Definition
A combined usage of fractional-order integral operators of viscoelasticity to describe rheological properties of viscoelastic bodies, operator-continued fraction technique, and the concepts of the mechanics of delayed fracture allows one to obtain effective solutions of several problems in the fracture mechanics of polymers and composites.
Introduction
Considered are the methods of theoretical studies of deformation and delayed fracture of viscoelastic bodies caused by slow subcritical crack growth under quasi-static conditions (i.e., when inertial effects due to straining can be neglected). The highly damaged material at the tips of growing cracks is described using the modern models of cohesive zones (Kaminsky, 1998, 2014; Schapery, 1986). The analysis is simplified by using small strain theory for the linear viscoelastic continuum because many viscoelastic materials (polymers, glass-reinforced...
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Kaminsky, A.A., Selivanov, M.F., Chornoivan, Y.O. (2020). Fractional-Order Operators in Fracture Mechanics. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55771-6_79
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