ice material.

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Li, Tianyi, Xin Gu, Qing Zhang, and Xiaozhou Xia. "Elastoplastic Constitutive Modeling for Reinforced Concrete in Ordinary State-Based Peridynamics." Journal of Mechanics 36, no. 6 (October 23, 2020): 799–811. http://dx.doi.org/10.1017/jmech.2020.50.

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ABSTRACTA non-local, ordinary state-based, peridynamic elastoplastic model is formulated to numerically simulate the fracture of reinforced concrete materials. Several basic definitions are first discussed to avoid confusion; and then, a detailed derivation of the force vector state is presented, leading to a unified expression of force state for one-, two- and three-dimensional elasticity problems. Furthermore, an ordinary state-based peridynamic (OSB PD) elastoplastic analysis approach is developed for both plastic compressible and incompressible materials, including the constitutive relationship, the yield function, the consistency condition and the plasticity flow rule. The peridynamic predictions of a quasi-static deformation of the steel rods are in good agreement with the analytical solution. Moreover, the OSB PD plasticity is verified by analyzing a square plate with or without a central hole suffering different loading-unloading paths. Finally, a two dimensional reinforced concrete clamped beam subjected to impact loading is simulated with the proposed OSB PD elastoplasticity, demonstrating its capability in capturing the damage characteristics and structural failure behavior. Simulation results show good accuracy of the peridynamics in simulating elastoplastic problems.

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Ren, Huilong, Xiaoying Zhuang, and Timon Rabczuk. "A new peridynamic formulation with shear deformation for elastic solid." Journal of Micromechanics and Molecular Physics 01, no. 02 (July 2016): 1650009. http://dx.doi.org/10.1142/s2424913016500090.

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We propose a new peridynamic formulation with shear deformation for linear elastic solid. The key idea lies in subtracting the rigid body rotation part from the total deformation. Based on the strain energy equivalence between classic local model and non-local model, the bond force vector is derived. A new damage rule of maximal deviatoric bond strain for elastic brittle fracture is proposed in order to account for both the tensile damage and shear damage. 2D and 3D numerical examples are tested to verify the accuracy of the current peridynamics. The new damage rule is applied to simulate the propagation of Mode I, II and III cracks.

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Fallah, Arash S., Ilias N. Giannakeas, Rizgar Mella, Mark R. Wenman, Yasser Safa, and Hamid Bahai. "On the Computational Derivation of Bond-Based Peridynamic Stress Tensor." Journal of Peridynamics and Nonlocal Modeling 2, no. 4 (July 2, 2020): 352–78. http://dx.doi.org/10.1007/s42102-020-00036-9.

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Abstract The concept of ‘contact stress’, as introduced by Cauchy, is a special case of a nonlocal stress tensor. In this work, the nonlocal stress tensor is derived through implementation of the bond-based formulation of peridynamics that uses an idealised model of interaction between points as bonds. The method is sufficiently general and can be implemented to study stress states in problems containing stress concentration, singularity, or discontinuities. Two case studies are presented, to study stress concentration around a circular hole in a square plate and conventionally singular stress fields in the vicinity of a sharp crack tip. The peridynamic stress tensor is compared with finite element approximations and available analytical solutions. It is shown that peridynamics is capable of capturing both shear and direct stresses and the results obtained correlate well with those obtained using analytical solutions and finite element approximations. A built-in MATLAB code is developed and used to construct a 2D peridynamic grid and subsequently approximate the solution of the peridynamic equation of motion. The stress tensor is then obtained using the tensorial product of bond force projections for bonds that geometrically pass through the point. To evaluate the accuracy of the predicted stresses near a crack tip, the J-integral value is computed using both a direct contour approximation and the equivalent domain integral method. In the formulation of the contour approximation, bond forces are used directly while the proposed peridynamic stress tensor is used for the domain method. The J-integral values computed are compared with those obtained by the commercial finite element package Abaqus 2018. The comparison provides an indication on the accurate prediction of the state of stress near the crack tip.

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Han, Junzhao, Guozhong Wang, Xiaoyu Zhao, Rong Chen, and Wenhua Chen. "Modeling of Multiple Fatigue Cracks for the Aircraft Wing Corner Box Based on Non-Ordinary State-Based Peridynamics." Metals 12, no. 8 (July 30, 2022): 1286. http://dx.doi.org/10.3390/met12081286.

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In the current research, we propose a novel non-ordinary state-based peridynamics (PD) fatigue model for multiple cracks’ initiation and growth under tension–tension fatigue load. In each loading cycle, the fatigue loading is redistributed throughout the peridynamic solid body, leading to progressive fatigue damage formation and expansion in an autonomous fashion. The proposed fatigue model parameters are first verified by a 3D numerical solution, and then, the novel model is used to depict the widespread fatigue damage evolution of the aircraft wing corner box. The modified constitutive damage model has been implemented into the peridynamic framework. Furthermore, the criteria and processes from multiple initiations to propagation are discussed in detail. It was found that the computational results obtained from the PD fatigue model were consistent with those from the test data. The angular errors of multiple cracks are within 2.66% and the number of cycles errors are within 15%. A comparison of test data and computational results indicates that the fatigue model can successfully capture multiple crack formations and propagation, and other behaviors of aluminum alloy material.

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Yakin, H. N., M. R. M. Rejab, Nur Hashim, and N. Nikabdullah. "A new quasi-brittle damage model implemented under quasi-static condition using bond-based peridynamics theory for progressive failure." Theoretical and Applied Mechanics, no. 00 (2023): 6. http://dx.doi.org/10.2298/tam230404006y.

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A novel quasi-brittle damage model implemented under quasistatic loading condition using bond-based peridynamics theory for progressive failure is proposed to better predict damage initiation and propagation in solid materials. Since peridynamics equation of motion was invented in dynamic configuration, this paper applies the adaptive dynamic relaxation equation to achieve steady-state in peridynamics formulation. To accurately characterise the progressive failure process in cohesive materials, we incorporate the dynamic equation with the novel damage model for quasi-brittle materials. Computational examples of 2D compressive and tensile problems using the proposed model are presented. This paper presents advancement by incorporating the adaptive dynamic equation approach into a new damage model for quasi-brittle materials. This amalgamation allows for a more accurate representation of the behavior of damaged materials, particularly in static or quasi-static loading situations, bringing the framework closer to reality. This research paves the way for the peridynamics formulation to be employed for a far broader class of loading condition behaviour than it is now able to.

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Imachi, Michiya, Hiroki Takahashi, and Satoyuki Tanaka. "Quasi-brittle fracture model in peridynamics." Proceedings of The Computational Mechanics Conference 2019.32 (2019): 281. http://dx.doi.org/10.1299/jsmecmd.2019.32.281.

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Roy, Pranesh, and Debasish Roy. "Peridynamics model for flexoelectricity and damage." Applied Mathematical Modelling 68 (April 2019): 82–112. http://dx.doi.org/10.1016/j.apm.2018.11.013.

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Fan, Lin, Song Rong Qian, and Teng Fei Ma. "The Numerical Methods of Peridynamics Theory Used in Failure Analysis of Materials." Advanced Materials Research 1030-1032 (September 2014): 223–27. http://dx.doi.org/10.4028/www.scientific.net/amr.1030-1032.223.

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In order to analysis the force situation of the material which is discontinuity,we can used the new theory called peridynamics to slove it.Peridynamics theory is a new method of molecular dynamics that develops very quickly.Peridynamics theory used the volume integral equation to constructed the model,used the volume integral equation to calculated the PD force in the horizon.So It doesn’t need to assumed the material’s continuity which must assumed that use partial differential equation to formulates the equation of motion. Destruction and the expend of crack which have been included in the peridynamics’ equation of motion.Do not need other additional conditions.In this paper,we introduce the peridynamics theory modeling method and introduce the relations between peridynamics and classic theory of mechanics.We also introduce the numerical integration method of peridynamics.Finally implementation the numerical integration in prototype microelastic brittle material.Through these work to show the advantage of peridynamics to analysis the force situation of the material.

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Zhou, Ji, and Songrong Qian. "Simulation of Brittle Materials Based on Ordinary State-based Peridynamics." Journal of Physics: Conference Series 2549, no. 1 (July 1, 2023): 012022. http://dx.doi.org/10.1088/1742-6596/2549/1/012022.

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Abstract We present a coupled model for brittle materials based on the ordinary state-based peridynamics. The ordinary state-based peridynamics theory is suitable for describing the plastic incompressibility problem and has good application prospects in the fracture damage simulation of brittle materials. The brittle material is a material with a compressive load-bearing capacity greater than the tensile load-bearing capacity and has the characteristics of incompressibility, which is consistent with the application scope of ordinary state-based peridynamics. The mechanical behavior of brittle materials is simulated and analyzed using the ordinary state-based peridynamics theory coupled with brittle materials, and the validity of the model is verified using the finite element method. The results show that the model can effectively capture the displacement field distribution of the brittle material, and the comparison of the finite element results displacement field is consistent. Finally, crack extension analysis is performed on the brittle material plate with prefabricated defects, where the cracks extend along the defect location, bifurcate, and finally penetrate the upper and lower surfaces of the material. The results show that the model can effectively predict the crack expansion path of the material, which provides a new research idea for the simulation of crack expansion in brittle materials.

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Wang, Fei, Yu’e Ma, Yanning Guo, and Wei Huang. "Studies on Quasi-Static and Fatigue Crack Propagation Behaviours in Friction Stir Welded Joints Using Peridynamic Theory." Advances in Materials Science and Engineering 2019 (October 31, 2019): 1–16. http://dx.doi.org/10.1155/2019/5105612.

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The friction stir welding (FSW) technology has been widely applied in aircraft structures. The heterogeneity of mechanical properties in weld and the hole in structure will lead the crack to turn. Peridynamics (PD) has inherent advantages in calculating crack turning. The peridynamic theory is applied to study the crack turning behaviour of FSW joints in this work. The compact tension (CT) samples with and without a hole are designed. The crack propagation testing under quasistatic and fatigue loads are performed. The peridynamic microplastic model is used and a three-stage fatigue calculation model is developed to simulate the quasistatic fracture and the fatigue crack growth. The results predicted by the peridynamic models are compared with the experimental ones. The effects of welding direction on quasistatic and fatigue crack propagation behaviours are investigated and the effect of hole position on crack path geometry is also studied. It is shown that the crack turning in FSWed CT samples can be captured by the peridynamic microplastic and the three-stage fatigue calculation models. The peridynamic crack growth rates agree with the experimental results. For CT specimen without a hole, the crack turns into the weld zone where the material is softer. The effect of welding direction on crack growth rates is not obvious. For CT sample with a hole, the crack propagation direction has been mainly controlled by the hole location and the welding direction has a slight effect on crack path.

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Roy, Pranesh, Anil Pathrikar, S. P. Deepu, and Debasish Roy. "Peridynamics damage model through phase field theory." International Journal of Mechanical Sciences 128-129 (August 2017): 181–93. http://dx.doi.org/10.1016/j.ijmecsci.2017.04.016.

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Zhang, Feng, Xinting Hou, Pihua Ji, Cheng Han, Lei Cheng, and Xiaoxiao Liu. "Dynamic simulation of aircraft electro-impulse de-icing using bond-based peridynamics." Advances in Mechanical Engineering 14, no. 11 (November 2022): 168781322211302. http://dx.doi.org/10.1177/16878132221130218.

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Electro-impulse de-icing is a lightweight type of mechanical de-icing system that consumes little energy, provides high reliability, and offers wide application prospects. In this study, the bond-based peridynamics theory was used to simulate the dynamic damage process and evolution law of aircraft electro-impulse de-icing. The ice layer was simplified as a brittle material that satisfies the linear elastic constitutive relation. A numerical analysis model of the ice layer, aircraft skin substrate, and their interface was established to simulate the dynamic responses under a high strain rate. Considering the anisotropy of ice adhesion on the substrate, the interfacial bonds were described as shear bonds and tensile bonds, and the critical elongations of the two were derived. The tensile and shear capacities of the ice on the substrate were then simulated using these critical elongations, and the peeling rates of single ice particles and interfacial ice layers were taken as indexes describing the efficacy of electro-impulse de-icing. The process of electro-impulse de-icing was then analyzed for an aluminum substrate with two adjacent clamped edges. Finally, the results of the peridynamic simulation were compared with those of existing experiments and finite element models to verify the effectiveness of the peridynamic approach.

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Cluni, Federico, Vittorio Gusella, Dimitri Mugnai, Edoardo Proietti Lippi, and Patrizia Pucci. "A mixed operator approach to peridynamics." Mathematics in Engineering 5, no. 5 (2023): 1–22. http://dx.doi.org/10.3934/mine.2023082.

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<abstract><p>In the present paper we propose a model describing the nonlocal behavior of an elastic body using a peridynamical approach. Indeed, peridynamics is a suitable framework for problems where discontinuities appear naturally, such as fractures, dislocations, or, in general, multiscale materials. In particular, the regional fractional Laplacian is used as the nonlocal operator. Moreover, a combination of the fractional and classical Laplacian operators is used to obtain a better description of the phenomenological response in elasticity. We consider models with linear and nonlinear perturbations. In the linear case, we prove the existence and uniqueness of the solution, while in the nonlinear case the existence of at least two nontrivial solutions of opposite sign is proved. The linear and nonlinear problems are also solved by a numerical approach which estimates the regional fractional Laplacian by means of its singular integral representation. In both cases, a numerical estimation of the solutions is obtained, using in the nonlinear case an approach involving a random variation of an initial guess of the solution. Moreover, in the linear case a parametric analysis is made in order to study the effects of the parameters involved in the model, such as the order of the fractional Laplacian and the mixture law between local and nonlocal behavior.</p></abstract>

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Buryachenko, Valeriy A. "Variational principles and generalized Hill’s bounds in micromechanics of linear peridynamic random structure composites." Mathematics and Mechanics of Solids 25, no. 3 (November 25, 2019): 682–704. http://dx.doi.org/10.1177/1081286519887222.

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We consider a static problem for statistically homogeneous matrix linear peridynamic composite materials (CMs). The basic feature of the peridynamic model considered is a continuum description of a material behavior as the integrated non-local force interactions between infinitesimal particles. In contrast to these classical local and non-local theories, the peridynamic equation of motion introduced by Silling ( J Mech Phys Solids 2000; 48: 175–209) is free of any spatial derivatives of displacement. Estimation of effective moduli of peridynamic CMs is performed by generalization of some methods used in locally elastic micromechanics. Namely, the admissible displacement and force fields are defined. The theorem of work and energy, Betti’s reciprocal theorem, and the theorem of virtual work are proved. Principles of minimum of both potential energy and complimentary energy are generalized. The strain energy bounds are estimated for both the displacement and force homogeneous volumetric boundary conditions. The classical representations of effective elastic moduli through the mechanical influence functions for elastic CM are generalized to the case of peridynamics, and the energetic definition of effective elastic moduli is proposed. Generalized Hill’s bounds on the effective elastic moduli of peridynamic random structure composites are obtained. In contrast to the classical Hill’s bounds, in the new bounds, comparable scales of the inclusion size and horizon are taken into account that lead to dependance of the bounds on both the size and shape of the inclusions. The numerical examples are considered for the 1D case.

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Rezaul Karim, Mohammad, Kai Kadau, Santosh Narasimhachary, Francesco Radaelli, Christian Amann, Kaushik Dayal, Stewart Silling, and Timothy C. Germann. "Crack nucleation at forging flaws studied by non-local peridynamics simulations." Mathematics and Mechanics of Solids 27, no. 6 (December 14, 2021): 1129–49. http://dx.doi.org/10.1177/10812865211057211.

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We present a computational study and framework that allows us to study and understand the crack nucleation process from forging flaws. Forging flaws may be present in large steel rotor components commonly used for rotating power generation equipment including gas turbines, electrical generators, and steam turbines. The service life of these components is often limited by crack nucleation and subsequent growth from such forging flaws, which frequently exhibit themselves as non-metallic oxide inclusions. The fatigue crack growth process can be described by established engineering fracture mechanics methods. However, the initial crack nucleation process from a forging flaw is challenging for traditional engineering methods to quantify as it depends on the details of the flaw, including flaw morphology. We adopt the peridynamics method to describe and study this crack nucleation process. For a specific industrial gas turbine rotor steel, we present how we integrate and fit commonly known base material property data such as elastic properties, yield strength, and S-N curves, as well as fatigue crack growth data into a peridynamic model. The obtained model is then utilized in a series of high-performance two-dimensional peridynamic simulations to study the crack nucleation process from forging flaws for ambient and elevated temperatures in a rectangular simulation cell specimen. The simulations reveal an initial local nucleation at multiple small oxide inclusions followed by micro-crack propagation, arrest, coalescence, and eventual emergence of a dominant micro-crack that governs the crack nucleation process. The dependence on temperature and density of oxide inclusions of both the details of the microscopic processes and cycles to crack nucleation is also observed. The results are compared with fatigue experiments performed with specimens containing forging flaws of the same rotor steel.

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Ren, Huilong, Xiaoying Zhuang, and Timon Rabczuk. "Implementation of GTN Model in Dual-horizon Peridynamics." Procedia Engineering 197 (2017): 224–32. http://dx.doi.org/10.1016/j.proeng.2017.08.099.

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You, H. Q., X. Xu, Y. Yu, S. Silling, M. D’Elia, and J. Foster. "Towards a unified nonlocal, peridynamics framework for the coarse-graining of molecular dynamics data with fractures." Applied Mathematics and Mechanics 44, no. 7 (July 2023): 1125–50. http://dx.doi.org/10.1007/s10483-023-2996-8.

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AbstractMolecular dynamics (MD) has served as a powerful tool for designing materials with reduced reliance on laboratory testing. However, the use of MD directly to treat the deformation and failure of materials at the mesoscale is still largely beyond reach. In this work, we propose a learning framework to extract a peridynamics model as a mesoscale continuum surrogate from MD simulated material fracture data sets. Firstly, we develop a novel coarse-graining method, to automatically handle the material fracture and its corresponding discontinuities in the MD displacement data sets. Inspired by the weighted essentially non-oscillatory (WENO) scheme, the key idea lies at an adaptive procedure to automatically choose the locally smoothest stencil, then reconstruct the coarse-grained material displacement field as the piecewise smooth solutions containing discontinuities. Then, based on the coarse-grained MD data, a two-phase optimization-based learning approach is proposed to infer the optimal peridynamics model with damage criterion. In the first phase, we identify the optimal nonlocal kernel function from the data sets without material damage to capture the material stiffness properties. Then, in the second phase, the material damage criterion is learnt as a smoothed step function from the data with fractures. As a result, a peridynamics surrogate is obtained. As a continuum model, our peridynamics surrogate model can be employed in further prediction tasks with different grid resolutions from training, and hence allows for substantial reductions in computational cost compared with MD. We illustrate the efficacy of the proposed approach with several numerical tests for the dynamic crack propagation problem in a single-layer graphene. Our tests show that the proposed data-driven model is robust and generalizable, in the sense that it is capable of modeling the initialization and growth of fractures under discretization and loading settings that are different from the ones used during training.

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Gu, X. B., and Q. H. Wu. "The Application of Nonordinary, State-Based Peridynamic Theory on the Damage Process of the Rock-Like Materials." Mathematical Problems in Engineering 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/9794605.

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Peridynamics has a great advantage over modeling the damage process of rock-like materials, which is assumed to be in a continuum interaction with each other across a finite distance. In the paper, an approach to incorporate classical elastic damage model in the nonordinary, state-based peridynamics is introduced. This method can model the dynamic damage process and stress change of rock-like materials. Then two instances about three-point bend experiment are simulated in the rock-like materials. Finally the conclusions are drawn that numerical results are close to the experimental results. So the method has a great predictable value in the geotechnical engineering.

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RAHMAN, R., and A. HAQUE. "A PERIDYNAMICS FORMULATION BASED HIERARCHICAL MULTISCALE MODELING APPROACH BETWEEN CONTINUUM SCALE AND ATOMISTIC SCALE." International Journal of Computational Materials Science and Engineering 01, no. 03 (September 2012): 1250029. http://dx.doi.org/10.1142/s2047684112500297.

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In this paper, a multiscale modeling framework has been established between peridynamics and atomistic models. Peridynamics (PD) formulation is based on continuum theory implying nonlocal force based interactions. Peridynamics (PD) and molecular dynamics (MD) have similarities since both use nonlocal force based interaction. It means continuum points in PD and MD atoms are separated by finite distance and exert force upon each other. In this work PD based continuum model of epoxy polymer is defined by meshless Lagrangian particles. MD is coupled with PD based continuum model through a hierarchical multiscale modeling framework. In this framework, PD particles at coarse scale interact with fine scale PD particles by transferring pressure, displacements and velocities among each other. Based on the same hierarchical coupling method, fine scale PD model is seamlessly interfaced with molecular model through an intermediate mesoscale region i.e. coarse-grain atomic model. At the end of this hierarchical downscaling, the information — such as deformation, energy and other important parameters — were captured in the atomistic region under the applied force at micro and macro regions. A two-dimensional plate of neat epoxy was considered for demonstration of such multiscale simulation platform. The region of interest in the 2D plate was interfaced with atomistic model by applying the proposed hierarchical coupling method. The results show reasonable consistency between PD and MD simulations.

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Ongaro, Greta, Alessandro Pontefisso, Elena Zeni, Francesco Lanero, Alessia Famengo, Federico Zorzi, Mirco Zaccariotto, et al. "Chemical and Mechanical Characterization of Unprecedented Transparent Epoxy–Nanomica Composites—New Model Insights for Mechanical Properties." Polymers 15, no. 6 (March 15, 2023): 1456. http://dx.doi.org/10.3390/polym15061456.

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Two nanomicas of similar composition, containing muscovite and quartz, but with different particle size distributions, have been used to prepare transparent epoxy nanocomposites. Their homogeneous dispersion, due to the nano-size, was achieved even without being organically modified, and no aggregation of the nanoparticles was observed, thus maximizing the specific interface between matrix and nanofiller. No exfoliation or intercalation has been observed by XRD, despite the significant dispersion of the filler in the matrix which produced nanocomposites with a loss in transparency in the visible domain of less than 10% in the presence of 1% wt and 3% wt of mica fillers. The presence of micas does not affect the thermal behavior of the nanocomposites, which remains similar to that of the neat epoxy resin. The mechanical characterization of the epoxy resin composites revealed an increased Young’s modulus, whereas tensile strength was reduced. A peridynamics-based representative volume element approach has been implemented to estimate the effective Young’s modulus of the nanomodified materials. The results obtained through this homogenization procedure have been used as input for the analysis of the nanocomposite fracture toughness, which has been carried out by a classical continuum mechanics–peridynamics coupling approach. Comparison with the experimental data confirms the capability of the peridynamics-based strategies to properly model the effective Young’s modulus and fracture toughness of epoxy-resin nanocomposites. Finally, the new mica-based composites exhibit high values of volume resistivity, thus being excellent candidates as insulating materials.

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Postek, Eligiusz, and Tomasz Sadowski. "Impact model of the Al2O3/ZrO2 composite by peridynamics." Composite Structures 271 (September 2021): 114071. http://dx.doi.org/10.1016/j.compstruct.2021.114071.

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Pathrikar, Anil, Shashi Bhushan Tiwari, Prashanthan Arayil, and Debasish Roy. "Thermomechanics of damage in brittle solids: A peridynamics model." Theoretical and Applied Fracture Mechanics 112 (April 2021): 102880. http://dx.doi.org/10.1016/j.tafmec.2020.102880.

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Zhao, Teng, and Yongxing Shen. "A Nonlocal Model for Dislocations with Embedded Discontinuity Peridynamics." International Journal of Mechanical Sciences 197 (May 2021): 106301. http://dx.doi.org/10.1016/j.ijmecsci.2021.106301.

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Cruz, Atila Lupim, and Mauricio Vicente Donadon. "An elastoplastic constitutive damage model based on peridynamics formulation." International Journal of Non-Linear Mechanics 142 (June 2022): 103978. http://dx.doi.org/10.1016/j.ijnonlinmec.2022.103978.

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Mitchell, John, Stewart Silling, and David Littlewood. "A position-aware linear solid constitutive model for peridynamics." Journal of Mechanics of Materials and Structures 10, no. 5 (November 6, 2015): 539–57. http://dx.doi.org/10.2140/jomms.2015.10.539.

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Song, Xiaoyu, and Nasser Khalili. "A peridynamics model for strain localization analysis of geomaterials." International Journal for Numerical and Analytical Methods in Geomechanics 43, no. 1 (September 12, 2018): 77–96. http://dx.doi.org/10.1002/nag.2854.

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Wang, Fei, Yu'e Ma, Yanning Guo, and Wei Huang. "Study on Transient Thermal Response for Functionally Graded Materials Based on Peridynamic Theory." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 37, no. 5 (October 2019): 903–8. http://dx.doi.org/10.1051/jnwpu/20193750903.

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The transient heat conduction formula of functionally graded materials (FGMs) is presented based on peridynamics (PD). The simplified micro-heat conductivity model for FGMs is proposed and the numerical discretization and the peridynamic numerical formation are also illustrated. A FORTRAN program is coded to implement calculations. The accuracy of the program is verified by comparing the FEM and analytical results with PD solution. The FGM rectangle plate composed by titanium alloy coating zirconium oxide is performed to calculate temperature fields. The effects of material gradient, porosity and temperature load on thermal response are studied. It is shown that the ceramic proportion of FGMs is increased with an increasing material shape parameter and the thermal shielding performance of FGMs is also improved. The effect of the porosity on thermal response is more and more significant with the increasing time step. The increasing temperature load only affects the temperature response of FGM ceramic area. The thickness of temperature distribution area is increased with the increasing of heat conduction time.

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Gu, Xin, Qing Zhang, and Erdogan Madenci. "Refined bond-based peridynamics for thermal diffusion." Engineering Computations 36, no. 8 (October 7, 2019): 2557–87. http://dx.doi.org/10.1108/ec-09-2018-0433.

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Purpose This paper aims to review the existing bond-based peridynamic (PD) and state-based PD heat conduction models, and further propose a refined bond-based PD thermal conduction model by using the PD differential operator. Design/methodology/approach The general refined bond-based PD is established by replacing the local spatial derivatives in the classical heat conduction equations with their corresponding nonlocal integral forms obtained by the PD differential operator. This modeling approach is representative of the state-based PD models, whereas the resulting governing equations appear as the bond-based PD models. Findings The refined model can be reduced to the existing bond-based PD heat conduction models by specifying particular influence functions. Also, the refined model does not require any calibration procedure unlike the bond-based PD. A systematic explicit dynamic solver is introduced to validate 1 D, 2 D and 3 D heat conduction in domains with and without a crack subjected to a combination of Dirichlet, Neumann and convection boundary conditions. All of the PD predictions are in excellent agreement with the classical solutions and demonstrate the nonlocal feature and advantage of PD in dealing with heat conduction in discontinuous domains. Originality/value The existing PD heat conduction models are reviewed. A refined bond-based PD thermal conduction model by using PD differential operator is proposed and 3 D thermal conduction in intact or cracked structures is simulated.

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Dai, Zili, Jinwei Xie, Zhitang Lu, Shiwei Qin, and Lin Wang. "Numerical Modeling on Crack Propagation Based on a Multi-Grid Bond-Based Dual-Horizon Peridynamics." Mathematics 9, no. 22 (November 10, 2021): 2848. http://dx.doi.org/10.3390/math9222848.

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Peridynamics (PD) is a novel nonlocal theory of continuum mechanics capable of describing crack formation and propagation without defining any fracture rules in advance. In this study, a multi-grid bond-based dual-horizon peridynamics (DH-PD) model is presented, which includes varying horizon sizes and can avoid spurious wave reflections. This model incorporates the volume correction, surface correction, and a technique of nonuniformity discretization to improve calculation accuracy and efficiency. Two benchmark problems are simulated to verify the reliability of the proposed model with the effect of the volume correction and surface correction on the computational accuracy confirmed. Two numerical examples, the fracture of an L-shaped concrete specimen and the mixed damage of a double-edged notched specimen, are simulated and analyzed. The simulation results are compared against experimental data, the numerical solution of a traditional PD model, and the output from a finite element model. The comparisons verify the calculation accuracy of the corrected DH-PD model and its advantages over some other models like the traditional PD model.

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Song, Ying, Haicheng Yu, and Zhuang Kang. "Numerical study on ice fragmentation by impact based on non-ordinary state-based peridynamics." Journal of Micromechanics and Molecular Physics 04, no. 01 (March 2019): 1850006. http://dx.doi.org/10.1142/s2424913018500066.

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Ice-structure interaction is currently one of the hot topics in engineering fields and has not been addressed. Traditional numerical methods derived from classical continuum mechanics have difficulties in solving such discontinuous problems of ice fragmentations. In the present paper, a non-ordinary state-based peridynamics formulation is presented to simulate the behavior of the ice under impact loads applied by a rigid ball. Ice is assumed as a viscoelastic-plastic material and simulated by the modified Drucker–Prager plasticity model. The failure criterion of ice is defined based on fracture toughness. A continuous contact algorithm is adopted to detect the contact between the rigid ball and ice particles. It is shown that numerical results are in good agreement with experimental data from open-literatures, and the non-ordinary state-based peridynamics model can capture the detail fragmentation features of ice under impact loads.

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42

Wu, Liwei, Dan Huang, Yepeng Xu, and Lei Wang. "A rate-dependent dynamic damage model in peridynamics for concrete under impact loading." International Journal of Damage Mechanics 29, no. 7 (January 24, 2020): 1035–58. http://dx.doi.org/10.1177/1056789519901162.

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To study the dynamic behavior and impact damage and failure of concrete materials and structures, a dynamic damage model was reformulated under the framework of the non-local peridynamic theory in this paper. The stretch rate of material bonds, equivalent to the strain rate in classical continuum mechanics, was introduced, and a rate-dependent peridynamic model describing the dynamic damage and failure of concrete materials was then proposed, taking both the dynamic failure of bonds and the rate-sensitivity of damage evolution under different stretch rate into account. The connection between the stretch rate and strength and tensile and compressive failure of concrete materials was established in the peridynamic model. To verify the proposed dynamic damage model for concrete failure, several typical examples simulating the mixed-mode fracture of concrete specimen were investigated. The failure mode, crack propagation paths and the crack propagation speed in the specimen in different cases were captured, which agree well with the experimental results and available numerical results. After model validation, the effect of the number and length of pre-existing cracks on the dynamic failure of concrete components was investigated further.

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Alebrahim, Reza, Pawel Packo, Mirco Zaccariotto, and Ugo Galvanetto. "Wave propagation improvement in two-dimensional bond-based peridynamics model." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 235, no. 14 (January 20, 2021): 2542–53. http://dx.doi.org/10.1177/0954406220985551.

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In this study, methods to mitigate anomalous wave propagation in 2-D Bond-Based Peridynamics (PD) are presented. Similarly to what happens in classical non-local models, an irregular wave transmission phenomenon occurs at high frequencies. This feature of the dynamic performance of PD, limits its potential applications. A minimization method based on the weighted residual point collocation is introduced to substantially extend the frequency range of wave motion modeling. The optimization problem, developed through inverse analysis, is set up by comparing exact and numerical dispersion curves and minimizing the error in the frequency-wavenumber domain. A significant improvement in the wave propagation simulation using Bond-Based PD is observed.

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Zhou, Yanqiao, Mingyi Zhang, Wansheng Pei, and Yapeng Wang. "A non-local frost heave model based on peridynamics theory." Computers and Geotechnics 145 (May 2022): 104675. http://dx.doi.org/10.1016/j.compgeo.2022.104675.

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Liu, Renwei, Yanzhuo Xue, Duanfeng Han, and Baoyu Ni. "Studies on model-scale ice using micro-potential-based peridynamics." Ocean Engineering 221 (February 2021): 108504. http://dx.doi.org/10.1016/j.oceaneng.2020.108504.

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Pathrikar, Anil, Md Masiur Rahaman, and D. Roy. "A thermodynamically consistent peridynamics model for visco-plasticity and damage." Computer Methods in Applied Mechanics and Engineering 348 (May 2019): 29–63. http://dx.doi.org/10.1016/j.cma.2019.01.008.

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MASUDA, Kazuyuki, and Yoshinori SHIIHARA. "An implementation of orthotropic elasto-plastic model on NOSB-peridynamics." Proceedings of The Computational Mechanics Conference 2018.31 (2018): 260. http://dx.doi.org/10.1299/jsmecmd.2018.31.260.

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Foster, John T., and Xiao Xu. "A generalized, ordinary, finite deformation constitutive correspondence model for peridynamics." International Journal of Solids and Structures 141-142 (June 2018): 245–53. http://dx.doi.org/10.1016/j.ijsolstr.2018.02.026.

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Shishkanov, Dmitry A., Maxim V. Vetchinnikov, and Yuriy N. Deryugin. "Peridynamics method for problems solve of solids destruction." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 24, no. 4 (December 31, 2022): 452–68. http://dx.doi.org/10.15507/2079-6900.24.202204.452-468.

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Abstract. The article investigates the method of peridynamics, which is an alternative approach to solving destruction problems based on integral equations. It is assumed that particles in a continuum interact with each other at a finite distance, as in molecular dynamics. Damage is part of the theory at the level of two-particle interactions, so damage finding and destruction occurs when solving the equation of motion. During this work, bondbased and state-based peridynamics models of destruction used in the Sandia Laboratory were described and implemented within the framework of the MoDyS molecular dynamics software package. In the bond-based model, the defining relationship is the bond stiffness function, which corrects the force of particle-particle interaction and imposes a restriction on the use of the Poisson’s ratio. The state-based model generalizes the bond-based approach and may be applied to materials with any Poisson’s ratio. The relationship of both models is ascertained. Calculation convergence is demonstrated on the example of a one-dimensional elasticity problem. The possibility of using the implemented models for fracture problems is also shown.

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Zhang, Haoran, Lisheng Liu, Xin Lai, Hai Mei, and Xiang Liu. "Thermo-Mechanical Coupling Model of Bond-Based Peridynamics for Quasi-Brittle Materials." Materials 15, no. 20 (October 21, 2022): 7401. http://dx.doi.org/10.3390/ma15207401.

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The mechanical properties of quasi-brittle materials, which are widely used in engineering applications, are often affected by the thermal condition of their service environment. Moreover, the materials appear brittle when subjected to tensile loading and show plastic characteristics under high pressure. These two phenomena manifest under different circumstances as completely different mechanical behaviors in the material. To accurately describe the mechanical response, the material behavior, and the failure mechanism of quasi-brittle materials with the thermo-mechanical coupling effect, the influence of the thermal condition is considered in calculating bond forces in the stretching and compression stages, based on a new bond-based Peridynamic (BB-PD) model. In this study, a novel bond-based Peridynamic, fully coupled, thermo-mechanical model is proposed for quasi-brittle materials, with a heat conduction component to account for the effect of the thermo-mechanical coupling. Numerical simulations are carried out to demonstrate the validity and capability of the proposed model. The results reveal that agreement could be found between our model and the experimental data, which show good reliability and promise in the proposed approach.

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Journal articles on the topic 'Peridynamics Model'

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