Analysis of dynamic crack propagation in two-dimensional elastic bodies by coupling the boundary element method and the bond-based peridynamics. (English) Zbl 1507.74431
Summary: A novel method for predicting dynamic crack propagation based on coupling the boundary element method (BEM) and bond-based peridynamics (BBPD) is developed in this work. The special feature of this method is that it can take full advantages of both the BEM and PD to achieve a higher level of accuracy and efficiency. Based on the scale of the structure and the location of cracks, the considered domain can be divided into a non-cracked region and a cracked region. For the non-cracked region, a meshfree boundary-domain integral equation method (meshfree-BDIEM) is employed in the analysis to reduce the dimension by one and to increase the computational efficiency. The bond-based PD is applied to simulate the cracked region, which can model the initiation and propagation of the cracks automatically. The boundary nodes from the BEM on the interfaces can interact with the material points from the PD directly. By using the displacement continuity and force equilibrium conditions on the interfaces, a combined model is obtained by merging the mass, stiffness, and force matrices from each region of the domain. Both the implicit and explicit BEM-PD coupled solution methods can deliver accurate results without inducing the ghost forces. Several benchmark problems of dynamic crack propagation have been modeled by using the method, which demonstrate that the developed BEM-PD coupled approach can be an efficient numerical tool to model the dynamic crack propagation problems.
MSC:
| 74R10 | Brittle fracture |
| 74A70 | Peridynamics |
| 74S15 | Boundary element methods applied to problems in solid mechanics |
Keywords:
dynamic crack propagation; peridynamics; boundary element method; implicit and explicit methods; coupling BEM with PDReferences:
| [1] | Madenci, E.; Oterkus, E., Peridynamic Theory and Its Applications (2014), Springer: Springer New York · Zbl 1295.74001 |
| [2] | Silling, S. A., Reformulation of elasticity theory for discontinuities and long-range forces, J. Mech. Phys. Solids, 48, 1, 175-209 (2000) · Zbl 0970.74030 |
| [3] | Zhang, H.; Zhang, X.; Liu, Y.; Qiao, P. Z., Peridynamic modeling of elastic biomaterial interface fracture, Comput. Methods Appl. Mech. Engrg., 390, Article 114458 pp. (2022) · Zbl 1507.74063 |
| [4] | Liu, Y. X.; Liu, L. S.; Mei, H.; Liu, Q. W.; Lai, X., A modified rate-dependent peridynamic model with rotation effect for dynamic mechanical behavior of ceramic materials, Comput. Methods Appl. Mech. Engrg., 388, Article 114246 pp. (2022) · Zbl 1507.74056 |
| [5] | Madenci, E.; Barut, A.; Dorduncu, M., Peridynamic Differential Operator for Numerical Analysis (2019), Springer: Springer New York · Zbl 07658003 |
| [6] | Cheng, Z. Q.; Sui, Z. B.; Yin, H.; Feng, H., Numerical simulation of dynamic fracture in functionally graded materials using peridynamic modeling with composite weighted bonds, Eng. Anal. Bound. Elem., 105, 31-46 (2019) · Zbl 1464.74011 |
| [7] | Shojaei, A.; Mudric, T.; Zaccariotto, M.; Galvanetto, U., A coupled meshless finite point/peridynamic method for 2D dynamic fracture analysis, Int. J. Mech. Sci., 119, 419-431 (2016) |
| [8] | Shojaei, A.; Zaccariotto, M.; Galvanetto, U., Coupling of 2D discretized peridynamics with a meshless method based on classical elasticity using switching of nodal behaviour, Eng. Comput., 34, 5 (2017) |
| [9] | Macek, R. W.; Silling, S. A., Peridynamics via finite element analysis, Finite Elem. Anal. Des., 43, 15, 1169-1178 (2007) |
| [10] | Kilic, B.; Madenci, E., Coupling of peridynamic theory and the finite element method, J. Mech. Mater. Struct., 5, 707-733 (2010) |
| [11] | Liu, W. Y.; Hong, J. W., A coupling approach of discretized peridynamics with finite element method, Comput. Methods Appl. Mech. Engrg., 245-246, 163-175 (2012) · Zbl 1354.74284 |
| [12] | Lubineau, G.; Azdoud, Y.; Han, F.; Rey, C.; Askari, A., A morphing strategy to couple non-local to local continuum mechanics, J. Mech. Phys. Solids, 60, 6, 1088-1102 (2012) |
| [13] | Han, F.; Lubineau, G.; Azdoud, Y., Adaptive coupling between damage mechanics and peridynamics: A route for objective simulation of material degradation up to complete failure, J. Mech. Phys. Solids, 94, 453-472 (2016) |
| [14] | Galvanetto, U.; Mudric, T.; Shojaei, A.; Zaccariotto, M., An effective way to couple FEM meshes and peridynamics grids for the solution of static equilibrium problems, Mech. Res. Commun., 76, 41-47 (2016) |
| [15] | Zaccariotto, M.; Tomasi, D.; Galvanetto, U., An enhanced coupling of PD grids to FE meshes, Mech. Res. Commun., Article S0093641317300824 pp. (2017) |
| [16] | Zaccariotto, M.; Mudric, T.; Tomasi, D.; Shojaei, A.; Galvanetto, U., Coupling of FEM meshes with peridynamic grids, Comput. Methods Appl. Mech. Engrg., 330, 471-497 (2018) · Zbl 1439.65103 |
| [17] | Li, H.; Zhang, H.; Zheng, Y., An implicit coupling finite element and peridynamic method for dynamic problems of solid mechanics with crack propagation, Int. J. Appl. Mech., 10, 04, Article 1850037 pp. (2018) |
| [18] | Bie, Y.; Cui, X.; Li, Z., A coupling approach of state-based peridynamics with node-based smoothed finite element method, Comput. Methods Appl. Mech. Engrg., 331, 675-700 (2018) · Zbl 1439.74392 |
| [19] | Sun, B.; Li, S.; Gu, Q., Coupling of peridynamics and numerical substructure method for modeling structures with local discontinuities, Comput. Model. Eng. Sci., 120, 739-757 (2019) |
| [20] | Liu, Y. J.; Li, Y. X.; Xie, W., Modeling of multiple crack propagation in 2-D elastic solids by the fast multipole boundary element method, Eng. Fract. Mech., 172, 1-16 (2017) |
| [21] | Liu, Y. J., On the displacement discontinuity method and the boundary element method for solving 3-D crack problems, Eng. Fract. Mech., 164, 35-45 (2016) |
| [22] | Wu, H.; Liu, Y. J.; Jiang, W., A fast multipole boundary element method for 3D multi-domain acoustic scattering problems based on the Burton-Miller formulation, Eng. Anal. Bound. Elem., 36, 5, 779-788 (2012) · Zbl 1351.74147 |
| [23] | Liu, Y. J., Fast Multipole Boundary Element Method: Theory and Applications in Engineering (2009), Cambridge University Press: Cambridge University Press Cambridge |
| [24] | Yang, Y.; Liu, Y. J., Modeling of cracks in two-dimensional elastic bodies by coupling the boundary element method with peridynamics, Int. J. Solids Struct., 217-218, 74-89 (2021) |
| [25] | Silling, S. A., Reformulation of elasticity theory for discontinuities and long-range forces, J. Mech. Phys. Solids, 48, 1, 175-209 (2000) · Zbl 0970.74030 |
| [26] | Silling, S. A.; Askari, E., A meshfree method based on the peridynamic model of solid mechanics, Comput. Struct., 83, 1526-1535 (2005) |
| [27] | Huang, D.; Lu, G.; Wang, C., An extended peridynamic approach for deformation and fracture analysis, Eng. Fract. Mech., 141, 196-211 (2015) |
| [28] | Yu, H.; Li, S., On energy release rates in peridynamics, J. Mech. Phys. Solids, 142, Article 104024 pp. (2020) |
| [29] | Yang, Y.; Lam, C. C.; Kou, K. P., Forced vibration analysis of functionally graded beams by the meshfree boundary-domain integral equation method, Eng. Anal. Bound. Elem., 72, 100-110 (2016) · Zbl 1403.74044 |
| [30] | Yang, Y.; Kou, K. P.; Iu, V. P.; Lam, C. C.; Zhang, C. Z., Free vibration analysis of two-dimensional functionally graded structures by a meshfree boundary-domain integral equation method, Compos. Struct., 110, 342-353 (2014) |
| [31] | Dipasquale, D.; Zaccariotto, M.; Galvanetto, U., Crack propagation with adaptive grid refinement in 2D peridynamics, Int. J. Fract., 190, 1-2, 1-22 (2014) |
| [32] | Cheng, Z.; Zhang, G.; Wang, Y.; Bobaru, B., A peridynamic model for dynamic fracture in functionally graded materials, Compos. Struct., 133, 529-546 (2015) |
| [33] | Lu, G.; Huang, D.; Qiao, P., An improved peridynamic approach for quasi-static elastic deformation and brittle fracture analysis, Int. J. Mech. Sci. (2015) |
| [34] | Kan, X.; Yan, J.; Li, S., On differences and comparisons of peridynamic differential operators and nonlocal differential operators, Comput. Mech., 68, 6, 1349-1367 (2021) · Zbl 1479.74012 |
| [35] | Kalthoff, J. F.; Winkler, S., Failure mode transition at high rates of shear loading, DGM information’s gesellschaft mbh, (Impact Loading and Dynamic Behavior of Materials, Vol. 1 (1988)), 185-195 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
