Large deformations of nonlinear viscoelastic and multi-responsive beams |
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Institution: | 1. Department of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow 119991, Russian Federation;2. Faculty of Mathematics, Mechanics and Computer Science, Southern Federal University, Rostov-on-Don 344090, Russian Federation;3. Department of Applied Mathematics and Cybernetics, Tver State University, Tver 170100 Russian Federation |
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Abstract: | This study presents analyses of deformations in nonlinear viscoelastic beams that experience large displacements and rotations due to mechanical, thermal, and electrical stimuli. The studied beams are relatively thin so that the effect of the transverse shear deformation is neglected, and the stretch along the transverse axis of the beams is also ignored. It is assumed that the plane that is perpendicular to the longitudinal axis of the undeformed beam remains plane during the deformations. The nonlinear kinematics of the finite strain beam theory presented by Reissner 27] is adopted, and a nonlinear viscoelastic constitutive relation based on a quasi-linear viscoelastic (QLV) model is considered for the beams. Deformation in beams due to mechanical, thermal, and electric field inputs are incorporated through the use of time integral functions, by separating the time-dependent function and nonlinear measures of field variables. The nonlinear measures are formulated by including higher order terms of the field variables, i.e. strain, temperature, and electric field. Responses of beams under mechanical, thermal, and electrical stimuli are illustrated and the effects of nonlinear constitutive relations on the overall deformations of the beams are highlighted. |
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Keywords: | Nonlinear viscoelastic Large deformations Multi-responsive materials Electro-active response Polymers |
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