Mathematical modelling of the incremental fields in a pre-stressed elastic composite in plane and antiplane states is done using complex variable theory. We formulate and solve the crack problem in all three classical modes by using complex potentials. Following Guz, and using the theory of Riemann-Hilbert problem, Cauchy's integral, Plemelj's functions we obtain the asymptotic behavior of the incremental fields in the vicinity of the crack tip. We obtain the critical values of the incremental stresses which produce crack propagation.
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Craciun, E.M. (2009). Initial Deformations On Behaviour Of Elastic Composites. In: de Borst, R., Sadowski, T. (eds) Lecture Notes on Composite Materials. Solid Mechanics And Its Applications, vol 154. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8772-1_6
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DOI: https://doi.org/10.1007/978-1-4020-8772-1_6
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