مدل جدید پری‌داینامیک مبتنی بر پیوند با قابلیت مدل‌سازی رفتار الاستوپلاستیک

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشگاه سمنان

چکیده

معادلات مکانیک کلاسیک شامل مشتقات جابه‌جایی می‌باشند، که نوعاً این امر موجب عدم توانایی در پیش‌بینی عیوب موجود در سازه‌های آسیب دیده می‌گردد. امروزه جهت رفع این چالش در شرایط خاص حاکم بر نوک ترک و ناپیوستگی‌های موجود در ماده، تئوری پری‌داینامیک به منظور مدل‌سازی آسیب‌های پیش‌رونده و گسیختگی در سازه‌های ترک‌خورده مطرح شده است. به جهت عدم توانایی پری‌داینامیک مبتنی بر پیوند برای پیش‌بینی آسیب در مواد نرم، هدف اصلی این مقاله ارائه یک مدل جدید در پری‌داینامیک مبتنی بر پیوند با قابلیت مدل‌سازی مواد الاستوپلاستیک به کمک روش خواص مادی متغیر است. به منظور اعتبارسنجی مدل، نتایج مدل پری‌داینامیک پیشنهادی برای دو مثال از صفحه‌ای با یک سوراخ مرکزی و نیز صفحه‌ای با یک ترک مرکزی تحت کشش با نتایج حاصل از نرم‌افزار آباکوس بر اساس مفروضات مکانیک پیوسته بررسی می‌گردند. نتایج مربوط به تنش فون‌میسز، اندازه ناحیه پلاستیک، کرنش پلاستیک معادل و جابه‌جایی‌های مدل پیشنهادی در مقایسه با نتایج حاصل از روش اجزای‌ محدود، مطابقت خوبی را نشان دادند، که بیان‌گر دقت خوب مدل پیشنهادی است.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

A New Bond-Based Peridynamic Model with the Ability to Model Elastoplastic Behavior

نویسندگان [English]

  • Mohammad Hadi Safari Naderi
  • Ahmad Ghasemi Ghalebahman
  • Meisam shakouri
Semnan University
چکیده [English]

The classical mechanics equations include displacement derivatives, which usually causes the inability to predict defects in damaged structures. Nowadays, in order to solve this challenge in the special conditions governing the crack tip and the discontinuities in the material, the theory of Peridynamics has been proposed to model progressive damage and rupture in cracked structures. Due to the inability of bond-based Peridynamics to predict failure in ductile materials, the main purpose of this paper is to present a new bond-based Peridynamics model with the ability to model elastoplastic materials using Variable Material Property method. For validation of the model, the results of the proposed Peridynamics model of two examples of a plate with a central hole and a plate with a central crack under tension are checked with those of ABAQUS software based on the assumptions of the continuum mechanics. The results related to von Mises stress, plastic zone size, equivalent plastic strain and displacements of the proposed model showed a good agreement as compared to the results by the finite element method, which indicates the good accuracy of the proposed model.

کلیدواژه‌ها [English]

  • Bond-based Peridynamics
  • Variable Material Properties approach
  • Elastoplastic modeling
  • Von Mises stress
  • Finite Element Method

مراجع

  1. Drucker, D. C., “A More Fundamental Approach to Plastic Stress-Strain Relations”, Proceedings of 1st US National Congress of Applied Mechanics, 487-491, 1951.
  2. Prager, W., “The Theory of Plasticity : A Survey of Recent Achievements”, Proceedings of the Institution of Mechanical Engineers, 169(1), pp. 41-57, 1955.
  3. Chen, W. F., and Han, D. J., “Plasticity for Structural Engineers”, Ross Publishing, 2007.
  4. De Souza Neto, E. A., Peric, D., and Owen, D.R., “Computational Methods for Plasticity : Theory and Applications”, John Wiley & Sons, 2011.
  5. Silling, S. A., “Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces”, Journal of the Mechanics and Physics of Solids, Vol. 48(1), pp. 175-209,
  6. Silling, S. A., and Askari, E., “A Meshfree Method Based on the Peridynamic Model of Solid Mechanics”, Computers & Structures, 83(17-18), pp. 1526-1535, 2005.
  7. Ballarini, R., “Bond-Based Peridynamic Modelling of Singular and Nonsingular Crack-tip Fields”, Meccanica, 53, pp. 3495-3515, 2018.
  8. Silling, S. A., “Peridynamic States and Constitutive Modeling”, Journal of Elasticity, Vol. 88, pp. 151-184,
  9. Tupek, M. R., and Radovitzky, R., “An Extended Constitutive Correspondence Formulation of Peridynamics Based on Nonlinear Bond-Strain Measures”, Journal of the Mechanics and Physics of Solid, Vol. 65, pp. 82-92, 2014.
  10. Gu, X., Zhang, Q., and Madenci, E., “Non-Ordinary State-Based Peridynamic Simulation of Elastoplastic Deformation and Dynamic Cracking of Polycrystal”, Engineering Fracture Mechanics, Vol. 218, pp. 106568,
  11. 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, pp. 111146,
  12. Li, T., and Gu, X., “Elastoplastic Constitutive Modeling for Reinforced Concrete in Ordinary State-Based Peridynamics”, Journal of Mechanics, 36, pp. 799-811, 2020.
  13. Cruz, A. L., and Donadon. M. V., “An Elastoplastic Constitutive Damage Model Based on Peridynamics Formulation”, International Journal of Non-Linear Mechanics, Vol. 142, pp. 103978, 2022.
  14. 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,
  15. Liu, Z., Zhang, J., Zhang, H., Ye, H., Zhang, H., and Zheng, Y., “Time-Discontinuous State-Based Peridynamics for Elasto-Plastic Dynamic Fracture Problems”, Engineering Fracture Mechanics, Vol. 266, pp. 108392,
  16. Foster, J. T., Silling S. A., and Chen, W. W., “Viscoplasticity Using Peridynamics”, International Journal for Numerical Methods in Engineering, Vol. 81(10), pp. 1242-1258,
  17. Lyu, Y., Zhang, J., Chang, J., Guo, S., and Zhang, J. J., “Integrating Peridynamics with Material Point Method for Elastoplastic Material Modeling”, Advances in Computer Graphics International Conference, pp. 228-239,
  18. Liu, S., Fang, G., Fu, M., Yan, X., Meng, S., and Liang, J., “A Coupling Model of Element-Based Peridynamics and Finite Element Method for Elastic-Plastic Deformation and Fracture Analysis”, International Journal of Mechanical Sciences, Vol. 220, pp. 107170,
  19. Kružík, M., Mora-Corral, C., and Stefanelli, U., “Quasistatic Elastoplasticity Via Peridynamics: Existence and Localization”, Continuum Mechanics and Thermodynamics, Vol. 30(5), pp. 1155-1184,
  20. Wu, L., and Huang, D., “Energy Dissipation Study in Impact: From Elastic and Elastoplastic Analysis in Peridynamics”, International Journal of Solids and Structures, Vol. 234, pp. 111279,
  21. 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,
  22. Liu, Z., Bie, Y., Cui, Z., and Cui, X., “Ordinary State-Based Peridynamics for Nonlinear Hardening Plastic Material’s Deformation and It’s Fracture Process”, Engineering Fracture Mechanics, Vol. 223, pp. 106782,
  23. Zhou, X. P., Zhang, T., and Qian, Q. 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, pp. 104857,
  24. 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(5), pp. 1159-1170, 2018.
  25. 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, pp. 102991,
  26. Kazemi, S. R., “Plastic Deformation Due to High-Velocity Impact Using Ordinary State-Based Peridynamic Theory”, International Journal of Impact Engineering, Vol. 137, pp. 103470, 2020.
  27. Zhang, T., Zhou, X. P., and Qian, Q. H., “Drucker-Prager Plasticity Model in the Framework of OSB-PD Theory with Shear Deformation”, Engineering with Computers, pp. 1-20,
  28. Macek, R. W., and Silling, S. A., “Peridynamics Via Finite Element Analysis”, Finite Elements in Analysis and Design, Vol. 43(15), pp. 1169-1178, 2007.
  29. Ladányi, G., and Jenei, I., “Analysis of Plastic Peridynamic Paterial with RBF Meshless Method”, Pollack Periodica, Vol. 3(3), 65-77, 2008.
  30. 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,
  31. Zhou, X. P., Gu, X. B., and Wang, Y. T., “Numerical Simulations of Propagation, Bifurcation and Coalescence of Cracks in Rocks”, International Journal of Rock Mechanics and Mining Sciences, Vol. 80, pp. 241-254,
  32. 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.
  33. Wang, Y. T., Zhou, X. P., and Kou, M. M., “Three-Dimensional Numerical Study on the Failure Characteristics of Intermittent Fissures under Compressive-Shear Loads”, Acta Geotechnica, Vol. 14, pp. 1161-1193,
  34. Wang, Y., Zhou, X., Wang, Y., 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,
  35. 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, pp. 107179,
  36. Sheikhbahaei, P., and Mossaiby, F., “A Review of Peridynamics and its Applications; Part1: The Models Based on Peridynamics”, Journal of Computational Methods in Engineering, Vol. 41(1), pp. 1-35, 2022 (In Persian).
  37. Jahed, H., and Dubey, R., “An Axisymmetric Method of Elastic-Plastic Analysis Capable of Predicting Residual Stress Field”, Journal of Pressure Vessel Technol, Vol. 119(3), pp. 264-273,
  38. Jahed, H., Sethuraman, R., and Dubey, R. N., “A Variable Material Property Approach for Solving Elastic-Plastic Problems”, International Journal of Pressure Vessels and Piping, Vol. 71(3), 285-291, 1997.
  39. Parker, A. P., “Autofrettage of Open-End Tubes Pressures, Stresses, Strains, and Code Comparisons”, Journal of Pressure Vessel Technol, Vol. 123(3), pp. 271-281,
  40. Madenci, E., and Oterkus, E., “Peridynamic Theory and its Applications”, Springer, 2014.
  41. Asgari, M., and Kouchakzadeh, M. A., “An Equivalent Von Mises Stress and Corresponding Equivalent Plastic Strain for Elastic–Plastic Ordinary Peridynamics”, Meccanica, Vol. 54, pp. 1001-1014, 2019.

فایل ها

هم رسانی

ارجاع به این مقاله

آمار

تحت نظارت وف ایرانی