Skip to main content
Log in

Development and modeling of filled silicone architectured membranes

  • Published:
Meccanica Aims and scope Submit manuscript


The main objective of this study is to generate anisotropic membranes stretched in their plane able to endure large deformations. In this perspective, different crenellated membranes were designed with a filled silicone rubber. The aim of this work is to build a constitutive equation which describes the mechanical behavior of such architectured membranes, by means of a simple decompostion of the strain energy. Since a filled silicone is used to make the architectured membrane, some non linear effects influence also the mechanical behavior of the structure. The main phenomenon is the Mullins effect and must be taken into account in the modeling. An equivalent constitutive equation is built for the architectured membrane by taking into account the mechanical behavior of the silicone and the geometrical parameters of the crenellated membrane. Firstly, a constitutive equation is chosen to describe the core of the membrane. Second, this equation is adapted to the behavior of the crenels and thirdly a coupling term describing the interactions between the crenels and the core of the membrane is developed. The implementation of the equivalent constitutive equation into a finite element code is finally validated on experimental data.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others


  1. Ashby M (2013) Designing architectured materials. Scr Mater 68:4–7

    Article  Google Scholar 

  2. Bazant ZP, Oh BH (1986) Efficient numerical integration on the surface of a sphere. Z Angew Math Mech 66:37–49

    Article  MATH  MathSciNet  Google Scholar 

  3. Bouaziz O (2013) Geometrically induced strain hardening. Scr Mater 68:28–30

    Article  Google Scholar 

  4. Bouaziz O, Brechet Y, Embury JD (2008) Heterogeneous and architectured materials: a possible strategy for design of structural materials. Adv Eng Mater 10:24–36

    Article  Google Scholar 

  5. Brechet Y, Embury J (2013) Architectured materials: expanding materials space. Scr Mater 68:1–3

    Article  Google Scholar 

  6. Diani J, Brieu M, Gilormini P (2006) Observation and modeling of the anisotropic visco-hyperelastic behavior of a rubberlike material. Int J Solids Struct 43:3044–3056

    Article  MATH  Google Scholar 

  7. Dunlop JW, Fratzl P (2013) Multilevel architectures in natural materials. Scr Mater 68:8–12

    Article  Google Scholar 

  8. Federico S, Grillo A, Imatani S, Giaquinta G, Herzog W (2008) An energetic approach to the analysis of anisotropic hyperelastic materials. Int J Eng Sci 46:164–181

    Article  MATH  MathSciNet  Google Scholar 

  9. Göktepe S, Acharya SNS, Wong J, Kuhl E (2010) Computational modeling of passive myocardium. Int J Numer Method Biomed Eng 27:1–12

    Article  Google Scholar 

  10. Holzapfel GA (2000) Nonlinear solid mechanics—a continuum approach for engineering. Wiley, Chichester

    MATH  Google Scholar 

  11. Machado G, Chagnon G, Favier D (2010) Analysis of the isotropic models of the Mullins effect based on filled silicone rubber experimental results. Mech Mater 42:841–851

    Article  Google Scholar 

  12. Machado G, Favier D, Chagnon G (2012a) Determination of membrane stress–strain full fields of bulge tests from SDIC measurements. Theory, validation and experimental results on a silicone elastomer. Exp Mech 52:865–880

    Article  Google Scholar 

  13. Machado G, Chagnon G, Favier D (2012b) Induced anisotropy by the Mullins effect in filled silicone rubber. Mech Mater 50:70–80

    Article  Google Scholar 

  14. Meunier L (2011) Contribution la conception, l’expérimentation et la modélisation de membranes hyperélastiques architcturées anisotropes. Ph.D. thesis, Université de Grenoble

  15. Mooney M (1940) A theory of large elastic deformation. J Appl Phys 11:582–592

    Article  MATH  ADS  Google Scholar 

  16. Mullins L (1948) Effect of stretching on the properties of rubber. Rubber Chem. Technol. 21:281–300

    Article  Google Scholar 

  17. Natali AN, Carniel EL, Gregersen H (2009) Biomechanical behaviour of oesophageal tissues: material and structural configuration, experimental data and constitutive analysis. Med Eng Phys. 31:1056–1062

    Article  Google Scholar 

  18. Nerurkar NL, Mauck RL, Elliott DM (2011) Modeling interlamellar interactions in angle-ply biologic laminates for annulus fibrosus tissue engineering. Biomech Model Mechanobiol 10:973–984

    Article  Google Scholar 

  19. Rebouah M, Machado G, Chagnon G, Favier D (2013) Anisotropic Mullins stress softening of a deformed silicone holey plate. Mech Res Commun 49:36–43

    Article  Google Scholar 

  20. Reese S, Raible T, Wriggers P (2001) Finite element modelling of orthotropic material behaviour in pneumatic membranes. Int J Solids Struct 38:9525–9544

    Article  MATH  Google Scholar 

  21. Rey T, Chagnon G, Le Cam J-B, Favier D (2013) Influence of the temperature on the mechanical behavior of unfilled and filled silicone rubbers above crystallization temperature. Polym Test 32:492–501

    Article  Google Scholar 

  22. Spencer AJM (1971) Theory of invariants. Contin Phys 1:239–352

    Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to G. Chagnon.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rebouah, M., Chagnon, G. & Favier, D. Development and modeling of filled silicone architectured membranes. Meccanica 50, 11–24 (2015).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: