Fiber buckling in a viscoelastic matrix

Within the framework of the three-dimensional linearized theory of stability, an approach for investigating fiber buckling in the structure of unidirectional fibrous viscoelastic composites is developed. For simplicity, a small fiber concentration is considered, and the buckling problem for a single elastic fiber in an infinite viscoelastic matrix is investigated. In this case, it is assumed that the fiber has an insignificant initial periodical imperfection, and the growth of this imperfection with time is studied. The state where this imperfection starts to grow indefinitely is taken as a fiber-buckling criterion, and the critical time is determined from this criterion.