Skip to main content
SpringerLink
Log in

Viscoelastic material design with negative stiffness components using topology optimization

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

An application of topology optimization to design viscoelastic composite materials with elastic moduli that soften with frequency is presented. The material is a two-phase composite whose first constituent is isotropic and viscoelastic while the other is an orthotropic material with negative stiffness but stable. A concept for this material based on a lumped parameter model is used. The performance of the topology optimization approach in this context is illustrated using three examples.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alabuzhev PM, Gritchin AA, Stepanov PT, Khon VF (1977) Some results of an investigation of a vibration protection system with stiffness correction. J Min Sci 13:338–341

    Google Scholar 

  • Alabuzhev PM, Grytchin AA, Kim LI, Migirenko GS, Khon VF, Stepanov PT (1989) Vibration protecting and measuring systems with quasi-zero stiffness. Taylor & Francis, New York

    Google Scholar 

  • Bruns TE, Tortorelli DA (2001) Topology optimization of nonlinear elastic structures and compliant mechanisms. Comput Method Appl Math 190:3443–3459

    MATH  Google Scholar 

  • Diaz AR, Benard A (2003) Designing materials with prescribed elastic properties using polygonal cells. Int J Numer Methods Eng 57:301–314

    Article  MATH  MathSciNet  Google Scholar 

  • Drugan WJ (2007) Elastic composite materials having a negative-stiffness phase can be stable. Phys Rev Lett 98:Article 055502

    Article  Google Scholar 

  • Falnes J (1995) On non-causal impulse response functions related to propagating water waves. Appl Ocean Res 17:379–389

    Article  Google Scholar 

  • Guest J, Prevost J, Belytschko T (2004) Achieving minimum length scale in topology optimization using nodal design variables and projection functions. Int J Numer Methods Eng 61:238–254

    Article  MATH  MathSciNet  Google Scholar 

  • Hsu YL, Hsu MS, Chen CT (2001) Interpreting results from topology optimization using density contours. Comput Struct 79:1049–1058

    Article  Google Scholar 

  • Jaglinski T, Kochmann D, Stone D, Lakes RS (2007) Composite materials with viscoelastic stiffness greater than diamond. Science 315:620–622

    Article  Google Scholar 

  • Lakes RS (1999) Viscoelastic solids. CRC, Boca Raton

    Google Scholar 

  • Lakes RS, Drugan WJ (2002) Dramatically stiffer elastic composite materials due to a negative stiffness phase? J Mech Phys Solids 50:979–1009

    Article  MATH  Google Scholar 

  • Lakes RS, Lee T, Bersie A, Wang YC (2001) Extreme damping in composite materials with negative stiffness inclusions. Nature 1410:565–567

    Article  Google Scholar 

  • Lee C-M, Goverdovskiy VN, Temnikov AI (2007) Design of springs with negative stiffness to improve vehicle driver vibration isolation. J Sound Vib 302:865–874

    Article  Google Scholar 

  • Lin C-Y, Chao L-S (2000) Automated image interpretation for integrated topology and shape optimization. Struct Multidisc Optim 20:125–137

    Article  Google Scholar 

  • Makris N, Inaudi JA, Kelly JM (1996) Macroscopic models with complex coefficients and causality. J Eng Mech 122:566–573

    Article  Google Scholar 

  • Platus DL (1991) Negative-stiffness-mechanism vibration isolation systems. Proc SPIE 1619:44–54

    Article  Google Scholar 

  • Prasad J (2007) Design of materials with special dynamic properties using negative stiffness components. PhD dissertation, Michigan State University

  • Prasad J, Diaz AR (2006) Synthesis of bistable periodic structures using topology optimization and a genetic algorithm. J Mech Des 128:1298–1306

    Article  Google Scholar 

  • Prasad J, Diaz AR (2007a) Conceptual design of materials exhibiting frequency-induced softening. ASME Proceedings of DETC2007, Paper DETC2007-34299

  • Prasad J, Diaz AR (2007b) Material design for frequency-induced softening using topology optimization. Proceedings of WCSMO-7, Seoul, 21–25 May 2007

  • Pritz T (1998) Frequency dependences of complex moduli and complex poisson’s ratio of real solid materials. J Sound Vib 214:83–104

    Article  Google Scholar 

  • Pritz T (1999) Verification of local Kramers Kronig relations for complex modulus by means of fractional derivative model. J Sound Vib 228:1145–1165

    Article  Google Scholar 

  • Sharnoff M (1964) Validity conditions for the Kramers-Kronig relations. Am J Phys 32:40–44

    Article  MathSciNet  Google Scholar 

  • Sigmund O (1994) Materials with prescribed constitutive parameters: an inverse homogenization problem. Int J Solids Struct 31:2313–2339

    Article  MATH  MathSciNet  Google Scholar 

  • Sigmund O (1995) Tailoring materials with prescribed elastic properties. Mech Mater 20:351–368

    Article  Google Scholar 

  • Sigmund O (2000) A new class of extremal composites. J Mech Phys Solids 48:397–428

    Article  MATH  MathSciNet  Google Scholar 

  • Sigmund O (2007) Morphology-based black and white filters for topology optimization. Struct Multidisc Optim 33:401–424

    Article  Google Scholar 

  • Svanberg K (1987) The method of moving asymptotes. Int J Numer Methods Eng 24:359–373

    Article  MATH  MathSciNet  Google Scholar 

  • Tai K, Prasad J (2007) Target-matching test problem for multiobjective topology optimization using genetic algorithms. Struct Multidisc Optim 34:333–345

    Article  Google Scholar 

  • Wang YC, Lakes RS (2004a) Extreme stiffness systems due to negative stiffness elements. Am J Phys 72:40–50

    Article  Google Scholar 

  • Wang YC, Lakes RS (2004b) Negative stiffness induced extreme viscoelastic mechanical properties: stability and dynamics. Philos Mag 35:3785–3801

    Article  Google Scholar 

  • Yi Y-M, Park S-H, Youn S-K (2000) Design of microstructures of viscoelastic composites for optimal damping characteristics. Int J Solids Struct 37:4791–4810

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Michigan State University, East Lansing, MI, 48824, USA

    J. Prasad & A. R. Diaz

Authors
  1. J. Prasad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. R. Diaz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. Prasad.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Prasad, J., Diaz, A.R. Viscoelastic material design with negative stiffness components using topology optimization. Struct Multidisc Optim 38, 583–597 (2009). https://doi.org/10.1007/s00158-008-0308-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-008-0308-6

Keywords

Search

Navigation