Chornoivan Y. Two-dimensional mixed problems of linear theory of viscoelasticity and fracture mechanics of orthotropic bodies

Basing on operator continued fractions method the effective approximate solutions of the following problems are found: 1) the problem of stress distribution in an viscoelastic orthotropic half-plane under concentrated normal to its boundary loading; 2) the problem of the pressure found under the flat-bottom punch that pressed with friction on viscoelastic orthotropic half-plane; 3) the problem of determination of contact sizes and pressure under the axis of the rigid cylinder that rolling with friction over viscoelastic orthotropic half-space. It is assumed that considered viscoelastic operators are resolvent. All possible viscoelastic properties are taking into account. The calculations for the modeling materials show the high precision of the used approximations. On the basis of the Leonov-Panasyuk-Dugdale crack model the solution of the problem of elastic orthotropic body cleavage by the rigid wedge of constant width. COD criterion is used as crack growth criterion. Using this solution the statementof the problem of viscoelastic orthotropic body cleavage by the rigid growing wedge is studied. The governing equations of the latter problem were obtained for the both of the main assumptions that generalized Dugdale model on viscoelastic bodies: 1) the assumption of constant stresses in process zone; 2) the assumption of constant length of process zone. Basing on operator continued fractions method and homogenization of viscoelastic properties the calculations for orthotropic viscoelastic binder/elastic fibers composites that modeled as homogeneous orthotropic media with effective mechanical properties were made. The results of calculations show qualitative and quantitative sides of such composites behavior under wedging as well as a high precision of method that were used to solve complex integral equations.