On Viscoelasticity in the Theory of Geometrically Linear Plates
Résumé
A phenomenological theory for viscoelastic plates is developed in a geometrically linear framework whereby present work is based on the direct approach for homogeneous plates. We confine our research to isotropic viscoelastic materials, assume stiffness laws by means of rheology, and generalize them in order to describe the behavior of shear-deformable thin-walled structures. The restriction to isotropy enables to utilize eigenspace projectors since stiffness tensors are coaxial in this special case. It is thus possible to formulate the system of tensor-valued differential equations in orthogonal subspaces and to simplify the calculation rules like those for scalar-valued expressions. The resulting behavior is illustrated exemplary by means of uniaxial tests. We furthermore provide information on material parameter determination.