Thermo-mechanical modelling of cellular ceramic composites by a multiphase approach of porous media

Refractory materials have a wide range of applications in the steel-making industry for example as lining of furnaces, oxygen converters or for ladles. Often, magnesia carbon bricks (MgO-C) are used. These are made of a periclase phase (MgO) with carbon inclusions and pores. In their applications, refractories are subjected to thermal and mechanical loads causing damage. The thermo-mechanical behaviour of MgO-C composites and hence their thermal stability could be improved significantly using cellular MgO-C composites based on carbon foams [1, 2]. The present contribution focuses on the development of a fully coupled phenomenological thermo-mechanical continuum model based on the theory of porous media (TPM) with a new kinematic coupling of the displacement field of all constituents. (© 2015 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)     

Characterization of Ni/Al hybrid foam from atomic to microscale

In this paper, the Ni/Al hybrid open-cell foams are characterized on different hierarchical levels by means of experiments and numerical modeling from the atomic to the microscale. In this case, it is possible to compare the elastic-plastic behavior at different scales in order to attain a deeper understanding of the multiscale properties of the Ni/Al hybrid foams. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermo-mechanical modelling of cellular hybrid refractories

Refractory materials are subjected to both quasi-static and dynamic thermal loading (thermal shock) causing damage up to mechanical failure. Typical refractories are magnesia carbon bricks consisting of periclase (MgO) and carbon inclusions. Recently, a significant improvement of the thermo-mechanical behaviour could be achieved by cellular hybrid composites made of periclase-filled carbon foams. The present contribution focuses on MgO-filled carbon foams and the investigation and optimisation of the structure-property relationship with respect to a reduction of thermally induced stresses and damage. It is a transient as well as static, fully coupled thermo-mechanical problem. According to the fact that, in general, refractories are brittle materials a linear elastic model, with a damage criterion was used. To optimise the structural morphology of the cellular refractories, the effect of micro structural changes has been determined. For the investigation of the thermal shock! behaviour, the results correlate very well with the experimentally motivated Hasselman relation. There is a significant size effect depending on the pore size. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Micropolar Theory of Porous Media: Constitutive Modelling

The extension of the classical mixture theory by the concept of volume fractions leads to the theory of porous media. In this article, the theory of porous media is generalised to micropolar constituents. The kinematic relations and the balance equations for a porous medium are developed without restricting the number of constituents. Based on the entropy inequality, the general form of the constitutive equations are derived for a binary medium consisting of a porous elastic skeleton saturated by a viscous pore-fluid. Both constituents are assumed to be compressible. Handling the saturation constraint by a Lagrangian multiplier leads to a compatibility of the proposed model to so-called hybrid and incompressible models.     

Continua with affine microstructure: Theoretical aspects and applications

In the present contribution we discuss an axiomatic stucture of extended continua with affine microstructure in the sense of Eringen [2]. Postulating and evaluating the observer-invariance of the balance of energy we obtain the governing balance equations of generalized continua which are closed by a specific set of kinematical assumptions and constitutive equations. Furthermore, we discuss two specific models characterized by an additional scalar (volumetrical) order parameter. Interestingly, the resulting effects lead to completely different interpretations of the results with respect to the coupling effects. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Galerkin‐type space‐time finite elements for volumetrically coupled problems

The study focuses on error estimation techniques for a coupled problem with two constituents based on the Theory of Porous Media. After developing space‐time finite elements for this mixed problem, we extend the numerical scheme to a coupled space‐time adaptive strategy. Therefore, an adjoint or dual problem is formulated and discussed, which is solved lateron numerically. One advantage of the presented technique is the high flexibility of the error indicator with respect to the error measure.     

Cellular rubber: Dependency between relaxation time and pretreatment

In this contribution we investigate experimentally a porous carbon-filled rubber. The main focus is on the dependency of the mechanical behaviour using different pretreatments. Therfore, cyclic tests and relaxation tests with different pretreatment are performed. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)