Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Structural and Multidisciplinary Optimization
Published in: Structural and Multidisciplinary Optimization 6/2019

13-12-2018 | Research Paper

Distortion energy-based topology optimization design of hyperelastic materials

Published in: Structural and Multidisciplinary Optimization | Issue 6/2019

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Highly stretchable material is widely used in the engineering field ranging from soft robots to stretchable electronics. Some highly stretchable 3D-architected mechanical metamaterials have been developed recently. However, failure of material is still the most critical design constraint when stretchability of the structure is considered, and existing topology optimization methods based on, e.g., von Mises stress failure criterion, are not accurate when applied to design hyperelastic materials under large deformation. To address this issue, this paper presents a topology optimization method based on distortion energy for designing nonlinear hyperelastic material against failure. For this purpose, a new objective function based on distortion energy for hyperelastic materials is proposed in the p-norm form. The adjoint method is applied to obtain the sensitivities, and the corresponding optimization problem is solved by the method of moving asymptotes. Excessive mesh distortion in low-density area is addressed through an interpolation scheme of the strain energy known as the fictitious domain method. Four numerical design examples are presented to demonstrate the validity and effectiveness of the proposed algorithm in significantly reducing local distortion energy concentration. One of these examples involves design of highly stretchable metamaterial where the optimized design is shown to sustain three times the finite strain of its base material under uniaxial tension without failure. Therefore, the proposed method has great potential in designing extremely stretchable materials such as stretchable electronics in the future.
previous article Configuration optimization for thin structures using level set method
next article Distributed-parametric optimization approach for free-orientation of laminated shell structures with anisotropic materials

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now
Literature
Alexandersen J, Sigmund O, Meyer KE, Lazarov BS (2018) Design of passive coolers for light-emitting diode lamps using topology optimisation. Int J Heat Mass Transf 122:138–149CrossRef
Amir O (2017) Stress-constrained continuum topology optimization: a new approach based on elasto-plasticity. Struct Multidiscip Optim 55(5):1797–1818
Andreassen E, Clausen A, Schevenels M, Lazarov BS, Sigmund O (2010) Efficient topology optimization in MATLAB using 88 lines of code. Struct Multidiscip Optim 43:1–16CrossRefMATH
Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69:635–654CrossRefMATH
Bruggi M (2008) On an alternative approach to stress constraints relaxation in topology optimization. Struct Multidiscip Optim 36:125–141MathSciNetCrossRefMATH
Bruns T, Tortorelli D (1998) Topology optimization of geometrically nonlinear structures and compliant mechanisms. In: 7th AIAA/USAF/NASA/ISSMO symposium on multidisciplinary analysis and optimization, multidisciplinary analysis optimization conferences. https://​doi.​org/​10.​2514/​6.​1998-4950
Bruns TE, Tortorelli DA (2001) Topology optimization of non-linear elastic structures and compliant mechanisms. Comput Methods Appl Mech Eng 190:3443–3459CrossRefMATH
Buhl T, Pedersen CB, Sigmund O (2000) Stiffness design of geometrically nonlinear structures using topology optimization. Struct Multidiscip Optim 19:93–104CrossRef
Chen F, Wang Y, Wang MY, Zhang Y (2017) Topology optimization of hyperelastic structures using a level set method. J Comput Phys 351:437–454MathSciNetCrossRef
Chen F, Xu W, Zhang H, Wang Y, Cao J, Wang MY et al (2018) Topology optimized design, fabrication, and characterization of a soft cable-driven gripper. IEEE Robot Autom Lett 3:2463–2470CrossRef
Cheng G-D, Cai Y-W, Liang X (2013) Novel implementation of homogenization method to predict effective properties of periodic materials. Acta Mech Sinica 29:550–556MathSciNetCrossRefMATH
Cheng L, Liu J, Liang X, To AC (2018a) Coupling lattice structure topology optimization with design-dependent feature evolution for additive manufactured heat conduction design. Comput Methods Appl Mech Eng 332:408–439MathSciNetCrossRef
Cheng L, Liang X, Belski E, Wang X, Sietins JM, Ludwick S et al (2018b) Natural frequency optimization of variable-density additive manufactured lattice structure: theory and experimental validation. J Manuf Sci Eng 140:105002CrossRef
Cheng L, Bai J, To AC (2019) Functionally graded lattice structure topology optimization for the design of additive manufactured components with stress constraints. Comput Methods Appl Mech Eng 344:334–359MathSciNetCrossRef
Cho S, Jung H-S (2003) Design sensitivity analysis and topology optimization of displacement–loaded non-linear structures. Comput Methods Appl Mech Eng 192:2539–2553CrossRefMATH
Dede EM, Joshi SN, Zhou F (2015) Topology optimization, additive layer manufacturing, and experimental testing of an air-cooled heat sink. J Mech Des 137:111403CrossRef
Duysinx P, Bendsøe MP (1998) Topology optimization of continuum structures with local stress constraints. Int J Numer Methods Eng 43:1453–1478MathSciNetCrossRefMATH
Fan Z, Zhang Y, Ma Q, Zhang F, Fu H, Hwang K-C et al (2016) A finite deformation model of planar serpentine interconnects for stretchable electronics. Int J Solids Struct 91:46–54CrossRef
Gao H, Klein P (1998) Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds. J Mech Phys Solids 46:187–218CrossRefMATH
Gaynor AT (2015) Topology optimization algorithms for additive manufacturing. Dissertation, Johns Hopkins University
Gray D, Tien J, Chen CJAM (2004) High-conductivity elastomeric electronics. Adv Mater 16:393 477–477, 2004CrossRef
Guest JK, Prévost JH, Belytschko T (2004) Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int J Numer Methods Eng 61:238–254MathSciNetCrossRefMATH
Hiller J, Lipson H (2012) Automatic design and manufacture of soft robots. IEEE Trans Robot 28:457–466CrossRef
James KA, Waisman H (2014) Failure mitigation in optimal topology design using a coupled nonlinear continuum damage model. Comput Methods Appl Mech Eng 268:614–631MathSciNetCrossRefMATH
Ji B, Gao H (2004) A study of fracture mechanisms in biological nano-composites via the virtual internal bond model. Mater Sci Eng A 366:96–103CrossRef
Jiang Y, Wang Q (2016) Highly-stretchable 3D-architected mechanical metamaterials. Sci Rep 6:34147CrossRef
Jones RM (2009) Deformation theory of plasticity. Bull Ridge Publishing, Blacksburgh
Kang Z, Tong L (2008) Topology optimization-based distribution design of actuation voltage in static shape control of plates. Comput Struct 86:1885–1893CrossRef
Khdir Y, Kanit T, Zaïri F, Nait-Abdelaziz M (2013) Computational homogenization of elastic–plastic composites. Int J Solids Struct 50:2829–2835CrossRef
Kim DH, Song J, Choi WM, Kim HS, Kim RH, Liu Z et al (2008) Materials and noncoplanar mesh designs for integrated circuits with linear elastic responses to extreme mechanical deformations. Proc Natl Acad Sci U S A 105(48):18675–18680
Kim JE, Kim DS, Ma PS, Kim YY (2010) Multi-physics interpolation for the topology optimization of piezoelectric systems. Comput Methods Appl Mech Eng 199:3153–3168MathSciNetCrossRefMATH
Kim DH, Lu N, Ma R, Kim YS, Kim RH, Wang S et al (2011) Epidermal electronics. Science 333(6044):838–843
Kiyono C, Vatanabe S, Silva E, Reddy J (2016) A new multi-p-norm formulation approach for stress-based topology optimization design. Compos Struct 156:10–19CrossRef
Klarbring A, Strömberg N (2013) Topology optimization of hyperelastic bodies including non-zero prescribed displacements. Struct Multidiscip Optim 47:37–48MathSciNetCrossRefMATH
Kögl M, Silva EC (2005) Topology optimization of smart structures: design of piezoelectric plate and shell actuators. Smart Mater Struct 14:387CrossRef
Li L (2018) Topology optimization of structures with microstructural and elastoplastic-damage effects. Dissertation, University Of Notre Dame
Li L, Khandelwal K (2017) Design of fracture resistant energy absorbing structures using elastoplastic topology optimization. Struct Multidiscip Optim 56:1447–1475MathSciNetCrossRef
Liu B, Guo D, Jiang C, Li G, Huang X (2019) Stress optimization of smooth continuum structures based on the distortion strain energy density. Comput Methods Appl Mech Eng 343:276–296
Luo Y, Kang Z (2012) Topology optimization of continuum structures with Drucker–Prager yield stress constraints. Comput Struct 90:65–75CrossRef
Luo Y, Wang MY, Kang Z (2015) Topology optimization of geometrically nonlinear structures based on an additive hyperelasticity technique. Comput Methods Appl Mech Eng 286:422–441MathSciNetCrossRefMATH
Luo Y, Li M, Kang Z (2016) Topology optimization of hyperelastic structures with frictionless contact supports. Int J Solids Struct 81:373–382CrossRef
Maute K, Tkachuk A, Wu J, Qi HJ, Ding Z, Dunn ML (2015) Level set topology optimization of printed active composites. J Mech Des 137:111402CrossRef
Pedersen CB, Buhl T, Sigmund O (2001) Topology synthesis of large-displacement compliant mechanisms. Int J Numer Methods Eng 50:2683–2705CrossRefMATH
Picelli R, Townsend S, Brampton C, Norato J, Kim H (2018) Stress-based shape and topology optimization with the level set method. Comput Methods Appl Mech Eng 329:1–23MathSciNetCrossRef
Rittel D, Wang Z, Merzer M (2006) Adiabatic shear failure and dynamic stored energy of cold work. Phys Rev Lett 96:075502CrossRef
Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidiscip Optim 33:401–424CrossRef
Trapper P, Volokh K (2010a) Elasticity with energy limiters for modeling dynamic failure propagation. Int J Solids Struct 47:3389–3396CrossRefMATH
Volokh K (2007a) Softening hyperelasticity for modeling material failure: analysis of cavitation in hydrostatic tension. Int J Solids Struct 44:5043–5055CrossRefMATH
Volokh K (2010) Comparison of biomechanical failure criteria for abdominal aortic aneurysm. J Biomech 43:2032–2034CrossRef
Volokh KY (2011) Modeling failure of soft anisotropic materials with application to arteries. J Mech Behav Biomed Mater 4:1582–1594CrossRef
Volokh K, Gao H (2005) On the modified virtual internal bond method. J Appl Mech 72:969–971CrossRefMATH
Volokh K, Ramesh K (2006) An approach to multi-body interactions in a continuum-atomistic context: application to analysis of tension instability in carbon nanotubes. Int J Solids Struct 43:7609–7627CrossRefMATH
Volokh KY, Trapper P (2008) Fracture toughness from the standpoint of softening hyperelasticity. J Mech Phys Solids 56(7):2459–2472
Wallin M, Ivarsson N, Tortorelli D (2018) Stiffness optimization of non-linear elastic structures. Comput Methods Appl Mech Eng 330:292–307MathSciNetCrossRef
Wang F, Lazarov BS, Sigmund O, Jensen JS (2014) Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems. Comput Methods Appl Mech Eng 276:453–472MathSciNetCrossRefMATH
Widlund T, Yang S, Hsu Y-Y, Lu N (2014) Stretchability and compliance of freestanding serpentine-shaped ribbons. Int J Solids Struct 51:4026–4037CrossRef
Yoon GH, Kim YY (2007) Topology optimization of material-nonlinear continuum structures by the element connectivity parameterization. Int J Numer Methods Eng 69:2196–2218MathSciNetCrossRefMATH
Zhang Y, Fu H, Su Y, Xu S, Cheng H, Fan JA et al (2013) Mechanics of ultra-stretchable self-similar serpentine interconnects. Acta Mater 61:7816–7827CrossRef
Zhang Y, Fu H, Xu S, Fan JA, Hwang K-C, Jiang J et al (2014) A hierarchical computational model for stretchable interconnects with fractal-inspired designs. J Mech Phys Solids 72:115–130CrossRef
Metadata
Title
Distortion energy-based topology optimization design of hyperelastic materials
Publication date
13-12-2018
Published in
Structural and Multidisciplinary Optimization / Issue 6/2019
Print ISSN: 1615-147X
Electronic ISSN: 1615-1488
DOI
https://doi.org/10.1007/s00158-018-2161-6

Other articles of this Issue 6/2019

Structural and Multidisciplinary Optimization 6/2019 Go to the issue

Research Paper

Incremental shifting vector and mixed uncertainty analysis method for reliability-based design optimization

Research Paper

Distributed-parametric optimization approach for free-orientation of laminated shell structures with anisotropic materials

Research Paper

Tension/compression anisotropy enhanced topology design

Research Paper

A multi-objective optimization framework for robust axial compressor airfoil design

Research Paper

Targeting the force-displacement response of thin-walled structures subjected to crushing load using curve decomposition and topometry optimization

Research Paper

A simplified model for structural stiffness and crashworthiness optimisation of composite fuselages

Premium Partners

    Image Credits