Summary
A constitutive equation for nonlinear viscoelasticity is used to model the mechanical response of solid polymers such as polycarbonate. The nonlinearity arises from a reduced time variable which causes stress relaxation to occur faster as strain increases. This constitutive equation is used to study the consequences of the interaction of the acceleration of stress relaxation with strain and the spatial variation of strain within the context of the structural theory of beams undergoing small displacements.
Two examples are presented — a cantilever beam under a concentrated force at the tip and a simply supported beam with an off center concentrated force. The regions with the greatest bending moments are also the regions of asccelerated stress relaxation. It is shown that there is a time after the transverse loads are applied when the stresses at the outer material elements in these cross sections decrease to such an extent that the location of the maximum stress begins to move to the interior of the cross section. In addition, the curvature begins to increase rapidly. The effect is analogous to that which occurs during the development of a plastic hinge in the context of elastic-perfectly plastic materials. These events can be interpreted as the onset and growth of a “viscoelastic hinge”.
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Wineman, A., Min, J.H. Viscoelastic hinge formation in beams. Acta Mechanica 140, 183–205 (2000). https://doi.org/10.1007/BF01182510
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DOI: https://doi.org/10.1007/BF01182510