Anisotropic viscohyperelastic behavior of intervertebral discs: Modeling and experimental validation

Biomechanical investigations of human cartilage, especially intervertebral discs (IVDs), have greatly helped to improve people's health over the last several decades. The study of the underlying biomechanical characteristics of cartilage tissues is a key issue to understand its physiological function and degeneration or damage behavior. The aim of this investigation is to describe the biomechnical behavior of healthy sheep IVDs under various loading conditions. Experimental and cartilage histological data, including fiber orientation, are used to develop a viscohyperelastic material model, which allowed us to numerically study the mechanical behavior of IVDs, consisting of a cartilaginous, fiber-reinforced ring surrounding a highly hydrated, gelatinous core. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite element simulation of deformation behaviour of cellular rubber components

This paper presents a new prospect of investigating the mechanical behaviour of cellular rubber using porous hyperelastic material model. There are number of hyperelastic material models to describe the behaviour of homogeneous elastomer, but very few to characterise the complex properties of cellular rubber. The analysis of dependence of material behaviour on pore density using the new material model is supported with experiments to characterise the actual material behaviour. The new material model which is based on Danielsson et al [1] decouples the influence of porosity from the mechanical properties of the solid material by introducing volume fraction of the pores as an explicit scalar variable. The finite element simulations are then followed by experiments on complex model to validate the material model. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lattice Boltzmann equation model for multi-component multi-phase flow with high density ratios

Multi-component multi-phase (MCMP) flows are very common in engineering or industrial problems, as well as in nature. Because the lattice Boltzmann equation (LBE) model is based on microscopic models and mesoscopic kinetic equations, it offers many advantages for the study of multi-component or multi-phase flow problems. While the original formulation of Shan and Chen’s (SC) model can incorporate some MCMP flow scenarios, the density ratio of the different components is greatly restricted to less than approximately 2.0. This obviously limits the applications of this MCMP LBE model. Hence, based on the original SC MCMP model and the improvements in the single-component multi-phase (SCMP) flow model reported by Yuan and Schaefer, we have developed a new model that can simulate a MCMP system with a high density ratio.     

Transverse isotropic flow in biphasic materials

Biological and artificial tissues like muscles, brain material, saturated paper or other functionally graded porous materials often show a transverse isotropic permeability caused by their inner structure. The transverse isotropic permeability influences the motion of the saturating fluid and with this the overall deformation state of the mixture body. Starting with the multi-phase Theory of Porous Media, a model is presented to describe this deformation affected by the anisotropic inner permeability. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Computational modelling of bubbles,droplets and particles in metals reduction and refining

A multi-phase framework is typically required for the CFD modelling of metals reduction processes. Such processes typically involve the interaction of liquid metals, a gas (often air) top space, liquid droplets in the top space and injection of both solid particles and gaseous bubbles into the bath. The exchange of mass, momentum and energy between the phases is fundamental to these processes. Multi-phase algorithms are complex and can be unreliable in terms of either or both convergence behaviour or in the extent to which the physics is captured. In this contribution, we discuss these multi-phase flow issues and describe an example of each of the main “single phase” approaches to modelling this class of problems (i.e., Eulerian–Lagrangian and Eulerian–Eulerian). Their utility is illustrated in the context of two problems – one involving the injection of sparging gases into a steel continuous slab caster and the other based on the development of a novel process for aluminium electrolysis. In the steel caster, the coupling of the Lagrangian tracking of the gas phase with the continuum enables the simulation of the transient motion of the metal–flux interface. The model of the electrolysis process employs a novel method for the calculation of slip velocities of oxygen bubbles, resulting from the dissolution of alumina, which allows the efficiency of the process to be predicted.     

Multiscale Modelling of the Effective Viscoplastic Material Behaviour of Textile-Reinforced Polymers Using XFEM

In this contribution a modelling approach using numerical homogenisation techniques is applied to predict the effective nonlinear material behaviour of composites from simulations of a representative volume element (RVE). Numerical models of the heterogeneous material structure in the RVE are generated using the eXtended Finite Element Method (XFEM) which allows for a regular mesh. Suitable constitutive relations account for the material behaviour of the constituents. The influence of the nonlinear matrix material behaviour on the composite is studied in a physically nonlinear FE simulation of the local material behaviour in the RVE ­ effective stress-strain curves are computed and compared to experimental observations. The approach is currently augmented by a damage model for the fibre bundle. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

FE2 Modelling of Hybrid Sandwich Composites

This paper presents a procedure to simulate the behaviour of a sandwich composite material. The classical solution to model this kind of structure is the plate theory. Nevertheless, because of the incapacity to take non-linear material behaviour into account, this method cannot be used to model our problem. Indeed, the sandwich structure contains metallic layers, and their behaviour is elasto-plastic. For these reasons, a numerical homogenisation will be presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical modelling of free surface flows in metallurgical vessels

A numerical model for simulating the transient behaviour of multi-fluid problems defined in 2D rectangular and cylindrical geometries is presented. The model uses a piecewise linear volume tracking scheme, and maintains sharp interfaces and captures fine-scale flow phenomena such as fragmentation and coalescence. The numerical model was applied to four problems of pyrometallurgical relevance – entrainment of matte in the flow of slag during skimming operations, splash resulting from a drop impinging on a bath, bubble rise in a liquid bath, and top-submerged gas injection. The numerical predictions are in good agreement with the published experimental results. The simulation of top-submerged gas injection showed, in detail, the phenomena of bubble formation, bubble rise, and splash drop formation and recoalescence with the bath. Data useful for engineering purposes such as pressure traces and time-averaged flow fields were obtained, allowing assessment of splash behaviour for given gas injection conditions. The numerical model has been shown to be versatile in being able to adapt to a wide range of multi-phase flow problems.     

Modelling the material behaviour of magnetorheological fluids under shear deformation

In recent years the interest in materials with specific adjustable properties has increased due to higher requirements on the material performance. Here a smart composite material is to be developed, whose stiffness can be varied subjected to a magnetic field. To realise this aim a magnetorheological fluid (MRF) embedded in a polymeric matrix material is considered. To model the material behaviour of the composite a homogenisation method will be applied. Amongst others this requires the knowledge of the multiaxial material behaviour of each constituent. The modelling of the material behaviour of MRF under shear deformation, which is the aim of this work, represents the first step in this process. (© 2011 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)     

Energetic modelling for carbon fibre reinforced carbon

In this contribution an energetic model for multi-phase materials is developed describing the influence of microstructure on different length scales as well as the evolution of phase changes. Restrictions on the energy functional are discussed. In such a non-convex framework, interfacial contributions serve for relaxing the total energy. Such models can be applied to describe the macroscopic material properties of carbon fibre reinforced carbon where phase transitions between regions of different texture of the carbon matrix are observed on nanoscale as well as columnar microstructures on microscale [2]. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of micro-cutting considering finite deformation crystal plasticity

Micro-machining processes on metalic microstructures are influenced by the crystal structure, i. e. the grain orientation. Furthermore, the chip formation underlies large deformations. To perform finite element simulations of micro-cutting processes, a large deformation material model is necessary in order to model the hyperelastic and finite plastic material behaviour. In the case of cp-titanium material with hcp-crystal structure the anisotropic behaviour must be considered by an appropriate set of slip planes and slip directions. In the present work the impact of the grain orientation on the plastic deformation is demonstrated by means of finite element simulations of a finite deformation single slip crystal plasticity model. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Asymptotics of generalized derangements

An adaptive wavelet-based method is proposed for solving TV(total variation)–Allen–Cahn type models for multi-phase image segmentation. The adaptive algorithm integrates (i) grid adaptation based on a threshold of the sparse wavelet representation of the locally-structured solution; and (ii) effective finite difference on irregular stencils. The compactly supported interpolating-type wavelets enjoy very fast wavelet transforms, and act as a piecewise constant function filter. These lead to fairly sparse computational grids, and relax the stiffness of the nonlinear PDEs. Equipped with this algorithm, the proposed sharp interface model becomes very effective for multi-phase image segmentation. This method is also applied to image restoration and similar advantages are observed.     

Granular materials: Parameter identification and modelling of localisation problems

The prediction of landsliding requires an exact knowledge of the mechanical behaviour of granular materials. This kind of materials, e. g., sand, have a very complex deformation behaviour, which depend on the stress state and on the loading history. In this work, the deformation behaviour of the solid skeleton is characterised via homogeneous triaxial tests on dry sand specimens. Additionally, an appropriate elasto-plastic material law to describe the solid skeleton in the frame of Theory of Porous Media (TPM) is used, which is implemented in the FE tool PANDAS. Furthermore, a single-surface yield criterion with isotropic hardening, which limits the elastic domain, and a non-associated plastic flow are employed. The determination of the material parameters of the linear elasticity law as well as the single-surface yield criterion are based on test data of triaxial experiments. The material parameters are identified using a derivative-based optimisation method (donlp2), which is coupled with PANDAS. Finally, a simulation of a benchmark test is presented to show shear band localisation effects, where the material behaviour is described by a triphasic porous media model based on the TPM, where the constituents are a deformable solid skeleton and two pore fluids, water and air. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Microstructural behaviour of transversal isotropic material

We discuss and simulate transversal isotropic material under tension loading. The preferential direction of the material is inclined under 45 degrees to the direction of the tensile resultant. In this configuration the deformation of a rectangular test specimen differ from the behaviour of isotropic material in the way, that beside Poissons effect additional displacement appear perpendicular to the tension direction. In classical continuum theories, this transverse deformations describe a typical S–shape. By using a non–local continuum theory, the effect of microstructural orientation is incorporated into the numerical model. Then, it depends on a phenomenological parameter of inner structure whether the energetically favoured configuration is classical or contains microstructural behaviour. In the second case, the transverse deformation is not described by the typical S–shape, but with higher forms of it. A simple experimental model will show the connection between the inner structure of the material and the rotational parameters within the non–local continuum theory. It is evident, that these parameters are responsible for the non–classical behaviour and give the possibility to find energetically favoured solutions. The results of the finite–element–analyses can help to understand constitutive parameters for the non–local continuum theory and to apply it to other specimens. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the macroscopic material behaviour of textile reinforced concrete undertensile loading

This paper concerns with the development of the macroscopic material behaviour of textile reinforced concrete (TRC) using an analytical approach. Therefore the heterogeneous structure of TRC is modelled on the mesoscopic level. The overall material behaviour on the macroscopic level is obtained by means of the homogenisation technique. The analytical approach is based on the micro mechanical solution for a single inclusion according to Eshelby . In extension of this solution for multidirectional reinforced concrete an effective field approximation is used. This approach considers the interactions between the different orientated rovings and the micro cracks in an average sense. For the mechanical modelling of the bond behaviour between roving and matrix after initiating of the macro cracking a slip based bond model with a multiple linear shear stress-slip relation is used. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A cohesive element approach for viscoelastic interface properties

This paper introduces a time dependent extension of the nonlinear traction separation law for an interface element. The constitutive equations of the load history dependent behaviour of the material are depicted and derived according to a generalized Maxwell‐model. This finite linear, viscoelastic approach allows the consideration of long term loading and time dependent material behaviour in thin layers. The implementation of the presented element formulation and the material approach are verified by numerical examples. The paper gives an outlook on further work and research topics. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)