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1. Full Text Peridynamic Petrov–Galerkin method: A generalization of the peridynamic theory of correspondence materials
by Bode, T and Weißenfels, C and Wriggers, P
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 01/2020, Volume 358, p. 112636
The Peridynamic Petrov–Galerkin (PPG) method is a meshfree approach based on the peridynamic integro-differential form of the momentum equation. The spurious... 
Petrov–Galerkin method | Peridynamic reduction | Smoothed particle hydrodynamics | Consistent linearization | Peridynamic correspondence formulation | Meshfree method
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2. Full Text A local strain-based implementation strategy for the extended peridynamic model with bond rotation
by Li, Wei-Jian and Zhu, Qi-Zhi and Ni, Tao
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 01/2020, Volume 358, p. 112625
The conventional grid displacements-based implementation of the extended peridynamic model with bond rotation may give rise to some difficulty in predicting... 
Extended peridynamic model (XPDM) | Poisson’s ratio | Solid materials | Local strain | Finite element/peridynamic coupling | Numerical implementation
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3. Full Text Adaptive coupling between damage mechanics and peridynamics: A route for objective simulation of material degradation up to complete failure
by Han, Fei and Lubineau, Gilles and Azdoud, Yan
Journal of the Mechanics and Physics of Solids, ISSN 0022-5096, 09/2016, Volume 94, pp. 453 - 472
The objective (mesh-independent) simulation of evolving discontinuities, such as cracks, remains a challenge. Current techniques are highly complex or involve... 
Peridynamics | Fracture | Coupling | Damage | Localization
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4. Full Text A novel conjugated bond linear elastic model in bond-based peridynamics for fracture problems under dynamic loads
by Zhou, Xiaoping and Wang, Yunteng and Shou, Yundong and Kou, Miaomiao
Engineering Fracture Mechanics, ISSN 0013-7944, 02/2018, Volume 188, pp. 151 - 183
A novel conjugated bond linear elastic model is proposed and implemented into the bond-based peridynamic (BB-PD) framework. In this model, micro-elastic PD... 
Linear elastic model | Conjugated bond-based peridynamics | Dynamic loads | The standard bond-based peridynamics | Crack propagation | MESHFREE METHOD | BRITTLE MATERIALS | LONG-RANGE FORCES | ARBITRARY EVOLVING CRACKS | MECHANICS | FREE GALERKIN METHODS | COMPUTER-SIMULATION | STATE-BASED PERIDYNAMICS | DISCRETIZED PERIDYNAMICS | FINITE-ELEMENT-METHOD | NUMERICAL-SIMULATION
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5. Full Text Two Cosserat peridynamic models and numerical simulation of crack propagation
by Chen, Zhuang and Wan, Ji and Chu, Xihua and Liu, Hui
Engineering Fracture Mechanics, ISSN 0013-7944, 04/2019, Volume 211, pp. 341 - 361
This work presents two schemes of Cosserat peridynamics based on Timoshenko beam element in Finite Element Method (FEM) and contact particle model in Discrete... 
Numerical simulation | Peridynamics | Cosserat continuum | Peridynamics horizon | Crack propagation
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6. Full Text Peridynamic analysis of fiber-reinforced composite materials Erkan Oterkus and Erdogan Madenci
by Oterkus, Erkan and Madenci, Erdogan
Journal of Mechanics of Materials and Structures, ISSN 1559-3959, 2012, Volume 7, Issue 1, pp. 45 - 84
Peridynamics | Composite | Nonlocal | Damage
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7. Full Text An application of non-ordinary state-based peridynamics theory in cutting process modelling of unidirectional carbon fiber reinforced polymer material
by Shang, Shuai and Qin, Xuda and Li, Hao and Cao, Xingfeng
Composite Structures, ISSN 0263-8223, 10/2019, Volume 226, p. 111194
The usage of carbon-fiber-reinforced polymer (CFRP) composite keeps increasing in modern industries. However, because of the complexity of CFRP structure, the... 
Peridynamic | Subsurface damage | Orthogonal cutting | CFRP | Cutting force
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8. Full Text Conditioning and error analysis of nonlocal operators with local boundary conditions
by Aksoylu, Burak and Kaya, Adem
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 06/2018, Volume 335, pp. 1 - 19
We study the conditioning and error analysis of novel nonlocal operators in 1D with local boundary conditions. These operators are used, for instance, in... 
Condition number | Integral operator | Peridynamics | Error analysis | Nonlocal diffusion | Preconditioning | MATHEMATICS, APPLIED | PERIDYNAMIC THEORY | DIFFUSION | MODEL
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9. Full Text A coupling approach of state-based peridynamics with node-based smoothed finite element method
by Bie, Y.H and Cui, X.Y and Li, Z.C
Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 04/2018, Volume 331, pp. 675 - 700
In this work, a novel approach to couple ordinary state-based peridynamics (OSPD) with node-based smoothed finite element method (NS-FEM) is proposed. In... 
Coupling approach | Finite element method | State-based peridynamics | Damage | Crack propagation | UPPER BOUND SOLUTIONS | INTEGRATION METHOD | CLASSICAL ELASTICITY | DUAL-HORIZON PERIDYNAMICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | DYNAMIC CRACK-PROPAGATION | ENGINEERING, MULTIDISCIPLINARY | CONTINUUM-MECHANICS | METHOD NS-FEM | FRACTURE-ANALYSIS | SOLID MECHANICS | DISCRETIZED PERIDYNAMICS | Analysis | Methods
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10. Full Text Viscoelastic material models in peridynamics
by Weckner, Olaf and Nik Mohamed, Nik Abdullah
Applied Mathematics and Computation, ISSN 0096-3003, 02/2013, Volume 219, Issue 11, pp. 6039 - 6043
In this paper we propose a new viscoelastic material model within the framework of the nonlocal peridynamic formulation of continuum mechanics. Using Fourier-... 
Peridynamics | Nonlocality | MATHEMATICS, APPLIED
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11. Peridynamic model of unilateral coated envelope material for aerostatics
by Zhou, Yicong and Zhao, Haitao and Chen, Ji'an and Chen, Zheng and Duan, Dengping
Fuhe Cailiao Xuebao/Acta Materiae Compositae Sinica, ISSN 1000-3851, 10/2018, Volume 35, Issue 10, pp. 2897 - 2905
Peridynamic parameter | Envelope material | Numerical emulation | Constitutive function | Peridynamics
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12. Full Text Combined peridynamic and finite element analyses for failure prediction in periodic and partially periodic perforated structures
by Diyaroglu, C and Madenci, E and Stewart, R.J and Zoubi, S.S
Composite Structures, ISSN 0263-8223, 12/2019, Volume 229, p. 111481
This study presents an approach for predicting the displacement and stress fields in fully-periodic or partially-periodic perforated structures. The distance... 
Unit cell | Peridynamics | Perforated | Failure | Structural genome
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13. Full Text Peridynamic homogenization of microstructures with orthotropic constituents in a finite element framework
by Diyaroglu, C and Madenci, E and Phan, N
Composite Structures, ISSN 0263-8223, 11/2019, Volume 227, p. 111334
This study presents a peridynamic approach for performing homogenization of complex material microstructures by using the current element technology of ANSYS.... 
Homogenization | Peridynamics | Microstructure | Orthotropic | Crack | Finite element
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14. Full Text Asymptotically compatible schemes and applications to robust discretization of nonlocal models
by Tian, Xiaochuan and Du, Qiang
SIAM Journal on Numerical Analysis, ISSN 0036-1429, 2014, Volume 52, Issue 4, pp. 1641 - 1665
Many problems in nature, being characterized by a parameter, are of interest both with a fixed parameter value and with the parameter approaching an asymptotic... 
Asymptotically compatible scheme | Local limit | State-based model | Nonlocal diffusion | Peridynamic models | Convergence analysis | Finite element | peridynamic models | MATHEMATICS, APPLIED | finite element | BOUNDARY-CONDITIONS | APPROXIMATIONS | nonlocal diffusion | state-based model | EQUATIONS | PERIDYNAMIC STATES | LAWS | convergence analysis | SOLID MECHANICS | asymptotically compatible scheme | DIFFUSION | local limit | FINITE-ELEMENT-METHOD | Finite element method | Approximation | Discretization | Asymptotic properties | Mathematical analysis | Horizon | Mathematical models | Compatibility
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15. Full Text Wave reflection and cut‐off frequencies in coupled FE‐peridynamic grids
by Giannakeas, Ilias N and Papathanasiou, Theodosios K and Bahai, Hamid
International Journal for Numerical Methods in Engineering, ISSN 0029-5981, 10/2019, Volume 120, Issue 1, pp. 29 - 55
Reflections are typically observed when pulses propagate across interfaces. Accordingly, spurious reflections might occur at the interfaces between different... 
coupling | bond‐based peridynamics | finite elements | perfectly matched layer | spurious reflections | MESHES | ARLEQUIN METHOD | IMPLEMENTATION | MODEL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | CONSERVATION | ENGINEERING, MULTIDISCIPLINARY | ELASTICITY THEORY | BRIDGING DOMAIN METHOD | bond-based peridynamics | ADAPTIVE REFINEMENT | DISCRETIZED PERIDYNAMICS | Solid mechanics | Coupling (molecular) | Descriptions | Computer simulation | Energy conservation | Solvers | Molecular dynamics | Wave reflection
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16. Full Text Fast interaction functions for bond-based peridynamics
by Miranda, H. David and Orr, John and Williams, Chris
European Journal of Computational Mechanics, ISSN 1779-7179, 05/2018, Volume 27, Issue 3, pp. 247 - 276
Numerical implementations of bond-based peridynamics are computationally intensive. We propose a new class of fast interaction functions for constitutive... 
concrete | damage | Peridynamics | fracture
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17. Full Text Numerical methods for the nonlocal wave equation of the peridynamics
by Coclite, G.M and Fanizzi, A and Lopez, L and Maddalena, F and Pellegrino, S.F
Applied Numerical Mathematics, ISSN 0168-9274, 2018
In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This... 
Trigonometric time discretization | Peridynamic equation | Quadrature formula | Spectral methods
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18. Full Text Peridynamic theory for progressive damage prediction in center-cracked composite laminates
by Kilic, B and Agwai, A and Madenci, E
Composite Structures, ISSN 0263-8223, 2009, Volume 90, Issue 2, pp. 141 - 151
Numerical studies on the failure of composites have mostly employed the finite element method. However, it can be rather challenging to predict failure using... 
Progressive | Peridynamic theory | Composites | Nonlocal | Failure | ELASTICITY | TENSILE TESTS | MATERIALS SCIENCE, COMPOSITES | STRENGTH | Laminated materials | Analysis
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19. Full Text Failure analysis of plates with singular and non-singular stress raisers by a coupled peridynamic model
by Zhang, Heng and Qiao, Pizhong and Lu, Linjun
International Journal of Mechanical Sciences, ISSN 0020-7403, 07/2019, Volume 157-158, pp. 446 - 456
A new numerical technique for whole failure progress analysis of notched plates is presented with the coupled peridynamic criterion (CPC) model, in which both... 
Coupled peridynamic criterion | Notched plates | Peridynamics | Failure analysis | CRACK ONSET | INITIATION | FINITE FRACTURE-MECHANICS | STRENGTH | FORMULATION | DEFORMATION | ENGINEERING, MECHANICAL | PREDICTION | MECHANICS | LAMINATED COMPOSITES | CRITERION | PROPAGATION | Analysis | Green technology
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20. Full Text Impact damage on a thin glass plate with a thin polycarbonate backing
by Hu, Wenke and Wang, Yenan and Yu, Jian and Yen, Chian-Fong and Bobaru, Florin
International Journal of Impact Engineering, ISSN 0734-743X, 12/2013, Volume 62, pp. 152 - 165
We present experimental and computational results for the impact of a spherical projectile on a thin glass plate with a thin polycarbonate backing plate,... 
Impact | Peridynamics | Multi-layer | Brittle fracture | Glass | MECHANICS | PERIDYNAMIC MODEL | STEEL SPHERES | DYNAMIC FRACTURE | ENGINEERING, MECHANICAL | SURFACES | Polycarbonates | Analysis | Fracture mechanics | Projectiles | Computation | Dynamics | Damage | Backing
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