In 2005, Park et al. demonstrated that the 2-fold surface of a d-AlNiCo quasicrystal exhibits an 8-fold frictional anisotropy, as measured by atomic-force microscopy, between the periodic and aperiodic directions [40, 41]. It has been well known that quasicrystals exhibit lower friction than their crystalline counterparts [38, 18, 51, 30, 12, 54]; however, the discovery of the frictional anisotropy allows for a unique opportunity to study the effect of periodicity on friction when chemical composition, oxidation, and wear are no longer variables. The work presented herein is focused on obtaining an understanding of the mechanisms of friction and the dependence of friction on the periodicity of a structure at the atomic level, focusing on the d-AlNiCo quasicrystal studied by Park et al. Using the LAMMPS [44] package to simulate the compression and sliding of an 'adamant' tip, see section 3.3, on a d-AlNiCo quasicrystalline approximant substrate, we have demonstrated, in preliminary results, an 8-fold frictional anisotropy, but in more careful studies the anisotropy is found to be much smaller. The simulations were accomplished using Widom-Moriarty pair potentials to define the interactions between the atoms [36, 56, 55, 9]. The studies presented in this work have shown a clear velocity dependence on the measured frictional response of the quasicrystalline approximant's surface. The final results show between a 1.026-fold and 1.127-fold anisotropy between sliding in the periodic and 'aperiodic' directions, depending on the sliding velocity.

The benefits of intentional friction damping to reduce the occurrence of wear and premature failure of turbomachinery bladed-disk assemblies are well known and many studies on this topic have focused on the analysis and prediction of the complicated nonlinear forced response exhibited by these structures. In this research, extensions of the recently introduced multi-harmonic Hybrid Frequency-Time method are proposed for the efficient analysis of the response of realistic structures featuring displacement-dependent nonlinearities, such as the friction and impact phenomena that may occur in the presence of friction dampers or when two parts of the same structure periodically contact each other. These theoretical extensions are adapted to the study of large scale, industrial bladed-disk structures that may feature cyclic symmetry or mistuning. Two analysis techniques are developed for the modeling of displacement-dependent nonlinearities. In the first technique friction dampers are modeled as nonlinear operators representing the contact forces acting on the blades, from the simple case of monodirectional friction with constant normal load to the more complex case of three dimensional contact with variable normal load. The analysis of the forced response of several nonlinear systems illustrates the capabilities of this approach as well as the complexity of the typical behavior exhibited by friction damped structures. The second technique introduced helps analyze structures experiencing intermittent contact or friction between two parts or sub-components of the same assembly. This method is applied to the study of the forced response of several simple systems and is used with great efficiency to predict the nonlinear behavior of a beam with a crack. This approach also allows the dampers to be modeled realistically as stand-alone components appended to the bladed disk assembly. In this case the bladed disk assembly as well as the friction dampers are modeled as independent structures that interact at their contacting interfaces. This allows the use of detailed finite element models of dampers rather than having to make simplifying assumptions regarding their geometry. These two methods are applied to the study of the nonlinear forced response a realistic bladed-disk assembly featuring a wedge damper model and a structure-like damper model.

The main objective of this research is the development of a volumetric wheel-soil ground contact model that is suitable for mobile robotics applications with a focus on efficient simulations of planetary rover wheels operating on compliant and irregular terrains. To model the interaction between a rover wheel and soft soil for use in multibody dynamic simualtions, the terrain material is commonly represented by a soil continuum that deforms substantially when in contact with the locomotion system of the rover. Due to this extensive deformation and the large size of the contact patch, a distributed representation of the contact forces is necessary. This requires time-consuming integration processes to solve for the contact forces and moments during simulation. In this work, a novel approach is used to represent these contact reactions based on the properties of the hypervolume of penetration, which is defined by the intersection of the wheel and the terrain. This approach is based on a foundation of springs for which the normal contact force can be calculated by integrating the spring deflections over the contact patch. In the case of an elastic foundation, this integration results in a linear relationship between the normal force and the penetration volume, with the foundation stiffness as the proportionality factor. However, due to the highly nonlinear material properties of the soft terrain, a hyperelastic foundation has to be considered and the normal contact force becomes proportional to a volume with a fractional dimension --- a hypervolume. The continuous soil models commonly used in terramechanics simulations can be used in the derivation of the hypervolumetric contact forces. The result is a closed-form solution for the contact forces between a planetary rover wheel and the soft soil, where all the information provided by a distributed load is stored in the hypervolume of interpenetration. The proposed approach is applied to simulations of rigid and flexible planetary rover wheels. In both cases, the plastic behaviour of the terrain material is the main source of energy loss during the operation of planetary rovers. For the rigid wheel model, a penetration geometry is proposed to capture the nonlinear dissipative properties of the soil. The centroid of the hypervolume based on this geometry then allows for the calculation of the contact normal that defines the compaction resistance of the soil. For the flexible wheel model, the deformed state of the tire has to be determined before applying the hypervolumetric contact model. The tire deformation is represented by a distributed parameter model based on the Euler-Bernoulli beam equations. There are several geometric and soil parameters that are required to fully define the normal contact force. While the geometric parameters can be measured, the soil parameters have to be obtained experimentally. The results of a drawbar pull experiment with the Juno rover from the Canadian Space Agency were used to identify the soil parameters. These parameters were then used in a forward dynamics simulation of the rover on an irregular 3-dimensional terrain. Comparison of the simulation results with the experimental data validated the planetary rover wheel model developed in this work.

The first part of this dissertation focuses on the development, implementation and validation of models that capture the behavior of joints in a realistic manner. These models are presented within the framework of finite element based, nonlinear multibody dynamics formulations that ensure unconditional nonlinear stability of the computation for systems of arbitrary topology. The proposed approach can be divided into three parts. First, the joint configuration: this purely kinematic part deals with the description of the configuration of the joint and the evaluation of the relative distance and relative tangential velocity between the contacting bodies. Second, the contact conditions: in most cases, contact at the joint is of an intermittent nature. And finally, the contact forces: this last part deals with the evaluation of the forces that arise at the interface between contacting bodies. The advantage of the proposed approach is that the three parts of the problem can be formulated and implemented independently. Many articulated rotor helicopters use hydraulic dampers, which provide high levels of damping but are also associated with high maintenance costs and difficulties in evaluating their conditions due to the presence of seals, lubricants and numerous moving parts, all operating in a rotating frame. To avoid problems associated with hydraulic dampers, the industry is now switching to elastomeric lead-lag dampers that feature simpler mechanical design, lower part count, and result in "dry" rotors. However, the design of robust elastomeric dampers is hampered by the lack of reliable analytical tools that can predict their damping behavior in the presence of large multi-frequency motions experienced by the rotor and thus the damper. The second part of this dissertation focuses on the development of an elastomeric damper model which predicts the behavior of the elastomeric damper based on a continuum mechanics approach: the configuration of the damper is modeled using a finite element approach, and material behavior is represented by a set of nonlinear constitutive laws and material parameters. The validated finite element model of the elastomeric damper is then coupled with a comprehensive, multibody dynamics analysis code to predict the behavior of complex systems featuring elastomeric components.

Rod seals are one of the most critical components of hydraulic systems. However, the fundamental physics of seal behavior is still poorly understood and the seal designers have virtually no analytical tools with which to predict the behavior of potential seal designs. In pursuit of a comprehensive physics based seal analysis/ design tool, in this work, a multi-scale multi-physics (MSMP) seal model is developed. The model solves the transient problem involving macro-scale viscoelastic deformation mechanics, macro-scale contact, micro-scale two phase fluid mechanics in the sealing zone, micro-scale asperity contact mechanics and micro-scale deformation mechanics of the sealing edge in a strongly coupled manner. The model takes into account surface roughness, mixed lubrication, cavitation and two phase flow, transient squeeze film effects and the dynamic operation as well as the effect of macro/micro/nano scale viscoelasticity. A hybrid finite element-finite volume-statistical computational framework is developed to solve the highly coupled multi-physics interactions of the MSMP model simultaneously. Surface characterization experiments are performed to extract the parameters like RMS roughness, asperity density, autocorrelation length and asperity radius needed by MSMP. To remove the high frequency noise without removing the high frequency real surface features, a wavelet transform based adaptive surface extraction method is implemented. Dynamic mechanical analysis (DMA) is performed to extract the macro-scale viscoelastic parameters of the seal. Through atomic force microscopy (AFM) experiments, the local micro/nano scale elastic moduli were found to be varying within two orders of magnitude higher than the bulk of the polymer. Significant differences in local stiffness, adhesion and the relaxation time scales of individual surface asperities were also observed. With the MSMP model, dynamic seal performance was analyzed. The results confirmed the mixed lubrication and the effect of surface roughness. Thicker fluid films during instroke and cavitation during the outstroke were found to be important for non-leakage. Seal behavior was a function of the complex dual dependence on the time varying sealed pressure and hydrodynamic effects. Viscoelasticity is seen to critically affect the leakage and friction characteristics. It produces thicker fluid films and produces a significant increase in Poiseuille component of flow during instroke. Ignoring viscoelasticity leads to under-prediction of the time required to reach the zero leakage state. Several high pressure - high frequency sealing applications were analyzed. In such applications, a new phenomenon of "secondary contact" was observed. Viscoelastic creep was seen to critically affect the contact pressure and hence the friction characteristics. In high frequency applications, viscoelasticity induced significant differences in Poiseuille flow and friction force from cycle to cycle. Cycle frequency was seen to play an important role in governing visco-elastohydrodynamics and the leakage of such seals. The seals need to be designed by considering the relationship between relaxation time scales of the polymer and the cycle frequencies. Study also revealed the presence of characteristics like "critical temperature" and "critical frequency". Using the multi-physics modeling capability of MSMP framework, several novel seal designs using smart materials like piezo-ceramic embedded polymers are proposed and analyzed. The MSMP computational framework developed here has a great potential to be used as a stand-alone seal design and analysis software in academic and industrial research.

Nowadays, high demands are made on filling materials in modern dentistry: Durability, Reliability &Aesthetic Requirements Thus, a group of physicists and an independent practicing dentist investigated 11 different teeth fillings (composite materials) as used in modern dental practices according to their stability and ability to withstand contact loadings.

<p>In the finite element simulation of problems with contact there arises</p><p>the need to change the mesh and continue the simulation on a new mesh.</p><p>This is encountered when the mesh has to be changed because the original mesh experiences severe distortion or the mesh is adapted to minimize errors in the solution. In such instances a crucial component is the transfer of data from the old mesh to the new one. </p><p>This work proposes a strategy by which such remeshing can be accomplished in the presence of mortar-discretized contact, </p><p>focusing in particular on the remapping of contact variables which must occur to make the method robust and efficient. </p><p>By splitting the contact stress into normal and tangential components and transferring the normal component as a scalar and the tangential component by parallel transporting on the contact surface an accurate and consistent transfer scheme is obtained. Penalty and augmented Lagrangian formulations are considered. The approach is demonstrated by a number of two and three dimensional numerical examples.</p> / Dissertation

<p>The main objectives of this research are: (i) to elaborate a unified nonlinear viscoelastic model for rubber-like materials, in finite strain, accounting for material softening under deformation, and for damage induced anisotropy, (ii) to conceive, implement and test, simple, robust and efficient frictional rolling and sliding contact algorithms, in steady-state, as alternatives to existing, general purpose, contact solving strategies, (iii) to develop and verify high fidelity and computationally efficient modeling tools for isotropic and anisotropic viscoelastic objects in steady-state motion, (iv) to investigate, numerically and through experimentation, the influence of various material parameters, including material nonlinearities such at the Payne effect and the Mullins effect, as well as geometric parameters and contact surface conditions, on viscoelastic rolling resistance, and (iv) to explore, analytically and through experimentation, the conditions under which favorable mechanical synergies occur between material components and develop novel composites with improved structural performances.</p><p>A new constitutive model that unifies the behavioral characterizations of rubber-like materials in a broad range of loading regimes is proposed. The model reflects two fundamental aspects of rubber behavior in finite strain: (i) the Mullins effect, and (ii) hyper-viscoelasticity with multiple time scales, including at high strain rates. Suitable means of identifying the system's parameters from simple uniaxial extension tests are explored. A directional approach extending the model to handle softening induced anisotropy is also discussed.</p><p>Novel, simple, and yet robust and efficient algorithms for solving steady-state, frictional, rolling/sliding contact problems, in two and three dimensions are presented. These are alternatives to powerful, well established, but in particular instances, possibly `cumbersome' general-purpose numerical techniques, such as finite-element approaches based on constrained optimization. The proposed algorithms are applied to the rolling resistance of cylinders and spheres.</p><p>Two and three-dimensional boundary element formulations of isotropic, transversely isotropic, and fully orthotropic, compressible and incompressible, viscoelastic layers of finite thickness are presented, in a moving frame of reference. The proposed formulations are based on two-dimensional Fourier series expansions of relevant mechanical fields in the continuum of the layers and support any linear viscoelastic material model characterized by general frequency-domain master-curves. These modeling techniques result in a compliance matrix for the upper boundary of the layers, including the effects of steady-state motion. Such characterizations may be used as components in various problem settings to generate sequences of high fidelity solutions for varying parameters. These are applied, in combination with appropriate contact solvers, to the rolling resistance of rigid cylinders and spheres.</p><p>The problem of a viscoelastic sphere moving across a rigid surface is significantly more complicated than that of a rigid indenter on a viscoelastic plane. The additional difficulties raised by the former may explain why previous work on this topic is so sparse. A new boundary element formulation for the multi-layered viscoelastic coating of a rigid sphere is developed. The model relies on the assumption of a relatively small contact surface in order to decouple equilibrium equations in the frequency domain. It is applied in combination with an adapted rolling contact solving strategy to the rolling resistance of a coated sphere.</p><p>New modeling approaches yielding rolling resistance estimates for rigid spheres (and cylinders) on viscoelastic layers of finite thicknesses are also introduced, as lower-cost alternatives to more comprehensive solution-finding strategies, including those proposed in this work. Application examples illustrate the capabilities of the different approaches over their respective ranges of validity.</p><p>The computational tools proposed in this dissertation are verified by comparison to dynamic finite element simulations and to existing solutions in limiting cases. The dependencies of rolling resistance on problem parameters are explored. It is for instance shown that, on orthotropic layers, the dissipated power varies with the direction of motion, which suggests new ways of optimizing the level of damping in various engineering applications of very high impact. Interesting lateral viscoelastic effects resulting from material asymmetry are unveiled. These phenomena could be harnessed to achieve smooth and `invisible' guides across three-dimensional viscoelastic surfaces, and hence suggest new ways of controlling trajectories, with a broad range of potential applications.</p><p>A new experimental apparatus is designed and assembled to measure viscoelastic rolling resistance. Experiments are conducted by rolling steel balls between sheets of rubber. Principal sources of measurement error, specific to the device, are discussed. Rolling resistance predictions are obtained using the computational tools presented in this dissertation, and compared to the measurements. Interesting conclusions are drawn regarding the fundamental influence of the Payne effect on viscoelastic rolling friction.</p><p>The work presented in this dissertations finally touches on the mechanical behavior of casing-infill composite tubes, as potential new lightweight structural elements. The axial behavior of composite circular tubes is addressed analytically. The influence of material parameters and geometry on structural performances are revealed and presented in original graphical forms. It is for instance shown that significantly improved overall stiffness and capacity at yield can be obtained using a moderately soft and highly auxetic infill, which further highlights the need to develop new lightweight auxetic materials, without compromising their stiffness. It is furthermore concluded that limited mechanical synergies can be expected in metal-polymer composite tubes, within the linear range of the materials involved. This prediction is confirmed by a bending experiment conducted on an Aluminum-Urethane composite tube. The experiment however reveals unexpected and quite promising mechanical synergies under large deformations. This novel composite has a potential influence on the design and performance of lightweight protecting structures against shocks and accelerations due to impacts, which justifies that it be characterized further.</p> / Dissertation

The work presented in this thesis is devoted to the study of mechanism of tyre force generation and its influence on handling dynamics of ground vehicles. The main part of the work involves the development of tyre models for use under steady-state and transient operating conditions. The general capability of these models is assessedin a full vehicle simulation environment. The interaction between tyre and vehicle dynamics is critically evaluated and the observed vehicle behaviour is related to the inherent characteristics of different tyre models. In the field of steady-state tyre modelling, two versions of a numerical tyre model are developed. The modelling procedure is carried out in accordance with the viscoelastic properties of rubber, which influence the mechanical properties of the tyre structure and play a significant role in the determination of friction in the tyre contact patch. Whilst the initial simple version of the tyre model assumes a parabolic pressure distribution along the contact, a later more elaborate model employs a numerical method for the calculation of the actual normal pressure distribution. The changes in the pressure distribution as a result of variations in the rolling velocity and normal load influence mainly the levels of self-aligning moment, whilst the force characteristics remain practically unaffected. The adoption of a velocity dependent friction law explains the force generating behaviour of tyres at high sliding velocities. The analysis is extended to the area of transient tyre behaviour with the development of a tyre model appropriate for the study of transient friction force generation within the contact patch. The model incorporates viscoelasticity and inertial contributions, and incorporates a numerical stick-slip law. These characteristics are combined together for the successful simulation of transient friction force generation. The methodologies developed for the modelling of transient friction and steady-state tyre force generation are combined and further extended in order to create a generic transient tyre model. This final model incorporates a discretised flexible viscoelastic belt with inertia and a separate fully-dynamic discretised tread, also with inertia and damping, for the simulation of actual prevailing conditions in the contact patch. The generic tyre model appears to be capable of performing under a variety of operating conditions, including periodic excitations and transient inputs which extend to the non-linear range of tyre behaviour. For the evaluation of the influence of the aforementioned tyre models on the handling responses of a vehicle, a comprehensive vehicle model is developed, appropriate for use in handling simulations. The two versions of the steady-state models and the generic transient model are interfaced with the vehicle model, and the response of the vehicle to a step-steer manoeuvre is compared with that obtained using the Magic Formula tyre model. The comparison between the responses is facilitated by the definition of a new measure, defined as the non-dimensional yaw impulse. It is found that the transience involved in tyre behaviour may largely affect the response of a vehicle to a prescribed input.

The main objective of this research is the development of a volumetric wheel-soil ground contact model that is suitable for mobile robotics applications with a focus on efficient simulations of planetary rover wheels operating on compliant and irregular terrains. To model the interaction between a rover wheel and soft soil for use in multibody dynamic simualtions, the terrain material is commonly represented by a soil continuum that deforms substantially when in contact with the locomotion system of the rover. Due to this extensive deformation and the large size of the contact patch, a distributed representation of the contact forces is necessary. This requires time-consuming integration processes to solve for the contact forces and moments during simulation. In this work, a novel approach is used to represent these contact reactions based on the properties of the hypervolume of penetration, which is defined by the intersection of the wheel and the terrain. This approach is based on a foundation of springs for which the normal contact force can be calculated by integrating the spring deflections over the contact patch. In the case of an elastic foundation, this integration results in a linear relationship between the normal force and the penetration volume, with the foundation stiffness as the proportionality factor. However, due to the highly nonlinear material properties of the soft terrain, a hyperelastic foundation has to be considered and the normal contact force becomes proportional to a volume with a fractional dimension --- a hypervolume. The continuous soil models commonly used in terramechanics simulations can be used in the derivation of the hypervolumetric contact forces. The result is a closed-form solution for the contact forces between a planetary rover wheel and the soft soil, where all the information provided by a distributed load is stored in the hypervolume of interpenetration. The proposed approach is applied to simulations of rigid and flexible planetary rover wheels. In both cases, the plastic behaviour of the terrain material is the main source of energy loss during the operation of planetary rovers. For the rigid wheel model, a penetration geometry is proposed to capture the nonlinear dissipative properties of the soil. The centroid of the hypervolume based on this geometry then allows for the calculation of the contact normal that defines the compaction resistance of the soil. For the flexible wheel model, the deformed state of the tire has to be determined before applying the hypervolumetric contact model. The tire deformation is represented by a distributed parameter model based on the Euler-Bernoulli beam equations. There are several geometric and soil parameters that are required to fully define the normal contact force. While the geometric parameters can be measured, the soil parameters have to be obtained experimentally. The results of a drawbar pull experiment with the Juno rover from the Canadian Space Agency were used to identify the soil parameters. These parameters were then used in a forward dynamics simulation of the rover on an irregular 3-dimensional terrain. Comparison of the simulation results with the experimental data validated the planetary rover wheel model developed in this work.