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The goal of this thesis is a physically motivated and thermodynamically consistent formulation of higher gradient inelastic material behavior. Thereby, the influence of the material microstructure is incorporated. Next to theoretical aspects, the thesis is complemented with the algorithmic treatment and numerical implementation of the derived model. Hereby, two major inelastic effects will be addressed: on the one hand elasto-plastic processes and on the other hand damage mechanisms, which will both be modeled within a continuum mechanics framework.

The topic of this thesis is the coupling of an atomistic and a coarse scale region in molecular dynamics simulations with the focus on the reflection of waves at the interface between the two scales and the velocity of waves in the coarse scale region for a non-equilibrium process. First, two models from the literature for such a coupling, the concurrent coupling of length scales and the bridging scales method are investigated for a one dimensional system with harmonic interaction. It turns out that the concurrent coupling of length scales method leads to the reflection of fine scale waves at the interface, while the bridging scales method gives an approximated system that is not energy conserving. The velocity of waves in the coarse scale region is in both models not correct. To circumvent this problems, we present a coupling based on the displacement splitting of the bridging scales method together with choosing appropriate variables in orthogonal subspaces. This coupling allows the derivation of evolution equations of fine and coarse scale degrees of freedom together with a reflectionless boundary condition at the interface directly from the Lagrangian of the system. This leads to an energy conserving approximated system with a clear separation between modeling errors an errors due to the numerical solution. Possible approximations in the Lagrangian and the numerical computation of the memory integral and other numerical errors are discussed. We further present a method to choose the interpolation from coarse to atomistic scale in such a way, that the fine scale degrees of freedom in the coarse scale region can be neglected. The interpolation weights are computed by comparing the dispersion relations of the coarse scale equations and the fully atomistic system. With this new interpolation weights, the number of degrees of freedom can be drastically reduced without creating an error in the velocity of the waves in the coarse scale region. We give an alternative derivation of the new coupling with the Mori-Zwanzig projection operator formalism, and explain how the method can be extended to non-zero temperature simulations. For the comparison of the results of the approximated with the fully atomistic system, we use a local stress tensor and the energy in the atomistic region. Examples for the numerical solution of the approximated system for harmonic potentials are given in one and two dimensions.

Thermoelasticity represents the fusion of the fields of heat conduction and elasticity in solids and is usually characterized by a twofold coupling. Thermally induced stresses can be determined as well as temperature changes caused by deformations. Studying the mutual influence is subject of thermoelasticity. Usually, heat conduction in solids is based on Fourier’s law which describes a diffusive process. It predicts unnatural infinite transmission speed for parts of local heat pulses. At room temperature, for example, these parts are strongly damped. Thus, in these cases most engineering applications are described satisfactorily by the classical theory. However, in some situations the predictions according to Fourier’s law fail miserable. One of these situations occurs at temperatures near absolute zero, where the phenomenon of second sound1 was discovered in the 20th century. Consequently, non-classical theories experienced great research interest during the recent decades. Throughout this thesis, the expression “non-classical” refers to the fact that the constitutive equation of the heat flux is not based on Fourier’s law. Fourier’s classical theory hypothesizes that the heat flux is proportional to the temperature gradient. A new thermoelastic theory, on the one hand, needs to be consistent with classical thermoelastodynamics and, on the other hand, needs to describe second sound accurately. Hence, during the second half of the last century the traditional parabolic heat equation was replaced by a hyperbolic one. Its coupling with elasticity leads to non-classical thermomechanics which allows the modeling of second sound, provides a passage to the classical theory and additionally overcomes the paradox of infinite wave speed. Although much effort is put into non-classical theories, the thermoelastodynamic community has not yet agreed on one approach and a systematic research is going on worldwide.Computational methods play an important role for solving thermoelastic problems in engineering sciences. Usually this is due to the complex structure of the equations at hand. This thesis aims at establishing a basic theory and numerical treatment of non-classical thermoelasticity (rather than dealing with special cases). The finite element method is already widely accepted in the field of structural solid mechanics and enjoys a growing significance in thermal analyses. This approach resorts to a finite element method in space as well as in time.

Dry Sliding and Rolling Tribotests of Carbon Black Filled EPDM Elastomers and Their FE Simulations
(2008)

Unlubricated sliding systems being economic and environmentally benign are already realized in bearings, where dry metal-plastic sliding pairs successfully replace lubricated metal-metal ones. Nowadays, a considerable part of the tribological research concentrates to realize unlubricated elastomer-metal sliding systems, and to extend the application field of lubrication-free slider elements. In this Thesis, characteristics of the dry sliding and friction are investigated for elastomer-metal sliding pairs. In this study ethylene-propylene-diene rubbers (EPDM) with and without carbon black (CB) filler were used. The filler content of the EPDMs was varied: EPDMs with 0-, 30-, 45- and 60 part per hundred rubber (phr) CB amount were investigated. Quasistatic tension and compression tests and dynamic mechanical thermal analysis (DMTA) were carried out to analyze the static a viscoelastic behavior of the EPDMs. The tribological properties of the EPDMs were investigated using dry roller (metal) – on – plate (rubber) type tests (ROP). During the ROP tests the normal load was varied. The coefficient of friction (COF) and the temperature were registered online during the tests, the loss volumes were determined after certain test durations. The worn surfaces of the rubbers and of the steel counterparts were analyzed using scanning electron microscope (SEM) to determine the wear mechanisms. Because possible chemical changes may take place during dry sliding due to the elevated contact temperature the chemical composition of the surfaces was also analyzed before and after the tribotests. For the latter investigations X-ray photoelectron spectroscopy (XPS), sessil drop tests and Raman spectroscopy were used. In addition, the dry sliding tribotests were simulated using finite element (FE) codes for the better understanding of the related wear mechanisms. Finally, as the internal damping effect of the elastomers plays a great role in the sliding wear process, their viscoelasticity has been taken into account. The effect of viscoelasticity was shown on example of rolling friction. To study the rolling COF for the EPDM with 30 phr CB (EPDM 30) an FE model was created which considered the viscoelastic behavior of the rubber during rolling. The results showed that the incorporated CB enhanced the mechanical and tribological properties (both COF and wear rate have been reduced) of the EPDMs. Further on, the CB content of the EPDM influences fundamentally the observed wear mechanisms. The wear characteristics changed also with the applied normal load. In case of the EPDM 30 a rubber tribofilm was found on the steel counterpart when tests were performed at high normal loads. Analysis of the chemical composition of the surfaces before and after the wear tests does not result in notable changes. It was demonstrated, that the FE method is powerful tool to model both, the dry sliding and rolling performances of elastomers.

In the present contribution, a general framework for the completely consistent integration of nonlinear dissipative dynamics is proposed, that essentially relies on Finite Element methods in space and time. In this context, fully flexible structures as well as hybrid systems which consist of rigid bodies and inelastic flexible parts are considered. Thereby, special emphasis is placed on the resulting algorithmic fulfilment of fundamental balance equations, and the excellent performance of the presented concepts is demonstrated by means of several representative numerical examples, involving in particular finite elasto-plastic deformations.

The present thesis is concerned with the simulation of the loading behaviour of both hybrid lightweight structures and piezoelectric mesostructures, with a special focus on solid interfaces on the meso scale. Furthermore, an analytical review on bifurcation modes of continuum-interface problems is included. The inelastic interface behaviour is characterised by elastoplastic, viscous, damaging and fatigue-motivated models. For related numerical computations, the Finite Element Method is applied. In this context, so-called interface elements play an important role. The simulation results are reflected by numerous examples which are partially correlated to experimental data.

On the Extended Finite Element Method for the Elasto-Plastic Deformation of Heterogeneous Materials
(2015)

This thesis is concerned with the extended finite element method (XFEM) for deformation analysis of three-dimensional heterogeneous materials. Using the "enhanced abs enrichment" the XFEM is able to reproduce kinks in the displacements and therewith jumps in the strains within elements of the underlying tetrahedral finite element mesh. A complex model for the micro structure reconstruction of aluminum matrix composite AMC225xe and the modeling of its macroscopic thermo-mechanical plastic deformation behavior is presented, using the XFEM. Additionally, a novel stabilization algorithm is introduced for the XFEM. This algorithm requires preprocessing only.