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This contribution aims at developing a formulation for the large viscoelastic deformation of hyperelastic beams and frames under various loading and boundary conditions. To do so, the kinematics of deformation in two-dimensional space is formulated and basic kinematics and kinetic quantities are introduced. The quasi-linear viscoelasticity theory is employed to capture the time-dependent behavior of the underlying material. The corresponding time integration scheme and the consistent tangent moduli are then presented. Because of the highly nonlinear nature of governing equations at the large regime of deformations including time dependency, a nonlinear finite element formulation in the total Lagrangian framework is developed. Several numerical examples are provided to investigate the applicability of derived formulations. It is observed that the formulation can successfully capture the relaxation and creep phenomena in visco-hyperelastic beams and frames. [ABSTRACT FROM AUTHOR]

In the present study, nanoindentation and macroindentation tests are performed on a soft polymer: polyurethane (PU). Strong viscoelasticity is represented by the force-displacement data on both scales. A finite element method based on an inverse procedure is employed to identify the nonlinear viscoelasticity of PU. An appropriate viscoelastic model is chosen, and the corresponding parameters are identified by matching the experimental responses with the predictions of the computational model. At the very beginning, the uniaxial tensile test, which has a homogeneous deformation, is used to prove the isotropic properties and incompressibility of PU and to identify the viscoelasticity as a reference and verification source. The comparison between the identified results from nanoindentation and macroindentation allows to quantifying the adhesion effects in nanoindentation. The quantification is treated with a traction-separation relationship incorporated into the numerical adhesive contact model. Comparable strain rates in the macro-, nanoindentation and uniaxial tensile tests are considered to identify the viscoelasticity. [ABSTRACT FROM AUTHOR]