journal article·2021-09Open access

3-Dimensional Bond-Based Peridynamic Representative Volume Element Homogenization

W. Xia, E. Oterkus, S. Oterkus

Physical Mesomechanics· Volume 24· Issue 5

Abstract

In this study, a 3-dimensional (3D) implementation of representative volume element homogenization using bond-based peridynamic formulation is presented. Periodic boundary condition is established by coupling the displacements of periodic point pairs. Homogenized (effective) material properties are obtained based on peridynamic displacement gradient tensor. The current approach is validated by considering a composite material without defects and comparing homogenized properties with results obtained from another homogenization approach. Next, the capability of the current approach is demonstrated by considering randomly generated cracks with arbitrary orientation and location. It can be concluded that the current approach can be an alternative approach to obtain 3-dimensional homogenized material properties for heterogeneous materials with defects.
Source: openalex_inverted_index · Quality: baseline

Research context

OpenAlex topics: Numerical methods in engineering · Electromagnetic Simulation and Numerical Methods · Geotechnical Engineering and Underground Structures

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

References (19)

Show source-provided references
1. Swan, C.C. and Kosaka, I., Voigt–Reuss Topology Optimization for Structures with Linear Elastic Material Behaviours, Int. J. Numer. Meth. Eng., 1997, vol. 40, no. 16, pp. 3033–3057. https://doi.org/10.1002/(SICI)1097-0207(19970830)40:16<3033::AID-NME196>3.0.CO;2-Z10.1002/(SICI)1097-0207(19970830)40:16<3033::AID-NME196>3.0.CO;2-Z ↗
2. Hill, R., The Elastic Behaviour of a Crystalline Aggregate, Proc. Phys. Soc. A, 1952, vol. 65(5), p. 349.10.1088/0370-1298/65/5/307 ↗
3. Kalamkarov, A.L., Andrianov, I.V., and Danishevskyy, V.V., Asymptotic Homogenization of Composite Materials And Structures, Appl. Mech. Rev., 2009, vol. 62(3), p. 030802. https://doi.org/10.1115/1.309083010.1115/1.3090830 ↗
4. Zi, G. and Belytschko, T., New Crack-Tip Elements for XFEM and Applications to Cohesive Cracks, Int. J. Numer. Meth. Eng., 2003, vol. 57, no. 15, pp. 2221–2240. https://doi.org/10.1002/nme.84910.1002/nme.849 ↗
5. Silling, S.A., Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces, J. Mech. Phys. Solids, 2000, vol. 48, no. 1, pp. 175–209. https://doi.org/10.1016/S0022-5096(99)00029-010.1016/S0022-5096(99)00029-0 ↗
6. Madenci, E. and Oterkus, E., Peridynamic Theory and Its Applications, New York: Springer, 2014. https://doi.org/10.1007/978-1-4614-8465-3_210.1007/978-1-4614-8465-3_2 ↗
7. Zhu, N., De Meo, D., and Oterkus, E., Modelling of Granular Fracture in Polycrystalline Materials Using Ordinary State-Based Peridynamics, Materials., 2016, vol. 9, no. 12, p. 977. https://doi.org/10.3390/ma912097710.3390/ma9120977 ↗
8. Imachi, M., Tanaka, S., Ozdemir, M., Bui, T.Q., Oterkus, S., and Oterkus, E., Dynamic Crack Arrest Analysis by Ordinary State-Based Peridynamics, Int. J. Fract., 2020, vol. 221, no. 2, pp. 155–169. https://doi.org/10.1007/s10704-019-00416-310.1007/s10704-019-00416-3 ↗
9. Basoglu, M.F., Zerin, Z., Kefal, A., and Oterkus, E., A Computational Model of Peridynamic Theory for Deflecting Behavior of Crack Propagation with Micro-Cracks, Comput. Mater. Sci., 2019, vol. 162, pp. 33–46. https://doi.org/10.1016/j.commatsci.2019.02.03210.1016/j.commatsci.2019.02.032 ↗
10. Candaş, A., Oterkus, E., and İmrak, C.E., Dynamic Crack Propagation and Its Interaction with Micro-Cracks in an Impact Problem, J. Eng. Mater. Technol. Trans. ASME, 2021, vol. 143(1), p. 011003. https://doi.org/10.1115/1.404774610.1115/1.4047746 ↗
11. Nguyen, C.T. and Oterkus, S., Peridynamics Formulation for Beam Structures to Predict Damage in Offshore Structures, Ocean Eng., 2019, vol. 173, pp. 244–267. https://doi.org/10.1016/j.oceaneng.2018.12.04710.1016/j.oceaneng.2018.12.047 ↗
12. Yang, Z., Vazic, B., Diyaroglu, C., Oterkus, E., and Oterkus, S., A Kirchhoff Plate Formulation in a State-Based Peridynamic Framework, Math. Mech. Solids, 2020, vol. 25, no. 3, pp. 727–738.10.1177/1081286519887523 ↗
13. Nguyen, C.T. and Oterkus, S., Peridynamics for the Thermomechanical Behavior of Shell Structures, Eng. Fract. Mech., 2019, vol. 219, p. 106623. https://doi.org/10.1016/j.engfracmec2019.10662310.1016/j.engfracmec2019.106623 ↗
14. Madenci, E., Barut, A., and Phan, N., Peridynamic Unit Cell Homogenization for Thermoelastic Properties of Heterogeneous Microstructures with Defects, Compos. Struct., 2018, vol. 188, pp. 104–115. https://doi.org/10.1016/j.compstruct.2018.01.00910.1016/j.compstruct.2018.01.009 ↗
15. De Meo, D. and Oterkus, E., Finite Element Implementation of a Peridynamic Pitting Corrosion Damage Model, Ocean Eng., 2017, vol. 135, pp. 76–83. https://doi.org/10.1016/j.oceaneng.2017.03.00210.1016/j.oceaneng.2017.03.002 ↗
16. Diyaroglu, C., Oterkus, S., Oterkus, E., and Madenci, E., Peridynamic Modeling of Diffusion by Using Finite-Element Analysis, IEEE Trans. Component. Packaging Manuf. Technol., 2017, vol. 7, no. 11, pp. 1823–1831. https://doi.org/10.1109/TCPMT.2017.273752210.1109/TCPMT.2017.2737522 ↗
17. Diyaroglu, C., Oterkus, S., Oterkus, E., Madenci, E., Han, S., and Hwang, Y., Peridynamic Wetness Approach for Moisture Concentration Analysis in Electronic Packages, Microelectron. Reliabil., 2017, vol. 70, pp. 103–111. https://doi.org/10.1016/j.microrel.2017.01.00810.1016/j.microrel.2017.01.008 ↗
18. Breitenfeld, M.S., Geubelle, P.H., Weckner, O., and Silling, S.A., Non-Ordinary State-Based Peridynamic Analysis of Stationary Crack Problems, Comp. Meth. Appl. Mech. Eng., 2014, vol. 272, pp. 233–250. https://doi.org/10.1016/j.cma.2014.01.00210.1016/j.cma.2014.01.002 ↗
19. Yu, W. and Tang, T., Variational Asymptotic Method for Unit Cell Homogenization of Periodically Heterogeneous Materials, Int. J. Solids Struct., 2007, vol. 44, no. 11–12, pp. 3738–3755. https://doi.org/10.1016/j.ijsolstr.2006.10.02010.1016/j.ijsolstr.2006.10.020 ↗