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)     

Parameter Identification for Inelastic Constitutive Models

The identification of material parameters of constitutive models is based on identification experiments. Since even specimens from the same lot show high deviations in the experimental data, the identification of the material parameters leads to different results for one and the same material. The number of identification experiments is usually not large enough for a statistical analysis of the deviations in the identified parameters. In order to overcome this problem we present a method of stochastic simulation which is based on time series analysis for generating artificial data with the same stochastic behaviour as the experimental data. The stochastic simulations allow an investigation of the confidence in the fits of the material parameters. We validate the stochastic simulations by comparing the results of the parameter identification from experimental data with the results from artificial data. The presented simulation method applied here turns out to be a suitable tool for generating artificial data for various kinds of analysis purposes. However, it is very important to take into account that the machines which perform the experiments do not maintain constant strain rates in the loading history of the tension and cyclic experiments.     

Identification of the Material Parameters of a Micropolar Model for Granular Materials

Granular frictional materials show a complex stress‐strain behaviour depending on the stress state and the load history. Furthermore, biaxial experiments exhibit the occurrence of shear band phenomena as the result of the localization of plastic strains. It is well known that the onset of shear bands is associated with microrotations of the granular microstructure, which has a significant influence on the macroscopic behaviour. Consequently, the macroscopic material must result in a micropolar model, which incorporates rotational degrees of freedom. After the formulation of the constitutive equations and the numerical implementation, it is necessary to determine all required material parameters. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Identification of material behavior via a Finite Element Model Updating strategy

In this paper an inverse and iterative method for the identification of material behavior is presented, based on the Finite Element Model Updating (FEMU) strategy. The FE simulations are performed with a commercial FE software code, using a self-implemented elastic material model at finite strain. The iterative identification procedure is based on an experimental test (numerical) whose measured kinematic values are compared to the corresponding simulated ones. Through an optimization algorithm the material parameters are varied in a way that the least-squares sum of the kinematic values is minimized and the optimal material parameters yielding the material behavior are identified. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Identification of optimal material models and parameters in finite strain plasticity

The numerical simulation of the behaviour of a workpiece during manufacturing depends to a large extent on the quality of the applied material model. In this work, a method for the identification of constitutive models and material parameters in engineering applications is proposed. The presented method is used in the setting of optimal experimental design and is based on successive optimization of a set of finite strain plasticity models with kinematic and/or isotropic hardening. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite thermo-viscoplasticity of amorphous glassy polymers: Experiments,modeling and simulations

The contribution is concerned with experimental procedures, constitutive modeling and the numerical simulations of finite thermo-viscoplastic behavior of glassy polymers. The experimental study involves both homogeneous and inhomogeneous tests at different temperatures under isothermal conditions. The true stress-true strain curves obtained from compressive homogeneous uniaxial and plane strain experiments are employed in the identification of adjustable material parameters. In contrast to the existing kinematic approaches to finite plasticity of glassy polymers, we propose a distinct kinematic framework constructed in the logarithmic strain space. This leads us to an algorithmically very attractive, additive kinematic structure in R⁶ similar to the geometrically linear theory. The proposed three-dimensional model is implemented into a finite element code. The load-displacement curves acquired from inhomogeneous experiments are compared against the results obtained from finite element analyses where the material parameters identified from homogeneous experiments are used. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The influence of the filler volume fraction on the mechanical behaviour of thermoplastic materials

Uniaxial experiments clarify that the mechanical behaviour of PTFE compounds depends strongly on the amount of filler particles. In order to describe these dependencies, a finite endochronic viscoplastic material model based on material isomorphisms has been applied to various glass fibre filled PTFE compounds. The model allows to characterize viscoplastic material behaviour with equilibrium hysteresis using a rate‐independent endochronic elastoplastic model in parallel connection with a nonlinear Maxwell model. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of viscoelastic material behaviour close to the glass transition temperature

In this contribution we investigate the mechanical behaviour of polyurethane over a range of different but constant temperatures from the glass to the viscoelastic state. Therefore uniaxial tension tests are performed on dogbone specimens under different isothermal conditions. In this manner an experimental data set is provided. As a theoretical basis we present the well known thermomechanically coupled one dimensional linear viscoelastic material model which is able to display the experimentally observed material behaviour. For this we adopt temperature dependent relaxation times. The introduced model parameters are identified via a standard parameter identification tool. Finally, the experimental results are compared with the ones of simulations of the identified model parameters. (© 2009 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)     

Magnetostrictive actuation of a smart beam with hysteretic material behaviour

Magnetostrictive materials can be used as actuators in smart structures technology. The relation between induced strain and the applied magnetic field is nonlinear and shows hysteretic behaviour. Thus the magnetomechanical coupling coefficient is not constant and should be defined as a function of strain or magnetic field in computations. In this study the hysteresis of a mechanically unconstrained actuator is determined using the Michelson interferometry. The hysteretic behaviour is modelled phenomenologically by a Preisach model. Using these experimental data for the modelling of an active structure with embedded magnetostrictive actuators, the actual coupling coefficient can be determined utilising the Preisach model. With this procedure the actuation strain of an embedded actuator, including the physical nonlinearities, can be calculated using the material characteristics obtained with an unconstrained actuator. For the determination of the actual coupling coefficient a strain- and field-dependent approach is used. For an experimental validation of the method outlined above, a magnetostrictive actuator is characterised experimentally and then applied to a cantilever aluminium beam. Then, the tip displacement of the actuated beam is measured with a laser triangulation sensor and compared with the numerical results. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parameter identification for rubber materials with artificial higher dimensional data

In general, laboratory test render only a limited number of experimental data. Consequently, the prediction of material behaviour becomes a difficult task and, moreover, a statistical analysis with a statistically based approach is almost impossible. As a remedy to increase the number of data, artificial data are generated by stochastic simulation. As a consequence an arbitrary number of data is available and the process of parameter identification can be analysed statistically. Here, the special challenge is the consideration of spatial and inhomogeneous problems. In this work artificial data are generated for a elastomer strip with hole under tension. The inhomogeneous stress/strain fields are optically measured with an Aramis/GOM system and have to be fitted to a stochastic model in order to generate artificial data. B-Splines are applied to fit the geometry of the test specimen and the measured data in space as well as in time. Parameter identifications applied and the resulting material parameters are statistically analysed. In the example, a statistical analysis of an Ogden model is performed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A physically motivated model for filled elastomers including strain rate and amplitude dependency in finite viscoelasticity

A microstructure-based model of rubber reinforcement, the so-called dynamic flocculation model (DFM), is presented describing filler-induced stress softening and hysteresis by the breakdown and reaggregation of strained filler clusters [1]. An extension of this model allows to consider incomplete deformation cycles that occur in the simulation of arbitrary deformation histories [2]. Good agreement between measurement and the model is obtained for CB-filled elastomers like NR, SBR or EPDM, loaded along various deformation histories. One very important aspect is that the model parameters can be directly referred to the physical properties. This benefit is used to extend the model to further essential effects like time- and rate-dependent material behavior. In the limit range above the glass transition temperature these viscoelastic effects originate mainly from the filler-filler interactions. In the material model these interactions are characterized by two material parameters s_v and s_d, respectively. The parameter s_v defines the strength of the virgin filler cluster, whereas s_d represents the strength according to the broken or damaged filler clusters. Both parameters can be defined as functions of time s_v,d = ŝ_v,d(t), which can be motivated by physical meaning [3]. Due to this extension it is possible to capture the very complex strain rate and amplitude dependency during loading and relaxation. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Young measure flow as a model for damage

Models for hysteresis in continuum mechanics are studied that rely on a time-discretised quasi-static evolution of Young measures akin to a gradient flow. The main feature of this approach is that it allows for local, rather than global minimisation. In particular, the case of a non-coercive elastic energy density of Lennard-Jones type is investigated. The approach is used to describe the formation of damage in a material; existence results are proved, as well as several results highlighting the qualitative behaviour of solutions. Connections are made to recent variational models for fracture.     

Phenomenological and Numerical Simulation of Shape Memory Alloys at Finite Strains

A phenomenological material law for pseudo elastic NiTi shape memory alloys (SMA) is presented. The model was derived from a thermodynamical framework and is well-suited to describe the thermomechanical coupled behaviour of the material. The material law, which was originally derived for small deformations, was extended to finite deformations using the Eulerian frame, in particular Hencky's logarithmic strain and the logarithmic rate. A first emphasis is on the physical interpretation of the material parameters and their identification. A second focus lies in the presentation of a structural example for the implementation of the material law into a commercial Finite Element code. Additionally a comparison of the numerical and experimental data of the presented example is performed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Young measure flow as a model for damage

Models for hysteresis in continuum mechanics are studied that rely on a time-discretised quasi-static evolution of Young measures akin to a gradient flow. The main feature of this approach is that it allows for local, rather than global minimisation. In particular, the case of a non-coercive elastic energy density of Lennard-Jones type is investigated. The approach is used to describe the formation of damage in a material; existence results are proved, as well as several results highlighting the qualitative behaviour of solutions. Connections are made to recent variational models for fracture.