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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]

The method of vertical lines in the case of quasi-static solid mechanics applying constitutive models of evolutionary-type yields after the spatial discretization by means of finite elements a system of differential-algebraic equations. It is of substantial interest how fast, accurate, and stable such computations can be carried out. Moreover, the questions are how simple the implementation can be done and how susceptible a procedure is to programming errors. In this article, this is investigated for half-explicit Runge-Kutta methods that are applied to small and finite strain viscoelasticity. The advantage of the method is given by a non-iterative scheme on element level. Additionally, it turns out that for models where linear elasticity is one ingredient in the constitutive model, the method leads to only one required LU-decomposition at the beginning of the entire computation, and in each time step, only one back-substitution step has to be carried out. This outperforms current finite element computations. Order investigations of various integration schemes and the automatic step-size behavior are studied. This new proposal is compared to a classical Backward-Euler implementation, high-order stiffly accurate diagonally implicit Runge-Kutta, and recently proposed Rosenbrock-type methods. Advantages and disadvantages of the applied schemes are discussed. [ABSTRACT FROM AUTHOR]