Hello All:
I'm interested in learning more about material instability, for example the localization criterions of Hill (1962) and Rudnicki and Rice (1975). I also am aware of work by Rice (1976), in which a perturbation is made to the displacement field in the form of a plane harmonic wave, resulting in a strong ellipticity instability condition that looks like Det(Q), where Q = c_ijkl + Sigma_jk, i.e. a competition between material softening and stress increase determines the instability. Furthermore, this stability criterion is developed assuming an infinite body.
My question is - are there relevant instability analyses done for surfaces (say surface wrinkling, buckling, etc), in which a non-infinite medium is assumed in developing the stability criterion? If so, could anyone suggest references in the literature?
Re: Material Instability - Questions
Not sure if I understand your question correctly. If I do, this paper cites some papers.
T. Li, Z.Y. Huang, Z.C. Xi, S.P. Lacour, S. Wagner, Z. Suo. "
Delocalizing strain in a thin metal film on a polymer substrate".
Mechanics of Materials.
37,261-273,(2005)
Re: Material Instability - Questions
This paper uses eigenvalue to assess stability of a hypo-elasticity boundary value problem.
Bardet, J. P., 1990, "Finite Element Analysis of Surface Instability in Hypo-Elastic Solids," Computer Methods in Applied Mechanics and Engineering, Vol. 78, pp. 273 - 296