Elastic instabilities caused by stress concentration

The qualitative behaviours of two linear bifurcation equations with variable coefficients, recently derived in connection with wrinkling instabilities in solid mechanics, are investigated by using WKB-type techniques. Although both problems feature turning points, we show that such occurrence might lead to essentially different asymptotic phenomena. In particular, it is shown here that turning points cannot always be used for identifying sites of high stress concentration in elastic solids