Numerical Analysis of Two Non-linear Soft Thin Layers
In a first part, we consider a bar with extremities subject to a given displacement and made by two elastic bodies with linear stress-strain relation separated by an adhesive layer of thickness h. The material of the adhesive is characterized by a non convex (piecewise quadratic) strain energy density with elastic modulus k. After considering the equilibrium problem of the bar and determining the stable and metastable solutions, we let (h,k) tending to zero and we obtain the corresponding asymptotic contact laws, linking the stress to the jump of the displacement at the adhesive interface. The second part of the paper is devoted to the bi-dimensional problem of two elastic bodies separated by a thin soft adhesive. The behaviour of the adhesive is non associated elastic-plastic. As in the first part, we study the asymptotic contact laws.
Unable to display preview. Download preview PDF.
- 3.Lebon, F., Rizzoni, R.: Aymptotic analysis of soft thin layers with nonconvex energy. In: Proc. 16th AIMETA Italian Congress, Ferrara (2003)Google Scholar
- 7.Aberayatne, R., Bhattacharya, K., Knowles, J.K.: Strain-energy functions with multiple local minima: Modeling phase transformations using finite thermoelasticity. In: Fu, Y.B., Ogden, R.W. (eds.) Nonlinear Elasticity: Theory and Applications. London Mathemathical Society Lecture Notes Series, vol. 283, pp. 433–490. Cambridge University Press, Cambridge (2001)CrossRefGoogle Scholar
- 8.Lebon, F., Ronel-Idrissi, S.: Asymptotic analysis of Mohr-Coulomb and Drucker-Prager soft thin layers. Steel Comp. Struct.: Int. J. 4, 133–148 (2004)Google Scholar
- 9.Aberayatne, R., Chu, C., James, R.D.: Kinetics of materials with wiggly energies: Theory and application to the evolution of twinning microstructures in a Cu-Al-Ni shape memory alloy. Phil. Mag. A73, 457–497 (1996)Google Scholar
- 11.Sagan, H.: An introduction to the calculus of variations. Dover, New York (1992)Google Scholar