Delayered fracture of transversally isotropic viscoelastic material with a crack under a cyclic load. (Q2782083)

The authors study the long-term fracture of transversally isotropic viscoelastic body as a result of slow subcritical growth of a plane circular macrocrack of normal separation under cyclic loading. The calculations are made by using a modified \(\delta_c\)-model of fracture which is based on the concept of the prefacture domain being constant in time. The investigation is carried out within the framework of the Boltzmann-Volterra theory for resolvent bounded operators of difference type which describe transversal isotropy of the material strain. The method of operator continued fractions is used to determine the analytical form of kernel of the irrational function of linear combination of the above-mentioned integral operators. Analytical and numerical calculations are made for the resolvent bounded operators of difference type with kernel in the form of fractional exponential Rabotnov's function.