Numerical Multiscale Modelling of Sandwich Plates

Sandwich plates present a complicated material behaviour, strongly depending on the considered materials and on the layer composition. Therefore, it is an increasing interest to feature a model of their mechanical behaviour. A multiscale model is developed in the paper. In the scope of this project, some layers show non-linear material behaviour at large strains and, as a consequence, the classical plate theory cannot be considered. At this stage, only linear elastic material behaviour and small deformations are taken into account, in order to validate the presented model; but to guaranty the possibility to consider non-linear material behaviour, a numerical homogenisation is chosen explicitly taking into account the stacking order and the material behaviour of the individual layers. A numerical homogenisation, or so-called FE2, consists of a Finite Element computation on a macroscale -here a plate which contains the plate kinematics and balance equations; but instead of applying the constitutive equations on this scale, the deformations are projected on a mesoscale where the mesostructure is fully resolved and another Finite Element computation is performed on this level. In this paper, a plate theory following Mindlin concept with five degrees of freedom is considered on the macroscale, and a three dimensional boundary value problem is solved in the mesoscale resolving the stacking order of the sandwich. Whereas the macroscale problem is implemented in a non-commercial FORTRAN code, the mesoscale is modelled using the commercial software ABAQUS® and an UMAT SUBROUTINE. In order to find an analytical tangent for the global iterations, a Multi-Level Newton Algorithm is applied, which enables a faster computation

Nanoindentation of Soft Polymers: Modeling, Experiments and Parameter Identification

Since the nanoindentation technique is able to measure the mechanical properties of extremely thin layers and small volumes with a high resolution, it also became one of the most important testing techniques for thin polymer layers and coatings. This work is focusing on the characterization of polymers using nanoindentation, which is dealt with by means of numerical computation, experiments and parameter identification. An analysis procedure is developed using the FEM based inverse method to evaluate the hyperelasticity and time-dependent properties. This procedure is firstly verified with a parameter re-identification concept. An important issue in this publication is to take into account the error contributions in real nanoindentation experiments. Therefore, the effects of surface roughness, adhesion force and the real shape of the tip are involved in the numerical model to minimize the systematic error between the experimental responses and the numerical predictions. The effects are quantified as functions or models with corresponding parameters to be identified

A Phase-Field Approach to Damage Modelling in Open-Cell Foams

Foams are complex and challenging materials. The damage process of the foam materials takes place on multiple scales changing several physical and structural properties of the material. In this study, the topology-based variable describing the connectivity state of a cell is introduced to formulate a non-variational phase-field model for the damage evolution in an open-cell foam. The material is considered consisting of the damaged and unimpaired phase with the proposed phase-field variable describing the separation of phases. The performance of the computational model is examined by means of the standard benchmarks such as tensile and simple shear test. The results show a qualitative correspondence with the two-dimensional artificial foam model used as a reference. Furthermore, the influence of the directional data extracted from the microstructure is investigated. The utilisation of the connectivity-based damage variable turns out to be a suitable choice for the simulation of the damage evolution in open-cell foam materials

On Fundamental Concepts of Multiphase Micropolar Materials

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Hybrid Metal Foams: Experimental Observations and Phenomenological Modelling

Metal foams are a very interesting class of microheterogeneous, cellular, lightweight materials which are often used as kinetic energy absorber. In this study open cell metal foams consisting of a 3D network of interconnected pores have been coated with nanocrystalline nickel via an electrodeposition technique. The resulting hybrid foams were submitted to several uniaxial and biaxial tests, where not only the stress-strain response but also the energy absorption capacity, size effects and damage behaviour were investigated. Metal foams exhibit localized deformation states under inelastic strain conditions that cause localisation of damage in crushing zones with a thickness of several pore layers. Building up of the crushing zones has been studied by using the digital image correlation (DIC) technique. The abovementioned strain localisation causes stress fluctuations which can be seen in macroscopic stress-strain diagrams. In this work a new modelling approach has been developed that allows for explicit consideration of such microstructural effects in a phenomenological way. The model is based on a qualitative phenomenological and rheological spring model. The size of a representative volume element (RVE) is equal to the thickness of a crushing zone and consists of several springs where each spring corresponds to one pore layer. By introducing a rheological model for the RVE in this way the constitutive equations still contain fundamental parameter but these are motivated by the microstructure, whereas the phenomenological model is able to account for microstructural effects

Thermo-mechanical properties of magnesia carbon foam composites

Refractory materials have a wide range of applications in steel-making industry. Often, magnesia carbon bricks (MgO-C) are used. These consist of a periclase phase (MgO) with inclusions of carbon and gas filled pores. The thermo-mechanical properties of MgO-C composites could significantly be improved using cellular MgO-C composites based on carbon foams. Modelling of MgO-C composite foams is not only a multi-phase, but also a multi-physics problem, in which both the displacement field and the temperature field have to be taken into account. In the present contribution, a fully coupled phenomenological thermo-mechanical continuum model was developed. The theory of porous media (TPM) with a kinematic coupling of the displacement and temperature fields of all constituents was used. Linear thermoelasticity with a multiplicative decomposition of the deformation gradient into an elastic and a thermal part for isotropic materials was extended to the mixture of MgO and C phase. The total macroscopic stress was calculated using the theory of mixture, including the contributions from the pore pressure

Implementation of the strongly pronounced non-linear viscoelasticity of an incompressible filled rubber

Filled rubber materials regularly show a pronounced non-linear viscoelasticity with very long relaxation times. In this contribution, a phenomenological description for an incompressible carbon black-filled EPDM (ethylene propylene diene monomer) is given, which also shows the abovementioned characteristic behaviour. In order to represent the non-linear viscoelastic material, the relaxation times of the model are chosen not as constant material parameters but as process-dependent functions. This contribution presents two different realisations of the model’s implementation. At first, this work provides an implementation of the material model, which is able to describe complex geometries and loading conditions. In this realisation, the three-dimensional model is implemented in the open source finite element library deal.II for finite deformations. Hence, real applications can be represented. In an alternative numerical solution, the model is reduced to the single case of uniaxial tension. The model is simplified to scalar equations, which are quite easy to handle for the implementation. This procedure provides a more simple identification process, but it presents the roblem that the model character is extremely restricted for the individual case of uniaxial tension. For the numerical realisation, at first, special attention has to be turned on the determination of the inelastic part of the kinematics. A detailed evaluation of the necessary evolution equations is provided in this contribution. Finally, he results of the different implementations are compared with respect to different loading conditions, like relaxation tests or cyclic loading

Biaxial Testing of Elastomers: Experimental Setup, Measurement and Experimental Optimisation of Specimen’s Shape

The present article deals with the setup and the control of a biaxial tension test device for characterising the material properties of elastomers. After a short introduction into the experimental setup a brief explanation of the benefits of a biaxial tension test is given. Furthermore the analysis of this test will be discussed. Therefore, the used optical field measurement by digital image correlation for analysing the strains is shortly introduced to the reader. Additionally, the basic concepts of the calculation of an inverse boundary problem for identifying the material’s parameters are imposed. However the main focus is laid on the experimental optimisation of the specimen’s geometry, whereupon a nearly hyperelastic, incompressible silicone is used to get the experimental results. The resulting geometry will be specially fitted to the requirements of elastomers. The tested geometries and the evaluation of the experiments will be explained as well as the resulting quality factor for the suitability of a specimen’s shape. After all, a short validation of the foregoing considerations will be presented

Error-Controlled Runge-Kutta Time Integration of a Viscoplastic Hybrid Two-Phase Model

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Kinematically Extended Continuum Theories: Correlation Between Microscopical Deformation and Macroscopical Strain Measures

The present work investigates the correlation between macrocscopical deformation modes and microscopical deformation modes. Thereby, the macroscopical deformation is represented by the strain-like quantities of the according macroscopical continuum theory while the microscopical deformation is expressed in the form of a Taylor series expansion. The use of an energy criterion makes it possible to derive a quantitative relation between microscopical and macroscopical deformation. The procedure is applied to different kinematically extended continuum theories on the macroscopical level. The investigation may help to select an optimal macroscopical continuum theory instead of choosing a theory based on phenomenological observations, whereby the optimal theory ist that one, which reflects the microscopical deformation behaviour best. The microscopical deformation behaviour depends on the topology of the microstructure under consideration. Thus, the optimal theory is affected by the topology of the microstructure