Response of beams of non-linear viscoelastic materials exhibiting strain-dependent stress relaxation

A constitutive equation for non-linear viscoelasticity is used to model the mechanical response of solid polymers such as polycarbonate. The non-linearity arises from a reduced time variable which causes stress relaxation to occur faster as strain increases. This constitutive equation has almost exclusively been used to study the response of materials subjected to homogeneous strains, and has been shown to account for the occurrence of 'yield' in homogeneous constant strain rate tests. Here, it is used in a study of the pure bending of beams. The classical assumptions of beam theory are made, i.e. plane sections remain plane so that, at each fixed time, the strains vary linearly through the depth of the beam. The interaction of this spatial variation of strain with the non-linear dependence of the reduced time on strain leads to a response which significantly differs from that determined using linear viscoelasticity theory. This interaction is explored by numerical simulation of the response of beams under conditions of curvature control and of bending moment control. The curvature and bending moment histories are: step change, constant rate, and constant rate increase and decrease to zero. The bending moment and curvature response histories, stress distributions, cross-section shape and other factors which relate to beam design are discussed. (C) 1997 Elsevier Science Ltd.