مروری بر تئوری پریداینامیک و کاربردهای آن؛ بخش اول: مدل‌های مبتنی بر پریداینامیک

1. Diehl, P., Lipton, R., Wick, T., and Tyagi, M., “A Comparative Review of Peridynamics and Phase-Field Models for Engineering Fracture Mechanics”, Computational Mechanics, Vol. 69, pp. 1259–1293, 2022.
2. Silling, S. A. and Askari, E., “A Meshfree Method Based on the Peridynamic Model of Solid Mechanics”, Computers & Structures, Vol. 83, No. 17-18, pp. 1526-1535, 2005.
3. Inglis, C. E., “Stresses in a Plate Due to the Presence of Cracks and Sharp Corners”, Transactions of the Institution of Naval Architectures, Vol. 55, pp. 219-241, 1913.
4. Gerstle, W. H., Introduction to Practical Peridynamics: Computational Solid Mechanics without Stress and Strain, World Scientific Publishing Company, 2015.
5. Griffith, A. A., “The Phenomena of Rupture and Flow in Solids”, Philosophical Transactions of the Royal Society of London, Vol. 221, No. 582-593, pp. 163-198, 1921.
6. Irwin, G. R., “Analysis of Stresses and Strains near the End of a Crack Traversing a Plate”, Journal of Applied Mechanics, Vol. 24, No. 3, pp. 361-364, 1957.
7. Clayton, J. D., Nonlinear Fracture Mechanics in Encyclopedia of Continuum Mechanics, Springer, pp. 1840-1846, 2020.
8. Dugdale, D. S., “Yielding of Steel Sheets Containing Slits”, Journal of the Mechanics and Physics of Solids, Vol. 8, No. 2, pp. 100-104, 1960.
9. Hutchinson, J., “Fundamentals of the Phenomenological Theory of Nonlinear Fracture Mechanics”, Journal of Applied Mechanics, Vol. 50, No. 4, pp. 1042-1051, 1983.
10. Saxena, A., Nonlinear Fracture Mechanics for Engineers, CRC Press, 1998.
11. Hillerborg, A., Modéer, M., and Petersson, P., “Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements”, Cement and Concrete Research, Vol. 6, No. 6, pp. 773-781, 1976.
12. Madenci, E. and Oterkus, E., Introduction in Peridynamic Theory and Its Applications, Springer, pp. 1-17, 2014.
13. Li, S., Lu, H., Jin, Y., Sun, P., Huang, X., and Bie, Z., “An Improved Unibond Dual-Parameter Peridynamic Model for Fracture Analysis of Quasi-Brittle Materials”, International Journal of Mechanical Sciences, Vol. 204, p. 106571, 2021.
14. Krajcinovic, D., Damage Mechanics, Elsevier, 1996.
15. O'Mara, W., Herring, R. B., and Hunt, L. P., Handbook of Semiconductor Silicon Technology, Crest Publishing House, 2007.
16. Kadau, K., Germann, T. C., and Lomdahl, P. S., “Molecular Dynamics Comes of Age: 320 Billion Atom Simulation on BlueGene/L”, International Journal of Modern Physics C, Vol. 17, No. 12, pp. 1755-1761, 2006.
17. Silling, S. A., “Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces”, Journal of the Mechanics and Physics of Solids, Vol. 48, No. 1, pp. 175-209, 2000.
18. Ha, Y. D. and Bobaru, F., “Studies of Dynamic Crack Propagation and Crack Branching with Peridynamics”, International Journal of Fracture, Vol. 162, No. 1, pp. 229-244, 2010.
19. Yang, D., He, X., Zhu, J., and Bie, Z., “A Novel Damage Model in the Peridynamics-Based Cohesive Zone Method (PD-CZM) for Mixed Mode Fracture with Its Implicit Implementation”, Computer Methods in Applied Mechanics and Engineering, Vol. 377, p. 113721, 2021.
20. Diehl, P., Prudhomme, S., and Lévesque, M., “A Review of Benchmark Experiments for the Validation of Peridynamics Models”, Journal of Peridynamics and Nonlocal Modeling, Vol. 1, No. 1, pp. 14-35, 2019.
21. Mossaiby, F., Sheikhbahaei, P., and Shojaei, A., “Multi-Adaptive Coupling of Finite Element Meshes with Peridynamic Grids: Robust Implementation and Potential Applications”, Engineering with Computers, 2022, https://doi.org/10.1007/s00366-022-01656-z.
22. Shojaei, A., Hermann, A., Cyron, C. J., Seleson, P., and Silling, S. A., “A Hybrid Meshfree Discretization to Improve the Numerical Performance of Peridynamic Models”, Computer Methods in Applied Mechanics and Engineering, Vol. 391, p. 114544, 2022.
23. Oterkus, E., “Peridynamics: Past, Present and Future”, AIP Conference Proceedings, Vol. 2384, No. 1, p. 020001, 2021.
24. Javili, A., Morasata, R., Oterkus, E., and Oterkus, S., “Peridynamics Review”, Mathematics and Mechanics of Solids, Vol. 24, No. 11, pp. 3714-3739, 2019.
25. Askari, E., Bobaru, F., Lehoucq, R., Parks, M., Silling, S., and Weckner, O., “Peridynamics for Multiscale Materials Modeling”, Journal of Physics: Conference Series, Washington, USA, Vol. 125, No. 1, p. 012078, 2008.
26. Liu, X., He, X., Wang, J., Sun, L., and Oterkus, E., “An Ordinary State-Based Peridynamic Model for the Fracture of Zigzag Graphene Sheets”, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 474, No. 2217, p. 20180019, 2018.
27. Jha, P. K. and Lipton, R., “Numerical Convergence of Nonlinear Nonlocal Continuum Models to Local Elastodynamics”, International Journal for Numerical Methods in Engineering, Vol. 114, No. 13, pp. 1389-1410, 2018.
28. Silling, S. A., Epton, M., Weckner, O., Xu, J., and Askari, E., “Peridynamic States and Constitutive Modeling”, Journal of Elasticity, Vol. 88, No. 2, pp. 151-184, 2007.
29. Asgari, M. and Kouchakzadeh, M. A., “An Equivalent Von Mises Stress and Corresponding Equivalent Plastic Strain for Elastic–Plastic Ordinary Peridynamics”, Meccanica, Vol. 54, No. 7, pp. 1001-1014, 2019.
30. Liu, S., Fang, G., Liang, J., and Lv, D., “A Coupling Model of XFEM/Peridynamics for 2D Dynamic Crack Propagation and Branching Problems”, Theoretical and Applied Fracture Mechanics, Vol. 108, p. 102573, 2020.
31. Mossaiby, F., Shojaei, A., Zaccariotto, M., and Galvanetto, U., “OpenCL Implementation of a High Performance 3D Peridynamic Model on Graphics Accelerators”, Computers & Mathematics with Applications, Vol. 74, No. 8, pp. 1856-1870, 2017.
32. Ladányi, G. and Gonda, V., “Review of Peridynamics: Theory, Applications, and Future Perspectives”, Strojniski Vestnik/Journal of Mechanical Engineering, Vol. 67, No. 12, 2021.
33. Bobaru, F., Foster, J. T., Geubelle, P. H., and Silling, S. A., Handbook of Peridynamic Modeling, Taylor & Francis, 2015.
34. Huang, D., Lu, G., and Qiao, P., “An Improved Peridynamic Approach for Quasi-Static Elastic Deformation and Brittle Fracture Analysis”, International Journal of Mechanical Sciences, Vol. 94, pp. 111-122, 2015.
35. Gerstle, W., Sau, N., and Silling, S., “Peridynamic Modeling of Concrete Structures”, Nuclear Engineering and Design, Vol. 237, No. 12-13, pp. 1250-1258, 2007.
36. Gerstle, W., Sau, N., and Aguilera, E., “Micropolar Peridynamic Modeling of Concrete Structures”, Proceedings of the 6th International Conference on Fracture Mechanics of Concrete Structures, Lviv, Ukraine, 2007.
37. Xu, C., Yuan, Y., Zhang, Y., and Xue, Y., “Peridynamic Modeling of Prefabricated Beams Post‐Cast with Steel Fiber Reinforced High‐Strength Concrete”, Structural Concrete, Vol. 22, No. 1, pp. 445-456, 2021.
38. Diana, V. and Carvelli, V., “An Electromechanical Micropolar Peridynamic Model”, Computer Methods in Applied Mechanics and Engineering, Vol. 365, p. 112998, 2020.
39. Diana, V., Labuz, J. F., and Biolzi, L., “Simulating Fracture in Rock Using a Micropolar Peridynamic Formulation”, Engineering Fracture Mechanics, Vol. 230, p. 106985, 2020.
40. Yan, X., Guo, L., and Li, W., “Improved Timoshenko Beam-Based Micropolar Peridynamic Method Incorporating Particle Geometry”, Engineering Fracture Mechanics, Vol. 254, p. 107909, 2021.
41. Diana, V. and Casolo, S., “A Bond-Based Micropolar Peridynamic Model with Shear Deformability: Elasticity, Failure Properties and Initial Yield Domains”, International Journal of Solids and Structures, Vol. 160, pp. 201-231, 2019.
42. Liu, W. and Hong, J. W., “Discretized Peridynamics for Linear Elastic Solids”, Computational Mechanics, Vol. 50, No. 5, pp. 579-590, 2012.
43. Prakash, N. and Seidel, G. D., “A Novel Two-Parameter Linear Elastic Constitutive Model for Bond Based Peridynamics”, 56th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Kissimmee, Florida, p. 0461, 2015.
44. Wang, Y., Zhou, X., Wang, Y., and Shou, Y., “A 3-D Conjugated Bond-Pair-Based Peridynamic Formulation for Initiation and Propagation of Cracks in Brittle Solids”, International Journal of Solids and Structures, Vol. 134, pp. 89-115, 2018.
45. Wang, Y., Zhou, X., and Shou, Y., “The Modeling of Crack Propagation and Coalescence in Rocks under Uniaxial Compression Using the Novel Conjugated Bond-Based Peridynamics”, International Journal of Mechanical Sciences, Vol. 128, pp. 614-643, 2017.
46. Wang, Y., Zhou, X., and Kou, M., “Three-Dimensional Numerical Study on the Failure Characteristics of Intermittent Fissures under Compressive-Shear Loads”, Acta Geotechnica, Vol. 14, No. 4, pp. 1161-1193, 2019.
47. Gu, X. and Zhang, Q., “A Modified Conjugated Bond-Based Peridynamic Analysis for Impact Failure of Concrete Gravity Dam”, Meccanica, Vol. 55, No. 3, pp. 547-566, 2020.
48. Zhou, X. and Yu, X., “A Vector Form Conjugated-Shear Bond-Based Peridynamic Model for Crack Initiation and Propagation in Linear Elastic Solids”, Engineering Fracture Mechanics, Vol. 256, p. 107944, 2021.
49. Zhou, X. and Shou, Y., “Numerical Simulation of Failure of Rock-Like Material Subjected to Compressive Loads Using Improved Peridynamic Method”, International Journal of Geomechanics, Vol. 17, No. 3, p. 04016086, 2017.
50. Zhu, Q. and Ni, T., “Peridynamic Formulations Enriched with Bond Rotation Effects”, International Journal of Engineering Science, Vol. 121, pp. 118-129, 2017.
51. Zhou, X., Wang, Y., Shou, Y., and Kou, M., “A Novel Conjugated Bond Linear Elastic Model in Bond-Based Peridynamics for Fracture Problems under Dynamic Loads”, Engineering Fracture Mechanics, Vol. 188, pp. 151-183, 2018.
52. Chen, Z., Wan, J., Chu, X., and Liu, H., “Two Cosserat Peridynamic Models and Numerical Simulation of Crack Propagation”, Engineering Fracture Mechanics, Vol. 211, pp. 341-361, 2019.
53. Chen, Z. and Chu, X., “Numerical Fracture Analysis of Fiber-Reinforced Concrete by Using the Cosserat Peridynamic Model”, Journal of Peridynamics and Nonlocal Modeling, Vol. 4, No. 1, pp. 88-111, 2022.
54. Zheng, G., Shen, G., Xia, Y., and Hu, P., “A Bond‐Based Peridynamic Model Considering Effects of Particle Rotation and Shear Influence Coefficient”, International Journal for Numerical Methods in Engineering, Vol. 121, No. 1, pp. 93-109, 2020.
55. Madenci, E., Barut, A., and Phan, N., “Bond-Based Peridynamics with Stretch and Rotation Kinematics for Opening and Shearing Modes of Fracture”, Journal of Peridynamics and Nonlocal Modeling, Vol. 3, No. 3, pp. 211-254, 2021.
56. Chen, Z., Wan, J., Xiu, C., Chu, X., and Guo, X., “A Bond-Based Correspondence Model and Its Application in Dynamic Plastic Fracture Analysis for Quasi-Brittle Materials”, Theoretical and Applied Fracture Mechanics, Vol. 113, p. 102941, 2021.
57. Zhou, X. and Tian, D., “A Novel Linear Elastic Constitutive Model for Continuum-Kinematics-Inspired Peridynamics”, Computer Methods in Applied Mechanics and Engineering, Vol. 373, p. 113479, 2021.
58. Tian, D. and Zhou, X., “A Continuum-Kinematics-Inspired Peridynamic Model of Anisotropic Continua: Elasticity, Damage, and Fracture”, International Journal of Mechanical Sciences, Vol. 199, p. 106413, 2021.
59. Zhou, X. and Ma, J., “A Novel Peridynamic Model Enriched with the Rotation Effects of Material Points”, Engineering Analysis with Boundary Elements, Vol. 134, pp. 591-611, 2022.
60. Masoumi, A., Ravandi, M., and Salehi, M., “A Modified Bond-Based Peridynamics Model Without Limitations on Elastic Properties”, arXiv, 2022, https://doi.org/10.48550/arXiv.2208.01266
61. Ekiz, E. and Javili, A., “The Variational Explanation of Poisson’s Ratio in Bond-Based Peridynamics and Extension to Nonlinear Poisson’s Ratio”, Journal of Peridynamics and Nonlocal Modeling, 2021, https://doi.org/10.1007/s42102-021-00068-9.
62. Han, D., Zhang, Y., Wang, Q., Lu, W., and Jia, B., “The Review of the Bond-Based Peridynamics Modeling”, Journal of Micromechanics and Molecular Physics, Vol. 4, No. 01, p. 1830001, 2019.
63. Silling, S. A. and Lehoucq, R. B., “Peridynamic Theory of Solid Mechanics”, Advances in Applied Mechanics, Vol. 44, pp. 73-168, 2010.
64. Fang, G., Liu, S., Liang, J., Fu, M., Wang, B., and Meng, S., “A Stable Non‐Ordinary State‐Based Peridynamic Model for Laminated Composite Materials”, International Journal for Numerical Methods in Engineering, Vol. 122, No. 2, pp. 403-430, 2021.
65. Javaheri, I., Luo, J., Lakshmanan, A., and Sundararaghavan, V., “Higher-Order Approximations for Stabilizing Zero-Energy Modes in Non-Ordinary State-Based Peridynamics Models”, AIAA Journal, Vol. 60, No. 8, pp. 4906-4922, 2022.
66. Li, P., Hao, Z., and Zhen, W., “A Stabilized Non-Ordinary State-Based Peridynamic Model”, Computer Methods in Applied Mechanics and Engineering, Vol. 339, pp. 262-280, 2018.
67. Luo, J. and Sundararaghavan, V., “Stress-Point Method for Stabilizing Zero-Energy Modes in Non-Ordinary State-Based Peridynamics”, International Journal of Solids and Structures, Vol. 150, pp. 197-207, 2018.
68. Madenci, E. and Dördüncü, M., “Non-Ordinary State-Based Peridynamics Free of Zero Energy Modes”, 15th U.S. National Congress on Computational Mechanics (USNCCM15), Texas, United States Of America, 2019.
69. Yaghoobi, A. and Chorzepa, M. G., “Higher-Order Approximation to Suppress the Zero-Energy Mode in Non-Ordinary State-Based Peridynamics”, Computers & Structures, Vol. 188, pp. 63-79, 2017.
70. Wan, J., Chen, Z., Chu, X., and Liu, H., “Improved Method for Zero-Energy Mode Suppression in Peridynamic Correspondence Model”, Acta Mechanica Sinica, Vol. 35, No. 5, pp. 1021-1032, 2019.
71. Yu, K., Xin, X., and Lease, K. B., “A New Method of Adaptive Integration with Error Control for Bond-Based Peridynamics”, Proceedings of the World Congress on Engineering and Computer Science, San Francisco, USA, Vol. 2, 2010.
72. Gerstle, W., Sau, N., and Silling, S., “Peridynamic Modeling of Plain and Reinforced Concrete Structures”, 18th International Conference on Structural Mechanics in Reactor Technology (SMiRT 18), Beijing, China, 2005.
73. Dayal, K. and Bhattacharya, K., “Kinetics of Phase Transformations in the Peridynamic Formulation of Continuum Mechanics”, Journal of the Mechanics and Physics of Solids, Vol. 54, No. 9, pp. 1811-1842, 2006.
74. Mikata, Y., “Analytical Solutions of Peristatic and Peridynamic Problems for a 1D Infinite Rod”, International Journal of Solids and Structures, Vol. 49, No. 21, pp. 2887-2897, 2012.
75. Buryachenko, V. A., Wanji, C., and Shengqi, Y., “Effective Thermoelastic Properties of Heterogeneous Thermoperistatic Bar of Random Structure”, International Journal for Multiscale Computational Engineering, Vol. 13, No. 1, pp. 55-71, 2015.
76. Kilic, B. and Madenci, E., “An Adaptive Dynamic Relaxation Method for Quasi-Static Simulations Using the Peridynamic Theory”, Theoretical and Applied Fracture Mechanics, Vol. 53, No. 3, pp. 194-204, 2010.
77. Rabczuk, T. and Ren, H., “A Peridynamics Formulation for Quasi-Static Fracture and Contact in Rock”, Engineering Geology, Vol. 225, pp. 42-48, 2017.
78. Rädel, M., Willberg, C., and Krause, D., “Peridynamic Analysis of Fibre-Matrix Debond and Matrix Failure Mechanisms in Composites under Transverse Tensile Load by an Energy-Based Damage Criterion”, Composites Part B: Engineering, Vol. 158, pp. 18-27, 2019.
79. Prakash, N. and Stewart, R. J., “A Multi-Threaded Method to Assemble a Sparse Stiffness Matrix for Quasi-Static Solutions of Linearized Bond-Based Peridynamics”, Journal of Peridynamics and Nonlocal Modeling, Vol. 3, No. 2, pp. 113-147, 2021.
80. Littlewood, D. J., Roadmap for Peridynamic Software Implementation, Sandia National Lab., 2015.
81. Zaccariotto, M., Luongo, F., and Galvanetto, U., “Examples of Applications of the Peridynamic Theory to the Solution of Static Equilibrium Problems”, The Aeronautical Journal, Vol. 119, No. 1216, pp. 677-700, 2015.
82. Pashazad, H. and Kharazi, M., “A Peridynamic Plastic Model Based on Von Mises Criteria with Isotropic, Kinematic and Mixed Hardenings under Cyclic Loading”, International Journal of Mechanical Sciences, Vol. 156, pp. 182-204, 2019.
83. Crisfield, M., “Snap-Through and Snap-Back Response in Concrete Structures and the Dangers of under‐Integration”, International Journal for Numerical Methods in Engineering, Vol. 22, No. 3, pp. 751-767, 1986.
84. Ni, T., Zaccariotto, M., Zhu, Q., and Galvanetto, U., “Static Solution of Crack Propagation Problems in Peridynamics”, Computer Methods in Applied Mechanics and Engineering, Vol. 346, pp. 126-151, 2019.
85. Dipasquale, D., Zaccariotto, M., and Galvanetto, U., “Crack Propagation with Adaptive Grid Refinement in 2D Peridynamics”, International Journal of Fracture, Vol. 190, No. 1, pp. 1-22, 2014.
86. Bobaru, F., Yang, M., Alves, L. F., Silling, S. A., Askari, E., and Xu, J., “Convergence, Adaptive Refinement, and Scaling in 1D Peridynamics”, International Journal for Numerical Methods in Engineering, Vol. 77, No. 6, pp. 852-877, 2009.
87. Shojaei, A., Mossaiby, F., Zaccariotto, M., and Galvanetto, U., “An Adaptive Multi-Grid Peridynamic Method for Dynamic Fracture Analysis”, International Journal of Mechanical Sciences, Vol. 144, pp. 600-617, 2018.
88. Silling, S., Littlewood, D., and Seleson, P., “Variable Horizon in a Peridynamic Medium”, Journal of Mechanics of Materials and Structures, Vol. 10, No. 5, pp. 591-612, 2015.
89. Zaccariotto, M., Shojaei, A., and Galvanetto, U., “Coupling of CCM and PD in a Meshless Way”, in Peridynamic Modeling, Numerical Techniques, and Applications, Elsevier Series in Mechanics of Advanced Materials, pp. 113-138, 2021.
90. Hermann, A., Shojaei, A., Steglich, D., Höche, D., Zeller-Plumhoff, B., and Cyron, C. J., “Combining Peridynamic and Finite Element Simulations to Capture the Corrosion of Degradable Bone Implants and to Predict Their Residual Strength”, International Journal of Mechanical Sciences, Vol. 220, p. 107143, 2022.
91. Gu, X., Zhang, Q., and Xia, X., “Voronoi‐Based Peridynamics and Cracking Analysis with Adaptive Refinement”, International Journal for Numerical Methods in Engineering, Vol. 112, No. 13, pp. 2087-2109, 2017.
92. Ren, H., Zhuang, X., Cai, Y., and Rabczuk, T., “Dual‐Horizon Peridynamics”, International Journal for Numerical Methods in Engineering, Vol. 108, No. 12, pp. 1451-1476, 2016.
93. Ren, H., Zhuang, X., and Rabczuk, T., “Dual-Horizon Peridynamics: A Stable Solution to Varying Horizons”, Computer Methods in Applied Mechanics and Engineering, Vol. 318, pp. 762-782, 2017.
94. Liu, W. and Hong, J. W., “A Coupling Approach of Discretized Peridynamics with Finite Element Method”, Computer Methods in Applied Mechanics and Engineering, Vol. 245, pp. 163-175, 2012.
95. Madenci, E. and Oterkus, E., “Coupling of the Peridynamic Theory and Finite Element Method”, in Peridynamic Theory and Its Applications, Springer, pp. 191-202, 2014.
96. Lee, J., Oh, S. E., and Hong, J. W., “Parallel Programming of a Peridynamics Code Coupled with Finite Element Method”, International Journal of Fracture, Vol. 203, No. 1, pp. 99-114, 2017.
97. Galvanetto, U., Mudric, T., Shojaei, A., and Zaccariotto, M., “An Effective Way to Couple FEM Meshes and Peridynamics Grids for the Solution of Static Equilibrium Problems”, Mechanics Research Communications, Vol. 76, pp. 41-47, 2016.
98. Zaccariotto, M., Tomasi, D., and Galvanetto, U., “An Enhanced Coupling of PD Grids to FE Meshes”, Mechanics Research Communications, Vol. 84, pp. 125-135, 2017.
99. Wildman, R. A., O’Grady, J. T., and Gazonas, G. A., “A Hybrid Multiscale Finite Element/Peridynamics Method”, International Journal of Fracture, Vol. 207, No. 1, pp. 41-53, 2017.
100. Yaghoobi, A. and Chorzepa, M. G., “Formulation of Symmetry Boundary Modeling in Non-Ordinary State-Based Peridynamics and Coupling with Finite Element Analysis”, Mathematics and Mechanics of Solids, Vol. 23, No. 8, pp. 1156-1176, 2018.
101. Madenci, E., Barut, A., Dorduncu, M., and Phan, N. D., “Coupling of Peridynamics with Finite Elements without an Overlap Zone”, AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Kissimmee, Florida, USA, p. 1462, 2018.
102. Li, H., Zhang, H., Zheng, Y., Ye, H., and Lu, M., “An Implicit Coupling Finite Element and Peridynamic Method for Dynamic Problems of Solid Mechanics with Crack Propagation”, International Journal of Applied Mechanics, Vol. 10, No. 04, p. 1850037, 2018.
103. Zaccariotto, M., Mudric, T., Tomasi, D., Shojaei, A., and Galvanetto, U., “Coupling of FEM Meshes with Peridynamic Grids”, Computer Methods in Applied Mechanics and Engineering, Vol. 330, pp. 471-497, 2018.
104. Bie, Y., Cui, X., and Li, Z., “A Coupling Approach of State-Based Peridynamics with Node-Based Smoothed Finite Element Method”, Computer Methods in Applied Mechanics and Engineering, Vol. 331, pp. 675-700, 2018.
105. Giannakeas, I. N., Papathanasiou, T. K., and Bahai, H., “Wave Reflection and Cut‐Off Frequencies in Coupled FE‐Peridynamic Grids”, International Journal for Numerical Methods in Engineering, Vol. 120, No. 1, pp. 29-55, 2019.
106. Ni, T., Zaccariotto, M., Zhu, Q., and Galvanetto, U., “Coupling of FEM and Ordinary State-Based Peridynamics for Brittle Failure Analysis in 3D”, Mechanics of Advanced Materials and Structures, Vol. 28, No. 9, pp. 875-890, 2021.
107. Kulkarni, S. S., Tabarraei, A., and Wang, X., “Study of Spurious Wave Reflection at the Interface of Peridynamics and Finite Element Regions”, ASME International Mechanical Engineering Congress and Exposition, Vol. 52149, p. V009T12A054, 2018.
108. Sun, W. and Fish, J., “Superposition-Based Coupling of Peridynamics and Finite Element Method”, Computational Mechanics, Vol. 64, No. 1, pp. 231-248, 2019.
109. Zhang, H., Li, H., Ye, H., Zheng, Y., and Zhang, Y., “A Coupling Extended Multiscale Finite Element and Peridynamic Method for Modeling of Crack Propagation in Solids”, Acta Mechanica, Vol. 230, No. 10, pp. 3667-3692, 2019.
110. Fang, G., Liu, S., Fu, M., Wang, B., Wu, Z., and Liang, J., “A Method to Couple State-Based Peridynamics and Finite Element Method for Crack Propagation Problem”, Mechanics Research Communications, Vol. 95, pp. 89-95, 2019.
111. Wang, X., Kulkarni, S. S., and Tabarraei, A., “Seamless Coupling of Peridynamics and Finite Element Method in Commercial Software of Finite Element to Solve Elasto-Dynamics Problems”, ASME International Mechanical Engineering Congress and Exposition, Salt Lake City, Utah, USA, vol. 59469, p. V009T11A043, 2019.
112. Pagani, A. and Carrera, E., “Coupling Three‐Dimensional Peridynamics and High‐Order One‐Dimensional Finite Elements Based on Local Elasticity for the Linear Static Analysis of Solid Beams and Thin‐Walled Reinforced Structures”, International Journal for Numerical Methods in Engineering, Vol. 121, No. 22, pp. 5066-5081, 2020.
113. Sun, W., Fish, J., and Zhang, G., “Superposition of Non-Ordinary State-Based Peridynamics and Finite Element Method for Material Failure Simulations”, Meccanica, Vol. 55, No. 4, pp. 681-699, 2020.
114. Yang, D., He, X., Yi, S., Deng, Y., and Liu, X., “Coupling of Peridynamics with Finite Elements for Brittle Crack Propagation Problems”, Theoretical and Applied Fracture Mechanics, Vol. 107, p. 102505, 2020.
115. Dong, Y., Su, C., and Qiao, P., “A Stability-Enhanced Peridynamic Element to Couple Non-Ordinary State-Based Peridynamics with Finite Element Method for Fracture Analysis”, Finite Elements in Analysis and Design, Vol. 181, p. 103480, 2020.
116. Liu, Q., Xin, X., and Ma, J., “Coupled Peridynamics Least Square Minimization with Finite Element Method in 3D and Implicit Solutions by Message Passing Interface”, Journal of Peridynamics and Nonlocal Modeling, 2021, https://doi.org/10.1007/s42102-021-00060-3.
117. Liu, Q. and Xin, X., “Revised Non-Ordinary State-Based Peridynamics and a New Framework for Coupling with Finite Element Method”, Engineering Fracture Mechanics, Vol. 242, p. 107483, 2021.
118. D'Elia, M., Littlewood, D., Trageser, J., Perego, M., and Bochev, P., An Optimization-Based Strategy for Peridynamic-FEM Coupling and for the Prescription of Nonlocal Boundary Conditions, Sandia National Lab, 2021.
119. Liu, S., Fang, G., Liang, J., and Fu, M., “A Coupling Method of Non-Ordinary State-Based Peridynamics and Finite Element Method”, European Journal of Mechanics-A/Solids, Vol. 85, p. 104075, 2021.
120. Pagani, A., Enea, M., and Carrera, E., “Quasi‐Static Fracture Analysis by Coupled Three‐Dimensional Peridynamics and High Order One‐Dimensional Finite Elements Based on Local Elasticity”, International Journal for Numerical Methods in Engineering, Vol. 123, No. 4, pp. 1098-1113, 2022.
121. Jin, S., Hwang, Y. K., and Hong, J. W., “Coupling of Non‐Ordinary State‐Based Peridynamics and Finite Element Method with Reduced Boundary Effect”, International Journal for Numerical Methods in Engineering, Vol. 122, No. 16, pp. 4033-4054, 2021.
122. Kefal, A., Diyaroglu, C., Yildiz, M., and Oterkus, E., “Coupling of Peridynamics and Inverse Finite Element Method for Shape Sensing and Crack Propagation Monitoring of Plate Structures”, Computer Methods in Applied Mechanics and Engineering, Vol. 391, p. 114520, 2022.
123. Zhang, Y., Madenci, E., and Zhang, Q., “ANSYS Implementation of a Coupled 3D Peridynamic and Finite Element Analysis for Crack Propagation under Quasi-Static Loading”, Engineering Fracture Mechanics, Vol. 260, p. 108179, 2022.
124. Sun, B., Sun, T., Shen, W., Wang, L., Zhang, F., and Ou, J., “An Efficient Coupling of Peridynamics with the Finite Element Method for Simulating Elastic Cracking”, Engineering Fracture Mechanics, Vol. 269, p. 108538, 2022.
125. Madenci, E., Roy, P., and Behera, D., “Coupling of Bond-Based Peridynamics with Finite Elements in ANSYS”, in Advances in Peridynamics, Springer, pp. 351-398, 2022.
126. Shen, F., Yu, Y., Zhang, Q., and Gu, X., “Hybrid Model of Peridynamics and Finite Element Method for Static Elastic Deformation and Brittle Fracture Analysis”, Engineering Analysis with Boundary Elements, Vol. 113, pp. 17-25, 2020.
127. Ha, Y. D., Lee, J., and Hong, J., “Fracturing Patterns of Rock-Like Materials in Compression Captured with Peridynamics”, Engineering Fracture Mechanics, Vol. 144, pp. 176-193, 2015.
128. Giannakeas, I. N., Papathanasiou, T. K., Fallah, A. S., and Bahai, H., “Coupling XFEM and Peridynamics for Brittle Fracture Simulation—Part I: Feasibility and Effectiveness”, Computational Mechanics, Vol. 66, No. 1, pp. 103-122, 2020.
129. Giannakeas, I. N., Papathanasiou, T. K., Fallah, A. S., and Bahai, H., “Coupling XFEM and Peridynamics for Brittle Fracture Simulation: Part II—Adaptive Relocation Strategy”, Computational Mechanics, Vol. 66, No. 3, pp. 683-705, 2020.
130. Chen, B., Yu, T., Natarajan, S., Zhang, Q., and Bui, T. Q., “Three-Dimensional Dynamic and Quasi-Static Crack Growth by a Hybrid XFEM-Peridynamics Approach”, Engineering Fracture Mechanics, Vol. 261, p. 108205, 2022.
131. Lubineau, G., Azdoud, Y., Han, F., Rey, C., and Askari, A., “A Morphing Strategy to Couple Non-Local to Local Continuum Mechanics”, Journal of the Mechanics and Physics of Solids, Vol. 60, No. 6, pp. 1088-1102, 2012.
132. Seleson, P., Beneddine, S., and Prudhomme, S., “A Force-Based Coupling Scheme for Peridynamics and Classical Elasticity”, Computational Materials Science, Vol. 66, pp. 34-49, 2013.
133. Shojaei, A., Mudric, T., Zaccariotto, M., and Galvanetto, U., “A Coupled Meshless Finite Point/Peridynamic Method for 2D Dynamic Fracture Analysis”, International Journal of Mechanical Sciences, Vol. 119, pp. 419-431, 2016.
134. Wang, X., Kulkarni, S. S., and Tabarraei, A., “Concurrent Coupling of Peridynamics and Classical Elasticity for Elastodynamic Problems”, Computer Methods in Applied Mechanics and Engineering, Vol. 344, pp. 251-275, 2019.
135. Yu, Y., Bargos, F. F., You, H., Parks, M. L., Bittencourt, M. L., and Karniadakis, G. E., “A Partitioned Coupling Framework for Peridynamics and Classical Theory: Analysis and Simulations”, Computer Methods in Applied Mechanics and Engineering, Vol. 340, pp. 905-931, 2018.
136. Han, F., Lubineau, G., Azdoud, Y., and Askari, A., “A Morphing Approach to Couple State-Based Peridynamics with Classical Continuum Mechanics”, Computer Methods in Applied Mechanics and Engineering, Vol. 301, pp. 336-358, 2016.
137. Bie, Y., Li, S., Hu, X., and Cui, X., “An Implicit Dual‐Based Approach to Couple Peridynamics with Classical Continuum Mechanics”, International Journal for Numerical Methods in Engineering, Vol. 120, No. 12, pp. 1349-1379, 2019.
138. Ongaro, G., Seleson, P., Galvanetto, U., Ni, T., and Zaccariotto, M., “Overall Equilibrium in the Coupling of Peridynamics and Classical Continuum Mechanics”, Computer Methods in Applied Mechanics and Engineering, Vol. 381, p. 113515, 2021.
139. Jiang, F. and Shen, Y., “A Quasi-Nonlocal Coupling Method for Bond-Based Peridynamics with Classical Continuum Mechanics”, Engineering Computations, Vol. 39, No. 2, pp. 554-573, 2021.
140. Seleson, P., Ha, Y. D., and Beneddine, S., “Concurrent Coupling of Bond-Based Peridynamics and the Navier Equation of Classical Elasticity by Blending”, International Journal for Multiscale Computational Engineering, Vol. 13, No. 2, pp. 91-113, 2015.
141. Diehl, P. and Prudhomme, S., “Coupling Approaches for Classical Linear Elasticity and Bond-Based Peridynamic Models”, Journal of Peridynamics and Nonlocal Modeling, Vol. 4, pp. 336-366, 2022.
142. Ni, T., Pesavento, F., Zaccariotto, M., Galvanetto, U., and Schrefler, B. A., “Numerical Simulation of Forerunning Fracture in Saturated Porous Solids with Hybrid FEM/Peridynamic Model”, Computers and Geotechnics, Vol. 133, p. 104024, 2021.
143. Jiang, F., Shen, Y., and Cheng, J., “An Energy-Based Ghost-Force-Free Multivariate Coupling Scheme for Bond-Based Peridynamics and Classical Continuum Mechanics”, Engineering Fracture Mechanics, Vol. 240, p. 107316, 2020.
144. Tong, Y., Shen, W., and Shao, J., “An Adaptive Coupling Method of State-Based Peridynamics Theory and Finite Element Method for Modeling Progressive Failure Process in Cohesive Materials”, Computer Methods in Applied Mechanics and Engineering, Vol. 370, p. 113248, 2020.
145. Oñate, E., Perazzo, F., and Miquel, J., “A Finite Point Method for Elasticity Problems”, Computers & Structures, Vol. 79, No. 22-25, pp. 2151-2163, 2001.
146. Liu, G., Meshfree Methods: Moving Beyond the Finite Element Method, CRC Press, 2009.
147. Mossaiby, F., Shojaei, A., Boroomand, B., Zaccariotto, M., and Galvanetto, U., “Local Dirichlet-Type Absorbing Boundary Conditions for Transient Elastic Wave Propagation Problems”, Computer Methods in Applied Mechanics and Engineering, Vol. 362, p. 112856, 2020.
148. Lee, S. and Ha, Y. D., “MPI-OpenMP Hybrid Parallelization for Multibody Peridynamic Simulations”, Journal of the Computational Structural Engineering Institute of Korea, Vol. 33, No. 3, pp. 171-178, 2020.
149. Fan, H. and Li, S., “Parallel Peridynamics–SPH Simulation of Explosion Induced Soil Fragmentation by Using OpenMP”, Computational Particle Mechanics, Vol. 4, No. 2, pp. 199-211, 2017.
150. Ha, Y. D., “An Extended Ghost Interlayer Model in Peridynamic Theory for High-Velocity Impact Fracture of Laminated Glass Structures”, Computers & Mathematics with Applications, Vol. 80, No. 5, pp. 744-761, 2020.
151. Boys, B., Dodwell, T. J., Hobbs, M., and Girolami, M., “PeriPy - a High Performance OpenCL Peridynamics Package”, Computer Methods in Applied Mechanics and Engineering, Vol. 386, p. 114085, 2021.
152. Trevett, N., OpenCL Introduction, Khronos Group, 2013.
153. Li, J., Zhao, J., Xu, F., and Liu, Y., “Accelerating Peridynamics Program Using GPU with CUDA and OpenACC”, The 8th International Conference on Computational Methods (ICCM2017), Guangxi, China, 2017.
154. Wang, X., Wang, Q., An, B., He, Q., Wang, P., and Wu, J., “A GPU Parallel Scheme for Accelerating 2D and 3D Peridynamics Models”, Theoretical and Applied Fracture Mechanics, Vol. 121, p. 103458, 2022.
155. Madenci, E., Barut, A., and Futch, M., “Peridynamic Differential Operator and Its Applications”, Computer Methods in Applied Mechanics and Engineering, Vol. 304, pp. 408-451, 2016.
156. Madenci, E., Dorduncu, M., Barut, A., and Futch, M., “Numerical Solution of Linear and Nonlinear Partial Differential Equations Using the Peridynamic Differential Operator”, Numerical Methods for Partial Differential Equations, Vol. 33, No. 5, pp. 1726-1753, 2017.
157. Behera, D., Ganapol, B., and Madenci, E., “Solution of the Neutron Diffusion Equation with the Peridynamic Differential Operator”, International Conference on Physics of Reactors: Reactor Physics Paving the Way Towards More Efficient Systems, PHYSOR Cancun, Mexico, pp. 1585-1595, 2018.
158. Gao, Y. and Oterkus, S., “Fluid-Elastic Structure Interaction Simulation by Using Ordinary State-Based Peridynamics and Peridynamic Differential Operator”, Engineering Analysis with Boundary Elements, Vol. 121, pp. 126-142, 2020.
159. Bazazzadeh, S., Shojaei, A., Zaccariotto, M., and Galvanetto, U., “Application of the Peridynamic Differential Operator to the Solution of Sloshing Problems in Tanks”, Engineering Computations, Vol. 36, No. 1, pp. 45-83, 2018.
160. Gao, Y. and Oterkus, S., “Nonlocal Numerical Simulation of Low Reynolds Number Laminar Fluid Motion by Using Peridynamic Differential Operator”, Ocean Engineering, Vol. 179, pp. 135-158, 2019.
161. Gao, Y. and Oterkus, S., “Non-Local Modeling for Fluid Flow Coupled with Heat Transfer by Using Peridynamic Differential Operator”, Engineering Analysis with Boundary Elements, Vol. 105, pp. 104-121, 2019.
162. Chang, H., Chen, A., Kareem, A., Hu, L., and Ma, R., “Peridynamic Differential Operator-Based Eulerian Particle Method for 2D Internal Flows”, Computer Methods in Applied Mechanics and Engineering, Vol. 392, p. 114568, 2022.
163. Nguyen, C. T., Oterkus, S., Oterkus, E., Amin, I., Ozdemir, M., El-Aassar, A., and Shawky, H., “Modelling of Eulerian Incompressible Fluid Flows by Using Peridynamic Differential Operator”, Ocean Engineering, Vol. 239, p. 109815, 2021.
164. Gao, Y. and Oterkus, S., “Multi-Phase Fluid Flow Simulation by Using Peridynamic Differential Operator”, Ocean Engineering, Vol. 216, p. 108081, 2020.
165. Shojaei, A., Galvanetto, U., Rabczuk, T., Jenabi, A., and Zaccariotto, M., “A Generalized Finite Difference Method Based on the Peridynamic Differential Operator for the Solution of Problems in Bounded and Unbounded Domains”, Computer Methods in Applied Mechanics and Engineering, Vol. 343, pp. 100-126, 2019.
166. Li, Z., Huang, D., Xu, Y., and Yan, K., “Nonlocal Steady-State Thermoelastic Analysis of Functionally Graded Materials by Using Peridynamic Differential Operator”, Applied Mathematical Modelling, Vol. 93, pp. 294-313, 2021.
167. Dorduncu, M. and Apalak, M. K., “Elastic Flexural Analysis of Adhesively Bonded Similar and Dissimilar Beams Using Refined Zigzag Theory and Peridynamic Differential Operator”, International Journal of Adhesion and Adhesives, Vol. 101, p. 102631, 2020.
168. Li, Z., Huang, D., Yan, K., and Xu, Y., “Large Deformation Analysis of Functionally Graded Beam with Variable Cross-Section by Using Peridynamic Differential Operator”, Composite Structures, Vol. 279, p. 114788, 2022.
169. Wan, J., Yang, D., Chu, X., and Qu, W., “A Micropolar Peridynamic Differential Operator and Simulation of Crack Propagation”, Engineering Fracture Mechanics, Vol. 269, p. 108532, 2022.
170. Dorduncu, M., Kutlu, A., Madenci, E., and Rabczuk, T., “Nonlocal Modeling of Bi-Material and Modulus Graded Plates Using Peridynamic Differential Operator”, Engineering with Computers, 2022, https://doi.org/10.1007/s00366-022-01699-2.
171. Haghighat, E., Bekar, A. C., Madenci, E., and Juanes, R., “A Nonlocal Physics-Informed Deep Learning Framework Using the Peridynamic Differential Operator”, Computer Methods in Applied Mechanics and Engineering, Vol. 385, p. 114012, 2021.
172. Bekar, A. C., Madenci, E., and Haghighat, E., “On the Solution of Hyperbolic Equations Using the Peridynamic Differential Operator”, Computer Methods in Applied Mechanics and Engineering, Vol. 391, p. 114574, 2022.
173. Madenci, E., Barut, A., and Dorduncu, M., Peridynamic Differential Operator for Numerical Analysis, Springer, 2019.
174. Hosseini, V. R. and Zou, W., “The Peridynamic Differential Operator for Solving Time-Fractional Partial Differential Equations”, Nonlinear Dynamics, Vol. 109, pp. 1823–1850, 2022.
175. Dorduncu, M., “Stress Analysis of Laminated Composite Beams Using Refined Zigzag Theory and Peridynamic Differential Operator”, Composite Structures, Vol. 218, pp. 193-203, 2019.
176. Dorduncu, M., “Stress Analysis of Sandwich Plates with Functionally Graded Cores Using Peridynamic Differential Operator and Refined Zigzag Theory”, Thin-Walled Structures, Vol. 146, p. 106468, 2020.
177. Liu, F., Hu, Y. m., Feng, G. q., Zhao, W. d., and Ren, H. l., “Study on Elastoplastic Analysis of Metal Plate Based on Peridynamic Differential Operator”, Thin-Walled Structures, Vol. 180, p. 109836, 2022.
178. Warren, T. L., Silling, S. A., Askari, A., Weckner, O., Epton, M. A., and Xu, J., “A Non-Ordinary State-Based Peridynamic Method to Model Solid Material Deformation and Fracture”, International Journal of Solids and Structures, Vol. 46, No. 5, pp. 1186-1195, 2009.
179. Silling, S. A. and Lehoucq, R. B., “Convergence of Peridynamics to Classical Elasticity Theory”, Journal of Elasticity, Vol. 93, No. 1, pp. 13-37, 2008.
180. Lehoucq, R. B. and Silling, S. A., “Force Flux and the Peridynamic Stress Tensor”, Journal of the Mechanics and Physics of Solids, Vol. 56, No. 4, pp. 1566-1577, 2008.
181. Li, J., Li, S., Lai, X., and Liu, L., “Peridynamic Stress Is the Static First Piola–Kirchhoff Virial Stress”, International Journal of Solids and Structures, Vol. 241, p. 111478, 2022.
182. Fallah, A. S., Giannakeas, I. N., Mella, R., Wenman, M. R., Safa, Y., and Bahai, H., “On the Computational Derivation of Bond-Based Peridynamic Stress Tensor”, Journal of Peridynamics and Nonlocal Modeling, Vol. 2, No. 4, pp. 352-378, 2020.
183. Macek, R. W. and Silling, S. A., “Peridynamics Via Finite Element Analysis”, Finite Elements in Analysis and Design, Vol. 43, No. 15, pp. 1169-1178, 2007.
184. Bie, Y., Liu, Z., Yang, H., and Cui, X., “Abaqus Implementation of Dual Peridynamics for Brittle Fracture”, Computer Methods in Applied Mechanics and Engineering, Vol. 372, p. 113398, 2020.
185. Huang, X., Bie, Z., Wang, L., Jin, Y., Liu, X., Su, G., and He, X., “Finite Element Method of Bond-Based Peridynamics and Its Abaqus Implementation”, Engineering Fracture Mechanics, Vol. 206, pp. 408-426, 2019.
186. Beckmann, R., Mella, R., and Wenman, M., “Mesh and Timestep Sensitivity of Fracture from Thermal Strains Using Peridynamics Implemented in Abaqus”, Computer Methods in Applied Mechanics and Engineering, Vol. 263, pp. 71-80, 2013.
187. Zhang, Y. and Madenci, E., “A Coupled Peridynamic and Finite Element Approach in ANSYS Framework for Fatigue Life Prediction Based on the Kinetic Theory of Fracture”, Journal of Peridynamics and Nonlocal Modeling, Vol. 4, No. 1, pp. 51-87, 2022.
188. Han, S., Diyaroglu, C., Oterkus, S., Madenci, E., Oterkus, E., Hwang, Y., and Seol, H., “Peridynamic Direct Concentration Approach by Using ANSYS”, IEEE 66th Electronic Components and Technology Conference (ECTC), Las Vegas, Nevada, USA, pp. 544-549, 2016.
189. Anicode, S. V. K. and Madenci, E., “Bond-and State-Based Peridynamic Analysis in a Commercial Finite Element Framework with Native Elements”, Computer Methods in Applied Mechanics and Engineering, Vol. 398, p. 115208, 2022.
190. Zhang, N., Gu, Q., Huang, S., Xue, X., and Li, S., “A Practical Bond-Based Peridynamic Modeling of Reinforced Concrete Structures”, Engineering Structures, Vol. 244, p. 112748, 2021.
191. Kahraman, T., Yolum, U., and Guler, M. A., “Implementation of Peridynamic Theory to LS-DYNA for Prediction of Crack Propagation in a Composite Lamina”, 10th European LS-DYNA Conference, Würzburg, Germany, 2015.
192. Kilic, B. and Madenci, E., “Coupling of Peridynamic Theory and the Finite Element Method”, Journal of Mechanics of Materials and Structures, Vol. 5, No. 5, pp. 707-733, 2010.
193. Oterkus, E., Madenci, E., Weckner, O., Silling, S., Bogert, P., and Tessler, A., “Combined Finite Element and Peridynamic Analyses for Predicting Failure in a Stiffened Composite Curved Panel with a Central Slot”, Composite Structures, Vol. 94, No. 3, pp. 839-850, 2012.
194. Sun, Y., Chen, B., Edwards, M. G., and Li, C., “Investigation of Hydraulic Fracture Branching in Porous Media with a Hybrid Finite Element and Peridynamic Approach”, Theoretical and Applied Fracture Mechanics, Vol. 116, p. 103133, 2021.
195. Ren, B., Fan, H., Bergel, G. L., Regueiro, R. A., Lai, X., and Li, S., “A Peridynamics–SPH Coupling Approach to Simulate Soil Fragmentation Induced by Shock Waves”, Computational Mechanics, Vol. 55, No. 2, pp. 287-302, 2015.
196. Fan, H., Bergel, G. L., and Li, S., “A Hybrid Peridynamics–SPH Simulation of Soil Fragmentation by Blast Loads of Buried Explosive”, International Journal of Impact Engineering, Vol. 87, pp. 14-27, 2016.
197. Fan, H. and Li, S., “A Peridynamics-SPH Modeling and Simulation of Blast Fragmentation of Soil under Buried Explosive Loads”, Computer Methods in Applied Mechanics and Engineering, Vol. 318, pp. 349-381, 2017.
198. Rahimi, M. N., Kolukisa, D. C., Yildiz, M., Ozbulut, M., and Kefal, A., “A Generalized Hybrid Smoothed Particle Hydrodynamics–Peridynamics Algorithm with a Novel Lagrangian Mapping for Solution and Failure Analysis of Fluid–Structure Interaction Problems”, Computer Methods in Applied Mechanics and Engineering, Vol. 389, p. 114370, 2022.
199. Tong, Q. and Li, S., “Multiscale Coupling of Molecular Dynamics and Peridynamics”, Journal of the Mechanics and Physics of Solids, Vol. 95, pp. 169-187, 2016.
200. Shafiei, Z., Sarrami, S., Azhari, M., Galvanetto, U., and Zaccariotto, M., “A Coupled Peridynamic and Finite Strip Method for Analysis of in-Plane Behaviors of Plates with Discontinuities”, Engineering with Computers, 2022, https://doi.org/10.1007/s00366-022-01665-y.
201. Yang, Y. and Liu, Y., “Modeling of Cracks in Two-Dimensional Elastic Bodies by Coupling the Boundary Element Method with Peridynamics”, International Journal of Solids and Structures, Vol. 217, pp. 74-89, 2021.
202. Yang, Y. and Liu, Y., “Analysis of Dynamic Crack Propagation in Two-Dimensional Elastic Bodies by Coupling the Boundary Element Method and the Bond-Based Peridynamics”, Computer Methods in Applied Mechanics and Engineering, Vol. 399, p. 115339, 2022.
203. Han, F., Lubineau, G., and Azdoud, Y., “Adaptive Coupling between Damage Mechanics and Peridynamics: A Route for Objective Simulation of Material Degradation up to Complete Failure”, Journal of the Mechanics and Physics of Solids, Vol. 94, pp. 453-472, 2016.
204. Shojaei, A., Zaccariotto, M., and Galvanetto, U., “Coupling of 2D Discretized Peridynamics with a Meshless Method Based on Classical Elasticity Using Switching of Nodal Behaviour”, Engineering Computations, Vol. 34, No. 5, pp. 1334-1366, 2017.
205. Diana, V. and Carvelli, V., “An Electromechanical Micropolar Peridynamic Model for Isotropic and Orthotropic Materials”, 14th World Congress on Computational Mechanics (WCCM) ECCOMAS Congress, Paris, 2021.
206. Wildman, R. and Gazonas, G., “A Dynamic Electro-Thermo-Mechanical Model of Dielectric Breakdown in Solids Using Peridynamics”, Journal of Mechanics of Materials and Structures, Vol. 10, No. 5, pp. 613-630, 2015.
207. Prakash, N. and Seidel, G. D., “Electromechanical Peridynamics Modeling of Piezoresistive Response of Carbon Nanotube Nanocomposites”, Computational Materials Science, Vol. 113, pp. 154-170, 2016.
208. Prakash, N. and Seidel, G. D., “Effects of Microscale Damage Evolution on Piezoresistive Sensing in Nanocomposite Bonded Explosives under Dynamic Loading Via Electromechanical Peridynamics”, Modelling and Simulation in Materials Science and Engineering, Vol. 26, No. 1, p. 015003, 2017.
209. Vieira, F. S. and Araújo, A. L., “Implicit Non-Ordinary State-Based Peridynamics Model for Linear Piezoelectricity”, Mechanics of Advanced Materials and Structures, 2021, https://doi.org/10.1080/15376494.2021.1995798.
210. Zeleke, M. A., Lai, X., and Liu, L., “A Peridynamic Computational Scheme for Thermoelectric Fields”, Materials, Vol. 13, No. 11, p. 2546, 2020.
211. Zeleke, M. A., Xin, L., and Liu, L. S., “Bond Based Peridynamic Formulation for Thermoelectric Materials”, Materials Science Forum, Vol. 883, pp. 51-59, 2017.
212. Ouchi, H., Katiyar, A., York, J., Foster, J. T., and Sharma, M. M., “A Fully Coupled Porous Flow and Geomechanics Model for Fluid Driven Cracks: A Peridynamics Approach”, Computational Mechanics, Vol. 55, No. 3, pp. 561-576, 2015.
213. Oterkus, S., Madenci, E., and Oterkus, E., “Fully Coupled Poroelastic Peridynamic Formulation for Fluid-Filled Fractures”, Engineering Geology, Vol. 225, pp. 19-28, 2017.
214. Celik, E., Guven, I., and Madenci, E., “Simulations of Nanowire Bend Tests for Extracting Mechanical Properties”, Theoretical and Applied Fracture Mechanics, Vol. 55, No. 3, pp. 185-191, 2011.
215. Guven, I. and Zelinski, B. J., “Peridynamic Modeling of Damage and Fracture in Em Windows and Domes”, Window and Dome Technologies and Materials XIV, San Diego, CA, vol. 9453, pp. 135-144, 2015.
216. Oterkus, E., Diyaroglu, C., Zhu, N., Oterkus, S., and Madenci, E., “Utilization of Peridynamic Theory for Modeling at the Nano-Scale” in Nanopackaging: From Nanomaterials to the Atomic Scale”, Springer, pp. 1-16, 2015.
217. Ahadi, A., Hansson, P., and Melin, S., “Indentation of Thin Copper Film Using Molecular Dynamics and Peridynamics”, Procedia Structural Integrity, Vol. 2, pp. 1343-1350, 2016.
218. Yolum, U., Taştan, A., and Güler, M. A., “A Peridynamic Model for Ductile Fracture of Moderately Thick Plates”, Procedia Structural Integrity, Vol. 2, pp. 3713-3720, 2016.
219. Ladányi, G. and Jenei, I., “Analysis of Plastic Peridynamic Material with Rbf Meshless Method”, Pollack Periodica, Vol. 3, No. 3, pp. 65-77, 2008.
220. Mitchell, J. A., A Nonlocal, Ordinary, State-Based Plasticity Model for Peridynamics, Sandia National Laboratories (SNL), 2011.
221. Vogler, T. and Lammi, C. J., A Nonlocal Peridynamic Plasticity Model for the Dynamic Flow and Fracture of Concrete, Sandia National Lab., 2014.
222. Littlewood, D. J., “Simulation of Dynamic Fracture Using Peridynamics, Finite Element Modeling, and Contact”, ASME International Mechanical Engineering Congress and Exposition, Vancouver, Canada, Vol. 44465, pp. 209-217, 2010.
223. Littlewood, D. J., “A Nonlocal Approach to Modeling Crack Nucleation in AA 7075-T651”, ASME International Mechanical Engineering Congress and Exposition, Vol. 54945, pp. 567-576, 2011.
224. Tupek, M. R., Rimoli, J. J., and Radovitzky, R., “An Approach for Incorporating Classical Continuum Damage Models in State-Based Peridynamics”, Computer Methods in Applied Mechanics and Engineering, Vol. 263, pp. 20-26, 2013.
225. O’Grady, J. and Foster, J., “Peridynamic Beams: A Non-Ordinary, State-Based Model”, International Journal of Solids and Structures, Vol. 51, No. 18, pp. 3177-3183, 2014.
226. Sun, S. and Sundararaghavan, V., “A Peridynamic Implementation of Crystal Plasticity”, International Journal of Solids and Structures, Vol. 51, No. 19-20, pp. 3350-3360, 2014.
227. Lai, X., Liu, L. S., Liu, Q. W., Cao, D. F., Wang, Z., and Zhai, P. C., “Slope Stability Analysis by Peridynamic Theory”, Applied Mechanics and Materials, Vol. 744, pp. 584-588, 2015.
228. Wu, C. and Ren, B., “A Stabilized Non-Ordinary State-Based Peridynamics for the Nonlocal Ductile Material Failure Analysis in Metal Machining Process”, Computer Methods in Applied Mechanics and Engineering, Vol. 291, pp. 197-215, 2015.
229. Madenci, E. and Oterkus, S., “Ordinary State-Based Peridynamics for Plastic Deformation According to Von Mises Yield Criteria with Isotropic Hardening”, Journal of the Mechanics and Physics of Solids, Vol. 86, pp. 192-219, 2016.
230. Ahmadi, M., Hosseini-Toudeshky, H., and Sadighi, M., “Peridynamic Micromechanical Modeling of Plastic Deformation and Progressive Damage Prediction in Dual-Phase Materials”, Engineering Fracture Mechanics, Vol. 235, p. 107179, 2020.
231. Lakshmanan, A., Luo, J., Javaheri, I., and Sundararaghavan, V., “Three-Dimensional Crystal Plasticity Simulations Using Peridynamics Theory and Experimental Comparison”, International Journal of Plasticity, Vol. 142, p. 102991, 2021.
232. Mousavi, F., Jafarzadeh, S., and Bobaru, F., “An Ordinary State-Based Peridynamic Elastoplastic 2D Model Consistent with J2 Plasticity”, International Journal of Solids and Structures, Vol. 229, p. 111146, 2021.
233. Javaheri, I., Luo, J., Lakshmanan, A., and Sundararaghavan, V., Higher-Order Approximations for Stabilizing Zero-Energy Modes in Peridynamics Crystal Plasticity Models with Large Horizon Interactions, AIAA SciTech 2022 Forum, San Diego, CA, p. 0073, 2022.
234. Lai, X., Liu, L., Li, S., Zeleke, M., Liu, Q., and Wang, Z., “A Non-Ordinary State-Based Peridynamics Modeling of Fractures in Quasi-Brittle Materials”, International Journal of Impact Engineering, Vol. 111, pp. 130-146, 2018.
235. Rahaman, M. M., Roy, P., Roy, D., and Reddy, J., “A Peridynamic Model for Plasticity: Micro-Inertia Based Flow Rule, Entropy Equivalence and Localization Residuals”, Computer Methods in Applied Mechanics and Engineering, Vol. 327, pp. 369-391, 2017.
236. Zhou, X., Shou, Y., and Berto, F., “Analysis of the Plastic Zone near the Crack Tips under the Uniaxial Tension Using Ordinary State‐Based Peridynamics”, Fatigue & Fracture of Engineering Materials & Structures, Vol. 41, No. 5, pp. 1159-1170, 2018.
237. Chen, W., Zhu, F., Zhao, J., Li, S., and Wang, G., “Peridynamics‐Based Fracture Animation for Elastoplastic Solids”, Computer Graphics Forum, Vol. 37, No. 1, pp. 112-124, 2018.
238. Oterkus, S. and Madenci, E., “Modeling Inelasticity in Peridynamics” in Peridynamic Modeling, Numerical Techniques, and Applications, Elsevier Series in Mechanics of Advanced Materials, pp. 205-221, 2021.
239. Javili, A., McBride, A., Mergheim, J., and Steinmann, P., “Towards Elasto-Plastic Continuum-Kinematics-Inspired Peridynamics”, Computer Methods in Applied Mechanics and Engineering, Vol. 380, p. 113809, 2021.
240. Madenci, E., Roy, P., and Behera, D., “Peridynamic Modeling of Elastoplastic Deformation”, in Advances in Peridynamics, Springer, pp. 185-199, 2022.
241. Li, W. J., You, T., Ni, T., Zhu, Q. Z., and Hien Poh, L., “The Extended Peridynamic Model for Elastoplastic and/or Fracture Problems”, International Journal for Numerical Methods in Engineering, 2022, https://doi.org/10.1002/nme.7060.
242. Zhang, T. and Zhang, J., “Numerical Estimate of Critical Failure Surface of Slope by Ordinary State-Based Peridynamic Plastic Model”, Engineering Failure Analysis, Vol. 140, p. 106556, 2022.
243. Zhou, X., Zhang, T., and Qian, H., “A Two-Dimensional Ordinary State-Based Peridynamic Model for Plastic Deformation Based on Drucker-Prager Criteria with Non-Associated Flow Rule”, International Journal of Rock Mechanics and Mining Sciences, Vol. 146, p. 104857, 2021.
244. Zhou, Z., Li, Z., Gao, C., Zhang, D., Wang, M., Wei, C., and Bai, S., “Peridynamic Micro-Elastoplastic Constitutive Model and Its Application in the Failure Analysis of Rock Masses”, Computers and Geotechnics, Vol. 132, p. 104037, 2021.
245. Zhang, T., Zhou, X., and Qian, Q., “The Peridynamic Drucker‐Prager Plastic Model with Fractional Order Derivative for the Numerical Simulation of Tunnel Excavation”, International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 46, No. 9, pp. 1620-1659, 2022.
246. Cruz, A. L. and Donadon, M. V., “An Elastoplastic Constitutive Damage Model Based on Peridynamics Formulation”, International Journal of Non-Linear Mechanics, Vol. 142, p. 103978, 2022.
247. Gerstle, W., Sau, N., and Aguilera, E., “Micropolar Peridynamic Constitutive Model for Concrete”, 19th International Conference on Structural Mechanics in Reactor Technology (SMiRT 19), Toronto, Canada, 2007.
248. Hordijk, D. A., “Tensile and Tensile Fatigue Behaviour of Concrete; Experiments, Modelling and Analyses”, Heron, Vol. 37, No. 1, pp. 1-79, 1992.
249. Sau, N., Medina-Mendoza, J., and Borbon-Almada, A. C., “Peridynamic Modelling of Reinforced Concrete Structures”, Engineering Failure Analysis, Vol. 103, pp. 266-274, 2019.
250. Yang, D., Dong, W., Liu, X., Yi, S., and He, X., “Investigation on Mode-I Crack Propagation in Concrete Using Bond-Based Peridynamics with a New Damage Model”, Engineering Fracture Mechanics, Vol. 199, pp. 567-581, 2018.
251. Aydin, B. B., Tuncay, K., and Binici, B., “Overlapping Lattice Modeling for Concrete Fracture Simulations Using Sequentially Linear Analysis”, Structural Concrete, Vol. 19, No. 2, pp. 568-581, 2018.
252. Gerstle, W., Sau, N., and Sakhavand, N., “On Peridynamic Computational Simulation of Concrete Structures”, Special Publication, Vol. 265, pp. 245-264, 2009.
253. Yaghoobi, A. and Chorzepa, M. G., “Fracture Analysis of Fiber Reinforced Concrete Structures in the Micropolar Peridynamic Analysis Framework”, Engineering Fracture Mechanics, Vol. 169, pp. 238-250, 2017.
254. Tong, Y., Shen, W., Shao, J., and Chen, J., “A New Bond Model in Peridynamics Theory for Progressive Failure in Cohesive Brittle Materials”, Engineering Fracture Mechanics, Vol. 223, p. 106767, 2020.
255. Yang, D., He, X., Liu, X., Deng, Y., and Huang, X., “A Peridynamics-Based Cohesive Zone Model (PD-CZM) for Predicting Cohesive Crack Propagation”, International Journal of Mechanical Sciences, Vol. 184, p. 105830, 2020.
256. Li, S., Lu, H., Huang, X., and Yang, J., “Improved Peridynamics Approach for the Progressive Fracture of Marine Concrete”, Ocean Engineering, Vol. 255, p. 111404, 2022.
257. Miranda, H. D., Orr, J., and Williams, C., “Fast Interaction Functions for Bond-Based Peridynamics”, European Journal of Computational Mechanics, Vol. 27, No. 3, pp. 247-276, 2018.
258. Hobbs, M., Hattori, G., and Orr, J., “Predicting Shear Failure in Reinforced Concrete Members Using a Three-Dimensional Peridynamic Framework”, Computers & Structures, Vol. 258, p. 106682, 2022.
259. Gu, X., Zhang, Q., Huang, D., and Yv, Y., “Wave Dispersion Analysis and Simulation Method for Concrete SHPB Test in Peridynamics”, Engineering Fracture Mechanics, Vol. 160, pp. 124-137, 2016.
260. Demmie, P. and Silling, S., “An Approach to Modeling Extreme Loading of Structures Using Peridynamics”, Journal of Mechanics of Materials and Structures, Vol. 2, No. 10, pp. 1921-1945, 2007.
261. Oterkus, E., Guven, I., and Madenci, E., “Impact Damage Assessment by Using Peridynamic Theory”, Central European Journal of Engineering, Vol. 2, No. 4, pp. 523-531, 2012.
262. Das, S., Hoffarth, C., Ren, B., Spencer, B., Sant, G., Rajan, S. D., and Neithalath, N., “Simulating the Fracture of Notched Mortar Beams through Extended Finite Element Method (XFEM) and Peridynamics”, Journal of Engineering Mechanics, Vol. 145, No. 7, p. 04019049, 2019.
263. Li, W. and Guo, L., “Meso-Fracture Simulation of Cracking Process in Concrete Incorporating Three-Phase Characteristics by Peridynamic Method”, Construction and Building Materials, Vol. 161, pp. 665-675, 2018.
264. Hai, L. and Ren, X., “Computational Investigation on Damage of Reinforced Concrete Slab Subjected to Underwater Explosion”, Ocean Engineering, Vol. 195, p. 106671, 2020.
265. Zhang, K., Ni, T., Sarego, G., Zaccariotto, M., Zhu, Q., and Galvanetto, U., “Experimental and Numerical Fracture Analysis of the Plain and Polyvinyl Alcohol Fiber-Reinforced Ultra-High-Performance Concrete Structures”, Theoretical and Applied Fracture Mechanics, Vol. 108, p. 102566, 2020.
266. Niazi, S., “Peridynamic Models for Crack Nucleation in Brittle and Quasi-Brittle Materials”, Ph.D. Thesis, The University of Nebraska-Lincoln, Lincoln, Nebraska, 2020.
267. Chen, W., Gu, X., Zhang, Q., and Xia, X., “A Refined Thermo-Mechanical Fully Coupled Peridynamics with Application to Concrete Cracking”, Engineering Fracture Mechanics, Vol. 242, p. 107463, 2021.
268. Zhang, Y. and Qiao, P., “A Fully-Discrete Peridynamic Modeling Approach for Tensile Fracture of Fiber-Reinforced Cementitious Composites”, Engineering Fracture Mechanics, Vol. 242, p. 107454, 2021.
269. Shi, C., Shi, Q., Tong, Q., and Li, S., “Peridynamics Modeling and Simulation of Meso-Scale Fracture in Recycled Coarse Aggregate (RCA) Concretes”, Theoretical and Applied Fracture Mechanics, Vol. 114, p. 102949, 2021.
270. Hattori, G., Hobbs, M., and Orr, J., “A Review on the Developments of Peridynamics for Reinforced Concrete Structures”, Archives of Computational Methods in Engineering, Vol. 28, No. 7, pp. 4655-4686, 2021.
271. Jin, Y., Li, L., Jia, Y., Shao, J., Rougelot, T., and Burlion, N., “Numerical Study of Shrinkage and Heating Induced Cracking in Concrete Materials and Influence of Inclusion Stiffness with Peridynamics Method”, Computers and Geotechnics, Vol. 133, p. 103998, 2021.
272. Zhang, N., Gu, Q., Xue, X., Huang, S., and Du, R., “Refined Simulation of Cracked Reinforced Concrete Beams Based on Enhanced Bond-Based Peridynamics”, International Journal of Structural Stability and Dynamics, p. 2250169, 2022, https://doi.org/10.1142/S0219455422501693.
273. Cheng, Z., Wu, Y., Chu, L., Tang, J., Yuan, C., and Feng, H., “Dynamic Fracture Simulation of Functionally Graded Engineered Cementitious Composite Structures Based on Peridynamics”, Acta Mechanica Solida Sinica, Vol. 35, No. 1, pp. 79-89, 2022.
274. Yaghoobi, A. and Chorzepa, M. G., “Meshless Modeling Framework for Fiber Reinforced Concrete Structures”, Computers & Structures, Vol. 161, pp. 43-54, 2015.
275. Yaghoobi, A., Chorzepa, M. G., Kim, S. S., and Durham, S. A., “Mesoscale Fracture Analysis of Multiphase Cementitious Composites Using Peridynamics”, Materials, Vol. 10, No. 2, p. 162, 2017.
276. Nikravesh, S. and Gerstle, W., “Improved State-Based Peridynamic Lattice Model Including Elasticity, Plasticity and Damage”, Computer Modeling in Engineering & Sciences, Vol. 116, No. 3, pp. 323-347, 2018.
277. Yang, D., He, X., Yi, S., and Liu, X., “An Improved Ordinary State-Based Peridynamic Model for Cohesive Crack Growth in Quasi-Brittle Materials”, International Journal of Mechanical Sciences, Vol. 153, pp. 402-415, 2019.
278. Gerstle, W., Sakhavand, N., and Chapman, S., “Peridynamic and Continuum Models of Reinforced Concrete Lap Splice Compared”, Proceedings of the 7th International Conference on Fracture Mechanics of Concrete and Concrete Structures, Korea Concrete Institute, Seoul, 2010.
279. Zhao, J., Chen, Z., Mehrmashhadi, J., and Bobaru, F., “A Stochastic Multiscale Peridynamic Model for Corrosion-Induced Fracture in Reinforced Concrete”, Engineering Fracture Mechanics, Vol. 229, p. 106969, 2020