Dynamics of a Soft Contractile Body on a Hard Support

  • A. Tatone
  • A. Di Egidio
  • A. Contento
Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 58)


The motion of a soft and contractile body on a hard support is described by fields of short range contact forces. Besides repulsion these forces are able to describe also viscous friction, damping and adhesion allowing the body to have complex motions which look rather realistic. The contractility is used to make the body behave like a living body with some basic locomotion capabilities. The simulated motions, showing jumping or crawling, are driven either by a contraction or by a contractile couple. Although only homogeneous deformations are allowed, the model arises from a general theory of remodeling in finite elasticity. The body is made of a viscoelastic incompressible neo-Hookean material.


Contact Force Rigid Support Dissipation Inequality Reference Shape Contact Traction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Argento, C., Jagota, A., Carter, W.C.: Surface formulation for molecular interactions of macroscopic bodies. J. Mech. Phys. Solids 45, 1161–1183 (1997)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Contento, A., Di Egidio, A., Dziedzic, J., Tatone, A.: Modeling the contact of stiff and soft bodies with a rigid support by short range force fields. TASK Quarterly 13, 1001–1027 (2009)Google Scholar
  3. 3.
    Di Carlo, A., Quiligotti, S.: Growth and balance. Mech. Res. Comm. 29, 449–456 (2002)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Gao, J., Luedtke, W.D., Gourdon, D., Ruths, M., Israelachvili, J.N., Landman, U.: Frictional forces and Amontons’ law: From the molecular to the macroscopic scale. J. Phys. Chem. B 108, 3410–3425 (2004), doi:10.1021/jp036362l.CrossRefGoogle Scholar
  5. 5.
    Germain, P.: The method of virtual power in continuum mechanics. Part 2: Microstructure. SIAM J. Appl. Math. 25, 556–575 (1973)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Greenwood, J.A.: Adhesion of elastic spheres. Proc. R. Soc. Lond. A 453, 1277–1297 (1997), doi:10.1098/rspa.1997.0070zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Gurtin, M.E.: A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations. J. Mech. Phys. Solids 50, 5–32 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Johnson, K.L., Kendall, K., Roberts, A.D.: Surface energy and the contact of elastic solids. Proc. R. Soc. Lond. A 324, 301–313 (1971), CrossRefGoogle Scholar
  9. 9.
    Mogilner, A.: Mathematics of cell motility: Have we got its number? J. Math. Biol. 58, 105–134 (2009)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Muller, V.M., Yushchenko, S.V., Derjaguin, B.V.: On the influence of molecular forces on the deformation of an elastic sphere and its sticking to a rigid plane. J. Colloid Interface Sci. 77, 91–101 (1980), doi:10.1016/0021-9797(80)90419-1CrossRefGoogle Scholar
  11. 11.
    Nardinocchi, P., Teresi, L.: On the active response of soft living tissues. J. Elasticity 88, 27–39 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Sauer, R.A., Li, S.: A contact mechanics model for quasi-continua. Int. J. Numer. Meth. Engng. 71, 931–962 (2007)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Sauer, R.A., Wriggers, P.: Formulation and analysis of a three-dimensional finite element implementation for adhesive contact at the nanoscale. Comp. Meth. Appl. Mech. Engng. 198, 3871–3883 (2009)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Spolenak, R., Gorb, S., Gao, H., Arzt, E.: Effects of contact shape on the scaling of biological attachments. Proc. R. Soc. Lond. A 461, 305–319 (2005)CrossRefGoogle Scholar
  15. 15.
    Wriggers, P.: Computational Contact Mechanics. John Wiley & Sons, Chichester (2006)zbMATHCrossRefGoogle Scholar
  16. 16.
    Yu, N., Polycarpou, A.A.: Adhesive contact based on the Lennard–Jones potential: A correction to the value of the equilibrium distance as used in the potential. J. Colloid Interface Sci. 278, 428–435 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • A. Tatone
    • 1
  • A. Di Egidio
    • 1
  • A. Contento
    • 1
  1. 1.Department of Structural, Hydraulic and Geotechnical EngineeringUniversity of L’AquilaL’AquilaItaly

Personalised recommendations