International Journal of Pure and Applied Mathematics Volume 81 No. 4 2012, 635-646 ISSN: 1311-8080 (printed version) url: http://www.ijpam.eu P A ijpam.eu GENERALIZED MODEL OF VISCOELASTIC DEFORMATION A. Aleksandrov 1 § , S. Lekova 2 , M. Milenova 3 1,2,3 Department of Applied Mechanics University of Chemical Technology and Metallurgy 8, Climent Ohridsky Blvd., Soﬁa 1756, BULGARIA Abstract: In this paper we consider generalized mathematical model describ- ing the process of viscoelastic deformation of polymer materials. It describes the polyethylene creep under diﬀusion of liquid environment not interacting chemi- cally with the polymer. We analyse here some results of certain tests produced with samples which have reached beforehand diﬀerent levels of saturation with cyclohexan and have been afterwards put under mechanical testing of a short creep in pure torsion and uniform loading. Analyzing the results we use the method of orthogonal expansions and at the same time extend it for a process with integrating properties (without self-settling). In this case it is necessary to separate the integral component, which is presented as signal-dependent. 1. Introduction In this paper we investigate a generalized model describing the process of viscoelastic deformation of polymer materials which are used in technologies, medicine, aviation, civil engineering, etc. We describe the polyethylene creep under diﬀusion of liquid environment not interacting chemically with the poly- mer. The orthogonal functions can be used for approximation of characteristics obtained in analytical or experimental way. It is convenient because it is not necessary to re-calculate already determined coeﬃcients in the expansion. This Received: September 12, 2012 c  2012 Academic Publications, Ltd. url: www.acadpubl.eu § Correspondence author