Topology Optimization of Energy-Dissipating Plastic Structures with Shear Modified Gurson–Tvergaard–Needleman Model
Publication: Journal of Structural Engineering
Volume 146, Issue 11
Abstract
This paper presents a density-based topology optimization framework for designing energy-dissipating plastic structures. In order to mitigate the material damage during the plastic energy dissipation process, the total material volume in a design is minimized while subjected to a minimum plastic work constraint and a maximum damage constraint. The Gurson–Tvergaard–Needleman (GTN) model with shear damage modifications is adopted to simulate the physics of ductile-damage mechanisms under various stress states. Path-dependent design sensitivities are analytically derived using the adjoint method within the framework of nonlinear finite element analysis. The effectiveness of the proposed framework is demonstrated by a series of numerical examples that shows the proposed framework can successfully limit damage in optimized plastic designs under the prescribed threshold by reconfiguring structural topologies. More notably, compared to the designs obtained with the von Mises plasticity model, damage constrained plastic designs with the GTN model have overall better ductility, higher load carrying capacity, and higher plastic work dissipation before failure initiation.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
The present work was supported in part by the US National Science Foundation through Grant No. CMMI-1762277. Any opinions, findings, conclusions, and recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the sponsors.
References
Alberdi, R., and K. Khandelwal. 2017. “Topology optimization of pressure dependent elastoplastic energy absorbing structures with material damage constraints.” Finite Elem. Anal. Des. 133 (Oct): 42–61. https://doi.org/10.1016/j.finel.2017.05.004.
Alberdi, R., G. Zhang, L. Li, and K. Khandelwal. 2018. “A unified framework for nonlinear path-dependent sensitivity analysis in topology optimization.” Int. J. Numer. Methods Eng. 115 (1): 1–56. https://doi.org/10.1002/nme.5794.
Anderson, T. L. 2017. Fracture mechanics: Fundamentals and applications. Boca Raton, FL: CRC Press.
Bao, Y., and T. Wierzbicki. 2004. “On fracture locus in the equivalent strain and stress triaxiality space.” Int. J. Mech. Sci. 46 (1): 81–98. https://doi.org/10.1016/j.ijmecsci.2004.02.006.
Barsoum, I., and J. Faleskog. 2007. “Rupture mechanisms in combined tension and shear—Micromechanics.” Int. J. Solids Struct. 44 (17): 5481–5498. https://doi.org/10.1016/j.ijsolstr.2007.01.010.
Beghini, L. L., A. Beghini, F. Baker William, and H. Paulino Glaucio. 2015. “Integrated discrete/continuum topology optimization framework for stiffness or global stability of high-rise buildings.” J. Struct. Eng. 141 (8): 04014207. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001164.
Bendsøe, M. P., and N. Kikuchi. 1988. “Generating optimal topologies in structural design using a homogenization method.” Comput. Methods Appl. Mech. Eng. 71 (2): 197–224. https://doi.org/10.1016/0045-7825(88)90086-2.
Bendsøe, M. P., and O. Sigmund. 2003. Topology optimization: Theory, methods and applications. Berlin: Springer.
Bendsøe, P. M., and O. Sigmund. 1999. “Material interpolation schemes in topology optimization.” Arch. Appl. Mech. 69 (9): 635–654. https://doi.org/10.1007/s004190050248.
Benzerga, A. A., and J.-B. Leblond. 2010. “Ductile fracture by void growth to coalescence.” In Advances in applied mechanics, edited by H. Aref and E. V. D. Giessen, 169–305. Amsterdam, Netherlands: Elsevier.
Benzerga, A. A., J.-B. Leblond, A. Needleman, and V. Tvergaard. 2016. “Ductile failure modeling.” Int. J. Fract. 201 (1): 29–80. https://doi.org/10.1007/s10704-016-0142-6.
Bourdin, B. 2001. “Filters in topology optimization.” Int. J. Numer. Methods Eng. 50 (9): 2143–2158. https://doi.org/10.1002/nme.116.
Bruns, T. E., and D. A. Tortorelli. 2001. “Topology optimization of non-linear elastic structures and compliant mechanisms.” Comput. Methods Appl. Mech. Eng. 190 (26): 3443–3459. https://doi.org/10.1016/S0045-7825(00)00278-4.
Changizi, N., and M. Jalalpour. 2017. “Stress-based topology optimization of steel-frame structures using members with standard cross sections: Gradient-based approach.” J. Struct. Eng. 143 (8): 04017078. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001807.
Christensen, P. W., and A. Klarbring. 2008. An introduction to structural optimization. Dordrecht, Netherlands: Springer.
Chu, C. C., and A. Needleman. 1980. “Void nucleation effects in biaxially stretched sheets.” J. Eng. Mater. Technol. 102 (3): 249–256. https://doi.org/10.1115/1.3224807.
Deaton, J. D., and R. V. Grandhi. 2014. “A survey of structural and multidisciplinary continuum topology optimization: Post 2000.” Struct. Multidiscip. Optim. 49 (1): 1–38. https://doi.org/10.1007/s00158-013-0956-z.
de Souza Neto, E. A., D. Peric, and D. R. J. Owen. 2011. Computational methods for plasticity: Theory and applications. West Sussex, UK: Wiley.
El-Tawil, S., H. Li, and S. Kunnath. 2014. “Computational simulation of gravity-induced progressive collapse of steel-frame buildings: Current trends and future research needs.” J. Struct. Eng. 140 (8): A2513001. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000897.
Galjaard, S., S. Hofman, N. Perry, and S. Ren. 2015. “Optimizing structural building elements in metal by using additive manufacturing.” In Proc., IASS Annual Symposia, 1–12. Amsterdam, Netherlands: International Association for Shell and Spatial Structures.
Garrison, W. M., and N. R. Moody. 1987. “Ductile fracture.” J. Phys. Chem. Solids 48 (11): 1035–1074. https://doi.org/10.1016/0022-3697(87)90118-1.
Gibson, I., D. W. Rosen, and B. Stucker. 2014. Additive manufacturing technologies. New York: Springer.
Gurson, A. L. 1977. “Continuum theory of ductile rupture by void nucleation and growth: Part I—Yield criteria and flow rules for porous ductile media.” J. Eng. Mater. Technol. 99 (1): 2–15. https://doi.org/10.1115/1.3443401.
Jewett, J. L., and J. V. Carstensen. 2019. “Experimental investigation of strut-and-tie layouts in deep RC beams designed with hybrid bi-linear topology optimization.” Eng. Struct. 197 (Oct): 109322. https://doi.org/10.1016/j.engstruct.2019.109322.
Khandelwal, K., and S. El-Tawil. 2007. “Collapse behavior of steel special moment resisting frame connections.” J. Struct. Eng. 133 (5): 646–655. https://doi.org/10.1061/(ASCE)0733-9445(2007)133:5(646).
Kiran, R., and K. Khandelwal. 2014. “Gurson model parameters for ductile fracture simulation in ASTM A992 steels.” Fatigue Fract. Eng. Mater. Struct. 37 (2): 171–183. https://doi.org/10.1111/ffe.12097.
Lee, S., and A. Tovar. 2014. “Outrigger placement in tall buildings using topology optimization.” Eng. Struct. 74 (Sep): 122–129. https://doi.org/10.1016/j.engstruct.2014.05.019.
Li, L., G. Zhang, and K. Khandelwal. 2017. “Topology optimization of energy absorbing structures with maximum damage constraint.” Int. J. Numer. Methods Eng. 112 (7): 737–775. https://doi.org/10.1002/nme.5531.
Li, L., G. Zhang, and K. Khandelwal. 2018. “Failure resistant topology optimization of structures using nonlocal elastoplastic-damage model.” Struct. Multidiscip. Optim. 58 (4): 1589–1618. https://doi.org/10.1007/s00158-018-1984-5.
Liang, Q. Q., B. Uy, and G. P. Steven. 2002. “Performance-based optimization for strut-tie modeling of structural concrete.” J. Struct. Eng. 128 (6): 815–823. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:6(815).
Liu, J., et al. 2018. “Current and future trends in topology optimization for additive manufacturing.” Struct. Multidiscip. Optim. 57 (6): 2457–2483. https://doi.org/10.1007/s00158-018-1994-3.
Mijar, A. R., C. C. Swan, J. S. Arora, and I. Kosaka. 1998. “Continuum topology optimization for concept design of frame bracing systems.” J. Struct. Eng. 124 (5): 541–550. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:5(541).
Nabaki, K., J. Shen, and X. Huang. 2019. “Stress minimization of structures based on bidirectional evolutionary procedure.” J. Struct. Eng. 145 (2): 04018256. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002264.
Nahshon, K., and J. W. Hutchinson. 2008. “Modification of the Gurson model for shear failure.” Eur. J. Mech. A Solids 27 (1): 1–17. https://doi.org/10.1016/j.euromechsol.2007.08.002.
Nielsen, K. L., and V. Tvergaard. 2010. “Ductile shear failure or plug failure of spot welds modelled by modified Gurson model.” Eng. Fract. Mech. 77 (7): 1031–1047. https://doi.org/10.1016/j.engfracmech.2010.02.031.
Qian, X. D., Y. S. Choo, J. Y. Liew, and J. Wardenier. 2005. “Simulation of ductile fracture of circular hollow section joints using the Gurson model.” J. Struct. Eng. 131 (5): 768–780. https://doi.org/10.1061/(ASCE)0733-9445(2005)131:5(768).
Rahmatalla, S., and C. C. Swan. 2003. “Form finding of sparse structures with continuum topology optimization.” J. Struct. Eng. 129 (12): 1707–1716. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:12(1707).
Sigmund, O., and K. Maute. 2013. “Topology optimization approaches.” Struct. Multidiscip. Optim. 48 (6): 1031–1055. https://doi.org/10.1007/s00158-013-0978-6.
Svanberg, K. 1987. “The method of moving asymptotes—A new method for structural optimization.” Int. J. Numer. Methods Eng. 24 (2): 359–373. https://doi.org/10.1002/nme.1620240207.
Tvergaard, V. 1982. “On localization in ductile materials containing spherical voids.” Int. J. Fract. 18 (4): 237–252. https://doi.org/10.1007/bf00015686.
Tvergaard, V. 1989. “Material failure by void growth to coalescence.” In Advances in applied mechanics, edited by J. W. Hutchinson and T. Y. Wu, 83–151. Amsterdam, Netherlands: Elsevier.
Tvergaard, V., and A. Needleman. 1984. “Analysis of the cup-cone fracture in a round tensile bar.” Acta Metall. 32 (1): 157–169. https://doi.org/10.1016/0001-6160(84)90213-X.
Zhang, G., R. Alberdi, and K. Khandelwal. 2018. “Topology optimization with incompressible materials under small and finite deformations using mixed u/p elements.” Int. J. Numer. Methods Eng. 115 (8): 1015–1052. https://doi.org/10.1002/nme.5834.
Zhang, G., L. Li, and K. Khandelwal. 2016a. “Topology optimization of structures with anisotropic plastic materials using enhanced assumed strain elements.” Struct. Multidiscip. Optim. 55 (6): 1965–1988. https://doi.org/10.1007/s00158-016-1612-1.
Zhang, X., S. Maheshwari, A. S. Ramos, and G. H. Paulino. 2016b. “Macroelement and macropatch approaches to structural topology optimization using the ground structure method.” J. Struct. Eng. 142 (11): 04016090. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001524.
Zuo, Z. H., Y. M. Xie, and X. Huang. 2011. “Optimal topological design of periodic structures for natural frequencies.” J. Struct. Eng. 137 (10): 1229–1240. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000347.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 146 • Issue 11 • November 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Jul 26, 2019
Accepted: May 5, 2020
Published online: Aug 19, 2020
Published in print: Nov 1, 2020
Discussion open until: Jan 19, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.