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Mathematical modelling of fracture in adhesive joints


Composite elastic materials are widely used in modem technology, especially in aircraft industry and civil engineering. Such materials exhibit variety of physical/chemical features and have special mechanical properties. Defects appearing during manufactur ing processes and exploitation reduce the strength of the composites and can even lead to a catastrophic failure. There are many investigations concerning the interaction between defects with bi-material interfaces in composites working under different loa ding conditions. However, most of them have been based on the classical transmission conditions (or ideal contact), which are not able to take into account fields of high gradients within the bonding region at the interface. In the proposed project we are planning to develop mathematical models for the so-called imperfect transmission conditions between the different materials. Recently, new results in this direction have been independently obtained by the Partner leader, Prof. G. Mishuris, and the proposer , Prof. A.B. Movchan. The results showed that, in some specific cases, behaviour of composite with defects depends strongly on properties of the interface. The plan of our work includes analysis of Wiener-Hopf problems associated with 3-D cracks on the int erfaces appearing in modellin of the crack propagation. And finally we will analyse various spectral problems for periodic composites with perfect and imperfect material bonding where each cell contains a crack. Such problems are important for the non-dest ructive control and for the analysis of stop bands for waves of acoustic frequencies within composite structures. All corresponding boundary value problems in combined domains with non-classical transmission conditions will be solved by reduction to bounda ry integral equations, together with the factorisation technique and asymptotic methods. The analytical and numerical solutions will provide new and very important tools

Call for proposal

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Funding Scheme

TOK - Marie Curie actions-Transfer of Knowledge


Senate House, Abercromby Square
United Kingdom

Participants (1)

Wincentego Pola 2