Time-dependent model for unidirectional composite with a viscoelastic matrix

•Operator form of creep compliance and relaxation modulus.•Construction of constitutive equations.•Time-dependent properties of unidirectional composite.•Relations of algebra of resolvent operators. Modelling of time-dependent properties of unidirectional fiber reinforced plastics on the basis of structural mechanics of composite materials and mechanics of hereditary media has been proposed in this research. The constitutive equations of unidirectional fiber reinforced plastics have been obtained using the Volterra correspondence principle and the algebraic properties of resolvent operators. Modelling of viscoelastic properties of a unidirectional composite material on the basis of EDT-10 epoxy resin has been shown.