This thesis concerns the analysis of dynamical systems suitable to be modelled by piecewise-smooth differential equations. In such systems the continuous-in-time dynamics is interrupted by discrete-in-time jumps in the state or governing equations of motion. Not only can this framework be used to describe existing systems with strong nonlinear behaviour such as impacts and friction, but the non-smooth properties can be exploited to design new mechanical devices. As suggested in this work it opens up the possibility of, for example, fast limit switches and energy transfer mechanisms. Particularly, the dynamics at the onset of low-velocity impacts in systems with recurrent dynamics, so called grazing bifurcations in impact-oscillators, are investigated. As previous work has shown, low-velocity impacts is a strong source of instability to the dynamics, and efforts to control the behaviour is of importance. This problem is approached in two ways in this work. One is to investigate the influence of parameter variations on the dynamic behaviour of the system. The other is to implement low-cost control strategies to regulate the dynamics at the grazing bifurcation. The control inputs are of impulsive nature, and utilizes the natural dynamics of the system to the greatest extent. The scientific contributions of this work is collected in five appended papers. The first paper consists of an experimental verification of a map that captures the correction to the smooth dynamics induced by an impact, known in the literature as the discontinuity map. It is shown that the lowest order expansion of the map accurately captures the transient growth rate of impact velocities. The second paper presents a constructive proof of a control algorithm for a rather large class of impact oscillators. The proof is constructive in the sense that it gives control parameters which stabilizes the dynamics at the onset of low-velocity impacts. In the third paper a piecewise-smooth quarter-car model is derived, and the control strategy is implemented to reduce impact velocities in the suspension system. In the fourth and fifth papers the grazing bifurcation of an impact oscillator with dry friction type damping is investigated. It turns out that the bifurcation is triggered by the disappearance of an interval of stable stick solutions. A condition on the parameters of the system is derived which differentiates between stable and unstable types of bifurcation scenarios. Additionally, a low-cost control strategy is proposed, similar to the one previously mentioned, to regulate the bifurcation scenario. / QC 20100811

In this work the influence of Under Sleeper Pads on the dynamic forces on a railway track is investigated. A special interest is devoted to the effect of using Under Sleeper Pads in a railway track with changing vertical stiffness. The contact force between wheel and rail and the ballast contact forces are examined. For the investigation a finite element model with the length of thirty sleepers is created and calculations are performed with the software LS-DYNA. Three different cases of varying vertical track stiffness are studied: the transition from an embankment to a bridge, a randomly varying track stiffness along the railway track and hanging sleepers.

This thesis presents a continuum model for asphalt concrete incorporating non- linear viscoelasticity, viscoplasticity, mechanically-induced damage and moisture- induced damage. The Schapery single-integral viscoelastic model describes the nonlinear viscoelastic response. The viscoplastic model of Perzyna models the time- dependent permanent deformations, using a Drucker-Prager yield surface which is modified to depend on the third deviatoric stress invariant to include more complex dependence on state of stress. Mechanically-induced damage is modeled using continuum damage mechanics, using the same modified Drucker-Prager law to determine damage onset and growth. A novel moisture damage model is proposed, modeling moisture-induced damage using continuum damage mechanics; adhesive moisture- induced damage to the asphalt mastic-aggregate bond and moisture-induced cohesive damage to the asphalt mastic itself are treated separately. The analytical model is implemented numerically for three-dimensional and plane strain finite element analyses, and a series of simulations is presented to show the performance of the model and its implementation. Sensitivity studies are conducted for all model parameters and results due to various simulations corresponding to laboratory tests are presented. In addition to the continuum model, results are presented for a micromechanical model using the nonlinear-viscoelastic-viscoplastic-damage model for asphalt mastic and a linear elastic model for aggregates. Initial results are encouraging, showing the strength and stiffness of the mix as well as the failure mode varying with moisture loading. These initial results are provided as a an example of the model's robustness and suitability for modeling asphalt concrete at the mix scale.

<p>In this work the influence of Under Sleeper Pads on the dynamic forces on a railway track is investigated. A special interest is devoted to the effect of using Under Sleeper Pads in a railway track with changing vertical stiffness. The contact force between wheel and rail and the ballast contact forces are examined. For the investigation a finite element model with the length of thirty sleepers is created and calculations are performed with the software LS-DYNA. Three different cases of varying vertical track stiffness are studied: the transition from an embankment to a bridge, a randomly varying track stiffness along the railway track and hanging sleepers.</p>

<p>This thesis concerns optimization of structures considering various uncertainties. The overall objective is to find methods to create solutions that are optimal both in the sense of handling the typical load case and minimising the variability of the response, i.e. robust optimal designs.</p><p>Traditionally optimized structures may show a tendency of being sensitive to small perturbations in the design or loading conditions, which of course are inevitable. To create robust designs, it is necessary to account for all conceivable variations (or at least the influencing ones) in the design process.</p><p>The thesis is divided in two parts. The first part serves as a theoretical background to the second part, the two appended articles. This first part includes the concept of robust design, basic statistics, optimization theory and meta modelling.</p><p>The first appended paper is an application of existing methods on a large industrial example problem. A sensitivity analysis is performed on a Scania truck cab subjected to impact loading in order to identify the most influencing variables on the crash responses.</p><p>The second paper presents a new method that may be used in robust optimizations, that is, optimizations that account for variations and uncertainties. The method is demonstrated on both an analytical example and a Finite Element example of an aluminium extrusion subjected to axial crushing.</p> / ROBDES

The development of adaptive finite element procedures for the solution of geometrically and physically nonlinear problems in structural mechanics is very important for the augmentation of the efficiency of FE-codes. In this contribution methods of mesh refinement as well as mesh coarsening are presented for a material model considering finite elasto-plastic deformations. For newly generated elements stresses, strains and internal variables have to be calculated. This implies the determination of the nodal values as well as the Gaussian point values of the new elements based on the transfer of data from the former mesh. Analogously, the coarsening of less important elements necessitates the determination of these values for the newly created father elements.

Irradiation induces a high concentration of defects in the structural materials of nuclear reactors, which are typically of body-centered cubic Iron (BCC Fe) and its alloys. The primary effect of irradiation is hardening which is caused by the blocking of dislocations with defects and defect clusters like point defects, self-interstitial loops, and voids. The dislocation-defect interactions are atomistic in nature due to the very small length and time scales involved, i.e., of the order of nanometers and picoseconds. To predict the effect of dislocation-defect interactions on the macroscopic mechanical and plastic behavior of the material, it is critically important to develop robust coupling schemes by which accurate atomic level physics of the rate-limiting kinetic processes can be informed into a coarse-grained model such as crystal plasticity. In this thesis we will develop an atomistically informed constitutive model. Relevant atomistic processes are identified from molecular dynamics simulations. The respective unit process studies are conducted using atomistic reaction pathway sampling methods like Nudged Elastic Band method. Stress-dependent activation energies and activation volumes are computed for various rate-liming unit processes like thermally activated dislocation motion via kinkpair nucleation, dislocation pinning due to self interstitial atom, etc. Constitutive laws are developed based on transition state theory, that informs the atomistically determined activation parameters into a coarse-grained crystal plasticity model. The macroscopic deformation behavior predicted by the crystal plasticity model is validated with experimental results and the characteristic features explained in the light of atomistic knowledge of the constituting kinetics. We also investigate on unique irradiation induced defects such as stacking fault tetrahedra, that are formed under non-irradiated condition. This thesis also includes our work on materials with internal interfaces that can resist irradiation induced damage. Overall, the research presented in this thesis involves the implementation and development of novel computational paradigm that encompasses computational approaches of various length and time scales towards robust predictions of the mechanical behavior of irradiated materials.

This thesis is concerned with the mathematical modelling of elastic-plastic deformation in regimes of stress far exceeding the yield stress. Such scenarios are typically encountered in violent impact testing, where millimetre-thick samples of metal are subjected to pressures on the order of the bulk modulus of the material. We begin with an overview of violent impact testing, with particular attention paid to a specific class of experiments known as isentropic compression experiments (ICEs), which will provide motivation for the mathematical modelling and analysis in subsequent chapters. In chapter 2, by appealing to sound notions from rational mechanics and thermodynamics, we construct a mathematical model which aims to encapsulate the essential phenomena involved in violent elastic-plastic deformation. This is followed in chapter 3 with a numerical analysis of the mathematical model in uniaxial strain, which is the geometry relevant ICEs. In chapters 4 and 5, we corroborate the observations made in chapter 3 via a systematic mathematical analysis. In particular, our focus will be on the elastic and plastic waves that can propagate through finite metal samples during isentropic compression. Finally, in chapter 6, we explore the applicability of our model to other geometries, specifically the radially axisymmetric expansion of a circular cavity embedded in an infinite elastic-plastic medium. We conclude with a summary of our findings and suggest some avenues for future investigation.

Experimental micromechanics of materials is a branch of science that seeks to build tight connections between composition, structure, processing and performance of materials under specific operating conditions required for particular technology applications. The present project is focused on the development of techniques that use the combination of electron, ion and X-ray microscopies to study the deformation behaviour of a particularly important class of metallic alloys used in the manufacture of aeroengines, namely, the so-called Ni-base superalloys. The complex hierarchical structure of these materials means that their macroscopic response is controlled to a great extent by the phenomena that play out on very fine scales, from angstroms (lattice spacing dimension) to nanometres (precipitates, phase boundaries, dislocations, chemical inhomogeneities) to microns (grains and their boundaries, defects and their clusters, dislocation pileups) to millimetres (component scale). Understanding the fine structure and deformation behaviour requires the development of specially configured experimental setup that allow the observation and quantification of deformation to external loading. In this study, FIB-SEM methods for sample characterization and fabrication were combined with synchrotron-based X-ray diffraction and imaging techniques, and backed up by theoretical analysis and numerical simulation, to elucidate the origins of the strength of these alloys. Micropillar compression tests using in-SEM nanoindentation were used to reveal the size dependence of the apparent strength, and connection was made with the dislocation-mediated crystal slip to provide an explanation of the observed Hall-Petch type dependence with a modified Hall-Petch equation considering both intrinsic and extrinsic characteristic lengths introduced. X-ray scattering was used in the polychromatic micro-Laue mode and using Bragg coherent diffractive imaging to reveal the crystal distortion arising due to plastic deformation. A Discrete dislocation dynamics in the 2.5D formulation was used to obtain a model description of the observed phenomena. The key outcome of the work presented in this thesis lies in the successful development of advanced observational tools and relevant theoretical or computational models for mesoscale plasticity problems for crystal with complex microstructure.

abstract: The objective of this research is to develop robust, accurate, and adaptive algorithms in the framework of the extended finite element method (XFEM) for fracture analysis of highly heterogeneous materials with complex internal geometries. A key contribution of this work is the creation of novel methods designed to automate the incorporation of high-resolution data, e.g. from X-ray tomography, that can be used to better interpret the enormous volume of data generated in modern in-situ experimental testing. Thus new algorithms were developed for automating analysis of complex microstructures characterized by segmented tomographic images. A centrality-based geometry segmentation algorithm was developed to accurately identify discrete inclusions and particles in composite materials where limitations in imaging resolution leads to spurious connections between particles in close contact.To allow for this algorithm to successfully segment geometry independently of particle size and shape, a relative centrality metric was defined to allow for a threshold centrality criterion for removal of voxels that spuriously connect distinct geometries. To automate incorporation of microstructural information from high-resolution images, two methods were developed that initialize signed distance fields on adaptively-refined finite element meshes. The first method utilizes a level set evolution equation that is directly solved on the finite element mesh through Galerkins method. The evolution equation is formulated to produce a signed distance field that matches geometry defined by a set of voxels segmented from tomographic images. The method achieves optimal convergence for the order of elements used. In a second approach, the fast marching method is employed to initialize a distance field on a uniform grid which is then projected by least squares onto a finite element mesh. This latter approach is shown to be superior in speed and accuracy. Lastly, extended finite element method simulations are performed for the analysis of particle fracture in metal matrix composites with realistic particle geometries initialized from X-ray tomographic data. In the simulations, particles fracture probabilistically through a Weibull strength distribution. The model is verified through comparisons with the experimentally-measured stress-strain response of the material as well as analysis of the fracture. Further, simulations are then performed to analyze the effect of mesh sensitivity, the effect of fracture of particles on their neighbors, and the role of a particles shape on its fracture probability. / Dissertation/Thesis / Doctoral Dissertation Aerospace Engineering 2015