Les géomatériaux tels les roches et le béton ont la particularité de s’amollir sous chargement dynamique, c.-à-d. que la vitesse du son diminue avec l’amplitude de forçage. Afin de reproduire ce comportement, un modèle de milieu continu à variables internes est proposé. Il est composé d’une loi de comportement donnant l’expression de la contrainte, et d’une équation d’évolution pour la variable interne. La viscoélasticité non linéaire de type Zener est prise en compte par l’ajout de variables internes supplémentaires. Les équations du mouvement forment un système de lois de conservation non linéaire et non homogène. Le système d’équations aux dérivées partielles est résolu numériquement à l’aide de la méthode des volumes finis. Une solution analytique du problème de Riemann de l’élastodynamique non linéaire est explicitée. Elle est utilisée pour évaluer les performances des méthodes numériques. Les résultats numériques sont en accord qualitatif avec les résultats expérimentaux d’expériences de résonance (NRUS) et d’acousto-élasticité dynamique (DAET). Des méthodes similaires sont développées en 2D pour réaliser des simulations de propagation d’ondes. Dans le cadre des méthodes de continuation reposant sur la décomposition en harmoniques, une méthode numérique est développée pour le calcul de solutions périodiques. Sur la base d’une discrétisation éléments finis des équations du mouvement, cette méthode fréquentielle donne des simulations de résonance rapides, ce qui est utile pour mener des validations expérimentales. / Geomaterials such as rocks and concrete are known to soften under a dynamic loading, i.e., the speed of sound diminishes with forcing amplitudes. To reproduce this behavior, an internal-variable model of continuum is proposed. It is composed of a constitutive law for the stress and an evolution equation for the internal variable. Nonlinear viscoelasticity of Zener type is accounted for by using additional internal variables. The equations of motion write as a nonlinear and nonhomogeneous system of conservation laws. This system of partial differential equations is solved numerically using finite-volume methods. An analytical solution to the Riemann problem of nonlinear elastodynamics is provided, which is used to benchmark the performances of the numerical methods. Numerical results are in qualitative agreement with experimental results from resonance experiments (NRUS) and dynamic acousto-elastic testing (DAET). Similar methods are developed in 2D to perform wave propagation simulations. In the framework of harmonic-based continuation methods, a numerical method is developed for the computation of periodic solutions. Based on a finite element discretization of the equations of motion, this frequency-domain method provides fast resonance simulations, which is useful to carry out experimental validations.

<p><p><p>This thesis aims toward developing strategies in the area of structural optimization and to implement these strategies in design processes. At</p><p> </p><em>GM Powertrain Sweden </em>where powertrains are designed and developed, two designs of a differential housing have been chosen for this thesis. The main tasks have been to perform a topology optimization of a model early in a design process, and a shape optimization on a model late in a design process. In addition the shape optimization strategies have also been applied on a fork shifter. This thesis covers the theory of different optimization strategies in general. The optimization processes are explained in detail and the results from the structural optimization of the differential housings as well as the fork shifter are shown and evaluated. The evaluation of the thesis provides enough arguments to suggest an implementation of the optimization strategies in design processes at <em>GM Powertrain</em><p>. A Structural Optimization group has great potential of closing the gap between structural designers and structural analysis engineers which in long terms mean that better structures can be developed in less time. To be competitive in the automotive industry these are two of the most important factors for being successful.</p></p></p>

This dissertation concerns failure modelling with material imperfections and element erosion in finite element analyses. The aim has been to improve the element erosion technique, which is simple to use and implement and also computationally inexpensive. The first part of the dissertation serves as an introduction to the topic and as a summary of the methodologies presented in the following part. The second part consists of seven appended papers. In paper A the standard element erosion technique is used for projectile penetration. In papers B and C a methodology that accounts for size effects is developed and applied to crack initiation in armour steel and tungsten carbide. A methodology to better predict the stress state at crack tips with coarse meshes is presented and applied to armour steel in paper D. Papers E and F concern the development of selective mass scaling which allows for larger time steps in explicit methods. Finally, in paper G the previously presented methodologies are used in combination and validated against experimental results on tungsten carbide. The computations show good agreement with the experimental results on failure initiation for both materials, while the computational results on the propagation of cracks show better agreement for the armour steel than for the tungsten carbide. / On the day of the public defence of the doctoral thesis, the status of articles I, III and IV was Accepted and article VII was Submitted.

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.