On the basic theorems in linear elastostatics for bodies containing edge cracks
The paper deals with an extension of the basic theorems of linear elastostatics for bodies containing edge cracks. In previous papers in this direction [e.g. \textit{K. B. Howell}, J. Elasticity 10, 407-427 (1980; Zbl 0459.73005)] it is proved that in order for work and energy theorem to hold [\textit{M. E. Gurtin} in Encyclopedia of physics, Vol. VIa/2, S. Flügge (ed.) (1972; Zbl 0277.73001); pp. 1-294], it is sufficient that the elastic tensor \({\mathcal C}\) is positive definite and the displacement field \({\mathfrak u}\) is bounded. As a consequence, uniqueness and Betti's theorem still hold under the same assumptions. The present paper extends the above mentioned results to the case in which \({\mathfrak u}\) can grow at the crack edge and \({\mathcal C}\) is not necessarily positive definite.
scientific article; zbMATH DE number 3882015