Elastomeric materials: Theoretical investigation and experiments

In this contribution we investigate an incompressible carbon–filled rubber experimentally and theoretically. On the experimental side we perform uniaxial tension tests and theoretically we use two different constitutive models, the Arruda–Boyce–Model and the Yeoh–Model, to describe the experimental observed behaviour. The model parameters are identified by a comercial fitting tool Origin Pro from National Instruments. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cellular rubber: Theoretical investigation on the basis of the mixture of theory and experiments

In this contribution we investigate a compressible cellular rubber experimentally and theoretically. In an appropriate model we apply the theory of porous media to describe the viscoelastic properties. The model parameters are identified by an algorithm based on evolution strategies. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A novel model to describe the intervertebral disc mechanical response

The main objective of the present work is the development of a simplified, efficient and easy-to-implement single-phase material model, which is able to describe the essential effects characterising the behaviour of multi-phase saturated materials, such as of intervertebral discs (IVDs). The presented new model mainly focuses on extending a viscoelastic material model in order to not only take the mechanical behaviour of the solid part into account, but also the fluid-flow-dependent behaviour of the material. By applying this model, the complexity and constitutive parameters are reduced, the implementation is more convenient and the experimental investigations can be better supported in comparison to multi-phase material models of IVDs. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Identification of Viscoelastic Properties and Damaging Effects of Highly Extensible Polyurea

The present work aims particular at the experimental identification of the viscoelastic properties of polyurea as well as on the onset of the damage. For the viscoelastic part, several relaxation experiments are performed. From the measured data a general viscoelastic model is derived where we use two different approaches. At first we identify a general Maxwell model (combining spring and damping elements for finite deformations) to use a prony series with N elements, which requires the identification of 2N + 1 parameters. At second, a model of generalized fractional elements [3] is employed. Both approaches are studied in detail and are compared to data from literature; furthermore a comparison concerning the effort is presented. Damaging effects of Polyurea are investigated using tensile tests with and without cyclic loading. In particular we focus on the the onset of damage by cavitation. To this end the recovered specimens were analyzed using a laser microscope; the surfaces of the ruptured areas are compared in terms of quantity and size of voids. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Characterisation of filled rubber with a pronounced non-linear viscoelasticity

This contribution presents the characterisation of an incompressible carbon black-filled elastomer as one characteristical example for highly filled rubber. It shows a strongly pronounced non-linear viscoelastic behaviour and the most important characteristic is the extremely long relaxation time which has to be taken into account. The material model is developed with respect to uniaxial tension data. The basis in the development of a phenomenological model is given by the basic elasticity. For this evaluation the long term relaxation behaviour results in a complex experimental procedure. Therefore, special attention has to be paid according to an optimised experimental process in order to get the necessary reference data in an adequate and reproduceable way [1]. With this model basis further investigations are taken into account concerning the time-dependent viscoelasticity. Therefore, cyclic deformations from zero up to a maximum of deformation are considered for different strain rates. Furthermore, the relaxation behaviour is investigated for multiple strain levels. The phenomena which are observed in the experimental results yield in a purely viscoelastic model, based on a rheological analogous model consisting of an equilibrium spring and several Maxwell-elements which contain nonlinear relations for the relaxation times of the dashpot elements [1,2]. The material model's numerical realisation is accomplished in two ways. Because of its numerical simplicity especially according to the parameter identification the model is restricted only to the simple case of uniaxial tension. A second, alternative implementation is executed providing the benefit that more complex deformation conditions can also be taken into account. Therefore, the general, three-dimensional finite model is implemented in an open-source Finite Element library [3]. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A microstructurally motivated anisotropic viscoelastic model for soft tissues

In this paper, a microstructurally motivated approach to take into account the anisotropic viscoelastic behaviour of soft biological tissues is proposed. The constitutive model is based on the assumption that this behaviour results from an interaction between collagen fibres and surrounding matrix constituents. Accordingly, a non–linear viscoelastic one–dimensional model for fibres and the nearby ground substance is developed. This model is then generalised to the anisotropic three–dimensional case. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling and Simulation of Curing Processes of Epoxy Resin

During the curing reaction, the adhesive changes its thermomechanical material behaviour from a viscous fluid to a viscoelastic solid. This phase transition is an exothermal chemical reaction which is accompanied by thermal expansion, chemical shrinkage and changes in temperature. In this work the numerical simulation of the curing process will be presented. The material model for the implementation is presented in [1]. For the implementation of the material model the consistent tangent operator has been derived. In the presentation, experimental data and simulation are shown. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling additive manufactured materials using a crystal plasticity model

In this contribution the macroscopic behaviour of additively manufactured Inconel 718 will be identified using a crystal plasticity model on the meso-level. The experimentally observed grain structures will be used to generate a representative volume element. Based on this RVE macroscopic mechanical parameters will be identified and compared with experimental results. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A viscoelastic constitutive modeling of rubber-like materials with the Payne effect

This paper aims to present a viscoelastic constitutive model of rubber-like materials, which can capture the Payne effect under dynamic cyclic loadings. The Payne effect is induced by a damage process of bond rupture inside the rubber-like materials, which leads to the storage and loss moduli changing with the dynamic strain amplitude. A viscoelastic constitutive relation is established based on the nonequilibrium thermodynamics for the rubber-like materials by constructing the Helmholtz free energy as the superposition of a hyperelastic model and a convolution viscous model. The neo-Hookean hyperelastic model and the convolution viscous model in terms of the Prony series are then employed in a modification that the material parameters concerned are treated as internal variables and can be identified through a simple but effective approach. At last, the Payne effect is effectively predicted in a good agreement with experimental results.     

Linear and nonlinear vibrations of fractional viscoelastic Timoshenko nanobeams considering surface energy effects

In this paper, the linear and nonlinear vibrations of fractional viscoelastic Timoshenko nanobeams are studied based on the Gurtin–Murdoch surface stress theory. Firstly, the constitutive equations of fractional viscoelasticity theory are considered, and based on the Gurtin–Murdoch model, stress components on the surface of the nanobeam are incorporated into the axial stress tensor. Afterward, using Hamilton's principle, equations governing the two-dimensional vibrations of fractional viscoelastic nanobeams are derived. Finally, two solution procedures are utilized to describe the time responses of nanobeams. In the first method, which is fully numerical, the generalized differential quadrature and finite difference methods are used to discretize the linear part of the governing equations in spatial and time domains. In the second method, which is semi-analytical, the Galerkin approach is first used to discretize nonlinear partial differential governing equations in the spatial domain, and the obtained set of fractional-order ordinary differential equations are then solved by the predictor–corrector method. The accuracy of the results for the linear and nonlinear vibrations of fractional viscoelastic nanobeams with different boundary conditions is shown. Also, by comparing obtained results for different values of some parameters such as viscoelasticity coefficient, order of fractional derivative and parameters of surface stress model, their effects on the frequency and damping of vibrations of the fractional viscoelastic nanobeams are investigated.     

Comparison of a biphasic and a multicomponent model describing viscoelastic swelling phenomena

Biological soft tissues like articular cartilage and their artificial replacement hydrogel have a multicomponent microstructure, consisting of a charged viscoelastic solid matrix saturated by a fluid, which is composed of the liquid solvent and the dissolved anions and cations. Such charged multiphasic materials exhibit a swelling behaviour under varying chemical conditions. These materials are best described by a macroscopic approach like the Theory of Porous Media (TPM). Starting from this point, a standard two-phase model is extended by dividing the fluid into the above mentioned components. Therein, the chemical relations describing the behaviour of the ions and their interaction with the other mixture constituents are incorporated. The resulting model covers mechanical as well as osmotic and electrostatic effects. For numerical and simplicity reasons, it is possible to describe the swelling phenomena by a simplified biphasic model, where the ions as a third degree of freedom and their time-dependent diffusion are neglected. Furthermore, the viscoelastic solid matrix can be replaced by an elastic material. Note that using the multicomponent model generally results in numerical problems, since the boundary conditions depend on the internal fixed charge density. It is shown that this problem can be solved by including the boundary conditions into the weak formulation. Finally, to compare the different behaviour of the above mentioned models by means of an swelling example, they are implemented into the FE tool PANDAS using stable Taylor-Hood elements for the spatial discretization. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Incompressible non‐Newtonian fluids: time asymptotic behaviour of weak solutions

We study the asymptotic behaviour in time of incompressible non‐Newtonian fluids in the whole space assuming that initial data also belong to L¹. Firstly, we consider the weak solution to the power‐law model with non‐zero external forces and we find the asymptotic behaviour in time of this solution in the same class of existence and uniqueness with p?. Secondly, we are interested in the asymptotic behaviour of weak solutions to the second grade model, and finally, we deal with the asymptotic behaviour in time of weak solutions to a simplified model of viscoelastic fluids of the Oldroyd type. Copyright © 2006 John Wiley & Sons, Ltd.     

Hysteresis Behaviour of 51CrV4 and Viscoplastic Modeling Aspects

In this work we investigate the material behaviour of steel 51CrV4 in classical uniaxial strain controlled tension tests of different strain rates interposed by relaxation steps, in which the equilibrium stress observed is significantly smaller than the stresses seen in slowest strain rate test. Also, some cyclic experiments with different strain rates and amplitudes were done to analyze the hysteresis behaviour of the material. Against this background of experimental data the modeling possibilties of two models are explored: the Lion model and the Chaboche model with kinematic hardening ansatz. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A material model of nonlinear fractional viscoelasticity

Multiscale methods are frequently used in the design process of textile reinforced composites. In addition to the models for the local material structure it is necessary to formulate appropriate material models for the constituents. While experiments have shown that the reinforcing fibers can be assumed as linear elastic, the material behavior of the polymer matrix shows certain nonlinearities. These effects are mainly due to strain rate dependent material behavior. Fractional order models have been found to be appropriate to model this behavior. Based on experimental observations of Polypropylene a one-dimensional nonlinear fractional viscoelastic material model has been formulated. Its parameters can be determined from uniaxial, monotonic tensile tests at different strain rates, relaxation experiments and deformation controlled processes with intermediate holding times at different load levels. The presence of a process dependent function for the viscosity leads to constitutive equations which form nonlinear fractional differential equations. Since no analytical solution can be derived for these equations, a numerical handling has been developed. After all, the stress-strain curves obtained from a numerical analysis are compared to experimental results. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computational modeling of cardiac tissue with strongly coupled electromechanics and orthotropic viscoelastic effects

Modeling of complex mechanisms leading to the functioning of the heart has been an active field of research since decades. Difficulties associated with in vivo experiments motivate the utilization of computational models in order to gain a better appreciation of heart electromechanics. Although rate dependent behaviour of the orthotropic passive heart tissue has been comprehensively studied in the literature [1], effects of this phenomenon on fully coupled cardiac electromechanics are unrevealed yet. Therefore, this contribution is concerned with the investigation of viscous effects on the electromechanical response of the myocardium. To this end, we adopt the fully implicit finite element framework which strongly couples the mechanical and electrophysiological problem of the myocardium in a mono- and bi-domain setting [2,3], respectively. Viscous effects, however, are consistently embedded into this framework by making use of the orthotropic viscoelastic material model for the passive myocardium, which considers different relaxation mechanisms for the different orientation directions [5]. The performance of the proposed model is assessed by comparing finite element simulations of spiral waves in heart tissue for elastic and viscoelastic formulations. We further investigate the influence of viscosity on the defibrillation phenomenon by means of the finite element formulation of bidomain electrophysiology. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Galerkin methods in time for semi-discrete viscoelastodynamics

In semi-discrete nonlinear elastodynamics, higher order energy and momentum conserving time stepping schemes turned out to be well suited for computing long time motions [1]. In comparison to standard ODE integrators, conserving schemes exhibit superior stability properties which are of utmost importance in a nonlinear .nite element framework. We show that conserving schemes are particularly well suited as starting point for the development of energy consistent schemes for dissipative dynamical systems. In particular, viscoelastic material behaviour is considered. A key advantage of energy consistent schemes lies in the fact that the equilibrium state of viscoelastic systems can be de.nitely reached, independent of the material parameters. In the paper, we compare two Galerkin methods for the temporal discretisation of semi-discrete nonlinear viscoelastodynamics: the standard continuous Galerkin (cG) method and an enhanced continuous Galerkin (eG) method which ful.ls the total energy balance exactly. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)