×

Simple strategy toward tailoring fracture properties of brittle architected materials. (English) Zbl 1534.74060

Summary: Based on standard stiffness (compliance) and stress designs in structural topology optimization (TO), this work proposes a simple strategy to tailor fracture properties of brittle architected materials. Material distribution in the design domain is customized through a stress-constrained strain-energy maximization TO framework. Structures consisting of a single-phase brittle material are studied. Mechanical fracture properties of the optimized structure including stiffness, toughness, strength, and failure displacement are thereafter quantified via the phase field modeling. Reported results show that the obtained architecture can achieve 6 times tougher and more than 1.5 times stronger compared with the stiffness-only TO result. Against to stress-only optimization, all concerned mechanical properties including stiffness, toughness, and strength can be improved by more than 15% simultaneously.
{© 2022 John Wiley & Sons, Ltd.}

MSC:

74R10 Brittle fracture
74P15 Topological methods for optimization problems in solid mechanics
74P10 Optimization of other properties in solid mechanics
74S99 Numerical and other methods in solid mechanics
Full Text: DOI

References:

[1] BendsøeMP, KikuchiN. Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng. 1988;71(2):197‐224. · Zbl 0671.73065
[2] BendsøeMP. Optimal shape design as a material distribution problem. Struct Optim. 1989;1(4):193‐202.
[3] SigmundO. A 99 line topology optimization code written in Matlab. Struct Multidisc Optim. 2001;21(2):120‐127.
[4] XieYM, StevenGP. A simple evolutionary procedure for structural optimization. Comput Struct. 1993;49(5):885‐896.
[5] XiaL, XiaQ, HuangX, XieYM. Bi‐directional evolutionary structural optimization on advanced structures and materials: a comprehensive review. Arch Comput Methods Eng. 2018;25(2):437‐478. · Zbl 1392.74074
[6] AllaireG. Shape Optimization by the Homogenization Method. 6th ed.Springer Science & Business Media; 2001.
[7] AllaireG, JouveF, ToaderAM. Structural optimization using sensitivity analysis and a level‐set method. J Comput Phys. 2004;194(1):363‐393. · Zbl 1136.74368
[8] DaD, XiaL, LiG, HuangX. Evolutionary topology optimization of continuum structures with smooth boundary representation. Struct Multidisc Optim. 2018;57(6):2143‐2159.
[9] GuoX, ZhangW, ZhongW. Doing topology optimization explicitly and geometrically—a new moving morphable components based framework. J Theoret Appl Mech. 2014;81(8):081009.
[10] SmithH, NoratoJA. A MATLAB code for topology optimization using the geometry projection method. Struct Multidisc Optim. 2020;62(3):1579‐1594.
[11] WangC, ZhaoZ, ZhouM, SigmundO, ZhangXS. A comprehensive review of educational articles on structural and multidisciplinary optimization. Struct Multidisc Optim. 2021;64:2827‐2880.
[12] DuysinxP, BendsøeMP. Topology optimization of continuum structures with local stress constraints. Int J Numer Methods Eng. 1998;43(8):1453‐1478. · Zbl 0924.73158
[13] DuysinxP, SigmundO. New developments in handling stress constraints in optimal material distribution. Proceedings of the 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization. 1998;4906.
[14] XiaL, ZhangL, XiaQ, ShiT. Stress‐based topology optimization using bi‐directional evolutionary structural optimization method. Comput Methods Appl Mech Eng. 2018;333:356‐370. · Zbl 1440.74322
[15] EmmendoerferHJr, FancelloEA. A level set approach for topology optimization with local stress constraints. Int J Numer Methods Eng. 2014;99(2):129‐156. · Zbl 1352.74238
[16] ZhangW, LiD, ZhouJ, DuZ, LiB, GuoX. A moving morphable void (MMV)‐based explicit approach for topology optimization considering stress constraints. Comput Methods Appl Mech Eng. 2018;334:381‐413. · Zbl 1440.74330
[17] YangR, ChenC. Stress‐based topology optimization. Struct Optim. 1996;12(2):98‐105.
[18] LeC, NoratoJ, BrunsT, HaC, TortorelliD. Stress‐based topology optimization for continua. Struct Multidisc Optim. 2010;41(4):605‐620.
[19] QianX. Undercut and overhang angle control in topology optimization: a density gradient based integral approach. Int J Numer Methods Eng. 2017;111(3):247‐272. · Zbl 07867061
[20] WangC, QianX. Heaviside projection-based aggregation in stress‐constrained topology optimization. Int J Numer Methods Eng. 2018;115(7):849‐871. · Zbl 07865075
[21] SilvadGA, AageN, BeckAT, SigmundO. Three‐dimensional manufacturing tolerant topology optimization with hundreds of millions of local stress constraints. Int J Numer Methods Eng. 2021;122(2):548‐578. · Zbl 07863081
[22] Giraldo‐LondoñoO, PaulinoGH. A unified approach for topology optimization with local stress constraints considering various failure criteria: von Mises, Drucker-Prager, Tresca, Mohr-coulomb, Bresler-Pister and Willam-Warnke. Proc Royal Soc A. 2020;476(2238):20190861. · Zbl 1472.74179
[23] BruggiM, VeniniP. A mixed FEM approach to stress‐constrained topology optimization. Int J Numer Methods Eng. 2008;73(12):1693‐1714. · Zbl 1159.74397
[24] BruggiM, DuysinxP. Topology optimization for minimum weight with compliance and stress constraints. Struct Multidisc Optim. 2012;46(3):369‐384. · Zbl 1274.74219
[25] XiaL, DaD, YvonnetJ. Topology optimization for maximizing the fracture resistance of quasi‐brittle composites. Comput Methods Appl Mech Eng. 2018;332:234‐254. · Zbl 1439.74304
[26] DaD, YvonnetJ, XiaL, LiG. Topology optimization of particle‐matrix composites for optimal fracture resistance taking into account interfacial damage. Int J Numer Methods Eng. 2018;115(5):604‐626. · Zbl 07865069
[27] DaD. Topology Optimization Design of Heterogeneous Materials and Structures. John Wiley & Sons; 2019.
[28] RussJB, WaismanH. A novel topology optimization formulation for enhancing fracture resistance with a single quasi‐brittle material. Int J Numer Methods Eng. 2020;121(13):2827‐2856. · Zbl 07841945
[29] LiP, WuY, YvonnetJ. A SIMP‐phase field topology optimization framework to maximize quasi‐brittle fracture resistance of 2D and 3D composites. Theor Appl Fract Mech. 2021;114:102919.
[30] WuC, FangJ, ZhouS, et al. Level‐set topology optimization for maximizing fracture resistance of brittle materials using phase‐field fracture model. Int J Numer Methods Eng. 2020;121(13):2929‐2945. · Zbl 07841950
[31] DaD, YvonnetJ. Topology optimization for maximizing the fracture resistance of periodic quasi‐brittle composites structures. Materials. 2020;13(15):3279.
[32] DaD, QianX. Fracture resistance design through biomimicry and topology optimization. Extreme Mech Lett. 2020;40:100890.
[33] DaD. Model reduction on 3D fracture resistance design. J Comput Phys. 2022;463:111274. · Zbl 07536773
[34] DaD, ChanYC, WangL, ChenW. Data‐driven and topological design of structural metamaterials for fracture resistance. Extreme Mech Lett. 2022;50:101528.
[35] JamesKA, WaismanH. Topology optimization of structures under variable loading using a damage superposition approach. Int J Numer Methods Eng. 2015;101(5):375‐406. · Zbl 1352.74243
[36] WuC, FangJ, ZhouS, et al. A path‐dependent level set topology optimization with fracture criterion. Comput Struct. 2021;249:106515.
[37] JeongSH, ParkSH, ChoiDH, YoonGH. Topology optimization considering static failure theories for ductile and brittle materials. Comput Struct. 2012;110:116‐132.
[38] LiL, ZhangG, KhandelwalK. Topology optimization of energy absorbing structures with maximum damage constraint. Int J Numer Methods Eng. 2017;112(7):737‐775. · Zbl 07867230
[39] JamesKA, WaismanH. Failure mitigation in optimal topology design using a coupled nonlinear continuum damage model. Comput Methods Appl Mech Eng. 2014;268:614‐631. · Zbl 1295.74083
[40] LiL, KhandelwalK. Design of fracture resistant energy absorbing structures using elastoplastic topology optimization. Struct Multidisc Optim. 2017;56(6):1447‐1475.
[41] HolmbergE, TorstenfeltB, KlarbringA. Stress constrained topology optimization. Struct Multidisc Optim. 2013;48(1):33‐47. · Zbl 1274.74341
[42] SigmundO. Morphology‐based black and white filters for topology optimization. Struct Multidisc Optim. 2007;33(4‐5):401‐424.
[43] LazarovBS, SigmundO. Filters in topology optimization based on Helmholtz‐type differential equations. Int J Numer Methods Eng. 2011;86(6):765‐781. · Zbl 1235.74258
[44] XuS, CaiY, ChengG. Volume preserving nonlinear density filter based on heaviside functions. Struct Multidisc Optim. 2010;41(4):495‐505. · Zbl 1274.74419
[45] AndreassenE, ClausenA, SchevenelsM, LazarovBS, SigmundO. Efficient topology optimization in MATLAB using 88 lines of code. Struct Multidisc Optim. 2011;43(1):1‐16. · Zbl 1274.74310
[46] FrancfortGA, MarigoJJ. Revisiting brittle fracture as an energy minimization problem. J Mech Phys Solids. 1998;46(8):1319‐1342. · Zbl 0966.74060
[47] BourdinB, FrancfortGA, MarigoJJ. Numerical experiments in revisited brittle fracture. J Mech Phys Solids. 2000;48(4):797‐826. · Zbl 0995.74057
[48] MieheC, WelschingerF, HofackerM. Thermodynamically consistent phase‐field models of fracture: Variational principles and multi‐field FE implementations. Int J Numer Methods Eng. 2010;83(10):1273‐1311. · Zbl 1202.74014
[49] NguyenTT, YvonnetJ, ZhuQZ, BornertM, ChateauC. A phase field method to simulate crack nucleation and propagation in strongly heterogeneous materials from direct imaging of their microstructure. Eng Fract Mech. 2015;139:18‐39.
[50] NguyenTT, YvonnetJ, ZhuQZ, BornertM, ChateauC. A phase‐field method for computational modeling of interfacial damage interacting with crack propagation in realistic microstructures obtained by microtomography. Comput Methods Appl Mech Eng. 2016;312:567‐595. · Zbl 1439.74243
[51] NatarajanS, AnnabattulaRK, Martínez‐PañedaE, et al. Phase field modelling of crack propagation in functionally graded materials. Compos Part B Eng. 2019;169:239‐248.
[52] SvanbergK. The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng. 1987;24(2):359‐373. · Zbl 0602.73091
[53] GeuzaineC, RemacleJF. Gmsh: a 3‐D finite element mesh generator with built‐in pre‐and post‐processing facilities. Int J Numer Methods Eng. 2009;79(11):1309‐1331. · Zbl 1176.74181
[54] AyachitU. The Paraview Guide: a Parallel Visualization Application. Kitware; 2015.
[55] HunterJD. Matplotlib: a 2D graphics environment. Comput Sci Eng. 2007;9(3):90‐95.
[56] ZehnderAT. Fracture Mechanics. Lecture Notes in Applied and Computational Mechanics. Springer; 2012.
[57] WegstUG, BaiH, SaizE, TomsiaAP, RitchieRO. Bioinspired structural materials. Nat Mater. 2015;14(1):23‐36.
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.