A class of methods and algorithms for the analysis of successive origination of holes in a pre-stressed viscoelastic body. Finite strains

Abstract

A class of methods and algorithms for the solution of two-dimensional quasi-static problems of stress distribution near holes is considered for finite strains. It is assumed that the holes have originated successively in a previously loaded body made of incompressible viscoelastic material. The problem is formulated on the basis of the theory of repeated superposition of large deformations. The mechanical properties of the material are described by convolution integral relations with the kernel of weak singularity. The solution is obtained using the approximate analytical methods (Signorini's technique, Laplace transform, and Muskhelishvili's technique). A special-purpose software for analytical calculations is used for the solution. Some numerical results are presented.