Objective
The key topic of the proposal is the mathematical reformulation of the fracture criteria for brittle elastic bodies. This reformulation is based on both, the detailed description of the behaviour of the stress-strain state near the crack front and the asymptotic analysis of the elasticity problem for the perturbed crack. The first item will be investigated by two approaches: the analysis of differential equations in 3D domains and the analysis of pseudodifferential equations on 2D surfaces which complement each other. The asymptotic analysis will be performed together with the justification of the asymptotic formulae using the modern technique of weighted spaces with detached asymptotics. Moreover, the asymptotic results will be interpreted in the framework of self-adjoint extensions of the Lame operator which helps to compare different fracture criteria and to solve particular problems on the propagation of cracks. 9The formulation of the fracture criteria as variational inequalities on the crack front answers plenty of questions which stand open in the theory of cracks in 3D elastic bodies, i.e. the shape of the growing crack is described by their solutions, the stable propagation of the crack is strictly dependent on the uniqueness of the solution, etc. The variational inequalities obtained from different fracture criteria involve the SAME pseudodifferential operator M on the crack front. The precise description of M by means of the geometric characteristics of the surfaces and the front of the crack and the study of its properties are the crucial point of the project. For cracks with possible contact of the crack surfaces the sensitivity of the contact zone with respect to variations of the exterior forces and to variations of the crack front will be investigated. Using the methods of asymptotic analysis already mentioned this sensitivity will be described with the help of a pseudodifferential operator on the boundary of the contact zone SIMILAR to M.
Topic(s)
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70569 Stuttgart
Germany