Browsing by Author "Karajan, Nils"

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Open Access
7th GACM Colloquium on Computational Mechanics for Young Scientists from Academia and Industry : proceedings ; a conference under the auspice of the German Association for Computational Mechanics (GACM) ; 11 - 13 October 2017, Stuttgart, Germany
(Stuttgart : Institute for Structural Mechanics, University of Stuttgart, 2017) Scheven, Malte von; Keip, Marc-André; Karajan, Nils
This book contains papers presented at the 7th GACM Colloquium on Computational Mechanics for Young Scientists from Academia and Industry (GACM 2017), which was held 11-13 October 2017 at the University of Stuttgart, Germany. The colloquium is hosted by the Institute for Structural Mechanics and the Institute of Applied Mechanics of the University of Stuttgart in collaboration with DYNAmore GmbH. The objective of GACM 2017 is to bring together young scientists who are engaged in academic and industrial research on Computational Mechanics and Computer Methods in Applied Sciences. It provides a platform to present and discuss recent results from research efforts and industrial applications. In more than 200 presentations by young scientists in 18 mini-symposia devoted to specific scientific areas and thematically arranged contributed sessions, current scientific developments and advances in engineering practice in this field are presented and discussed. The contributions from young researchers are supplemented by plenary lectures from three senior scientists from academia and industry as well as from the GACM Best PhD Award winners 2015 and 2016.
Open Access
An extended biphasic description of the inhomogeneous and anisotropic intervertebral disc
(2009) Karajan, Nils; Ehlers, Wolfgang (Prof. Dr.-Ing.)
It is the aim of this contribution to develop a finite element model, which is as simple as possible, but at the same time complex enough to capture many of the occurring tissue properties of the intervertebral disc (IVD). In order to better understand these properties from an engineering point of view, the needed basic anatomical knowledge is briefly reviewed in the beginning of this treatise, thereby addressing the lumbar spine with focus on the IVD and its material properties. In particular, the IVD appears as the largest avascular part of the body and its microstructure leads to an electro-chemically active material with anisotropic, inhomogeneous and strongly dissipative behaviour. In the following main part of this work, the complete continuum-mechanical modelling process is extensively discussed as well as the numerical treatment of the resulting governing equations. Starting from the thermodynamically consistent Theory of Porous Media (TPM), two phases and three components are introduced for the description of IVD tissue. In particular, this is the extracellular matrix (solid skeleton) carrying fixed negative charges which is saturated by a pore fluid consisting of a solvent (liquid) as well as anions and cations of a dissolved salt. Following the idea of superimposed continua, an individual motion function is introduced for each of the constituents, whereas the components of the pore fluid are always expressed relative to the deforming solid skeleton. In order to capture the finite kinematics of the inelastic solid skeleton, its deformation gradient is multiplicatively split into inelastic and elastic parts. Next, the materially independent balance equations are derived from the respective master balances and accustomed to the soft biological tissue under study. In order to keep the resulting set of equations as simple as possible, while still keeping the ability to reproduce osmotic effects, an assumption according to Lanir is made. In this context, the tissue is regarded to be always immediately in electro-chemical equilibrium, which allows to describe the electro-chemically active tissue using only an extended biphasic model. Applying van't Hoff's law finally allows to compute the occurring osmotic pressure as a function of the solid displacement. Moreover, in order to characterise the inhomogeneous anisotropic and viscoelastic solid skeleton as well as the viscous pore fluid, several constitutive equations need to be formulated, thereby depending on a thermodynamically admissible set of process variables. Herein, the endangerment of postulating nonphysical constitutive assumptions is avoided by strictly following the restrictions resulting from the evaluation of the entropy inequality. Finally, the chosen constitutive functions of the solid skeleton are based on Ogden-type strain energy functions, which automatically include several simpler material laws. The viscoelastic contribution is based on a generalised Maxwell model which is dominated by the concept of internal variables with linear evolution equations. Finally, the superimposed dissipative effect of the viscous pore fluid is captured using the famous Darcy filter law. As a last step, the applicability of the derived model is proven with realistic computations of the IVD. Herein, the resulting set of governing partial differential equations is discretised in time and space using the finite difference method and the mixed finite element method, respectively. The theoretically introduced material parameters are determined using experimental data as well as material parameters obtained from a vast collection of related literature sources. Since many parameters appear in a coupled manner, their identification is often only possible via inverse computations. Following this, a numerical sensitivity analysis is carried out yielding an indication for the relevant parameters in experiments concerning a motion segment in a short-duration compression-flexion experiment as well as in long-term loading situations. Subsequently, the efficiency of the implementation is demonstrated by a parallel simulation of a lumbar spine segment carried out on 84 processors simultaneously, thereby exhibiting almost one million degrees of freedom.