<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.

Today, nonhomogeneous materials are used in many technological applications. Nonhomogeneity can be introduced intentionally in order to improve the thermomechanical performance of material systems. The concept of functionally graded materials (FGMs) is an example of such an application. Nonhomogeneity can also be an intrinsic property of some of the natural materials such as natural soil. The main interest in this study is on the contact mechanics of nonhomogeneous surfaces. There is an extensive volume of literature on the contact mechanics of nonhomogeneous materials. In most of these studies, the elastic gradation is assumed to exist in depth direction. But, it is known that elastic gradation may also exist laterally. This may either occur naturally as in the case of natural soil or may be induced as a result of the applied processing technique as in the case of FGMs. The main objective in this study is therefore to examine the effect of the lateral nonhomogeneities on the contact stress distribution at the surface of an elastically graded material. In the model developed to examine this problem, a laterally graded surface is assumed to be in sliding contact with a rigid stamp of arbitrary profile. The problem is formulated using the theory of elasticity and reduced to a singular integral equation. The integral equation is solved numerically using a collocation approach. By carrying out parametric studies, the effects of the nonhomogeneity constants, coefficient of friction and stamp location on the contact stress distribution and on the required contact forces are studied.

ABSTRACT CONTACT MECHANICS OF GRADED MATERIALS WITH TWODIMENSIONAL MATERIAL PROPERTY VARIATIONS G&ouml / kay, Kemal M.S., Department of Mechanical Engineering Supervisor: Asst. Prof. Dr. Serkan Dag September 2005, 62 pages Ceramic layers used as protective coatings in tribological applications are known to be prone to cracking and debonding due to their brittle nature. Recent experiments with functionally graded ceramics however show that these material systems are particularly useful in enhancing the resistance of a surface to tribological damage. This improved behavior is attributed to the influence of the material property gradation on the stress distribution that develops at the contacting surfaces. The main interest in the present study is in the contact mechanics of a functionally graded surface with a two &ndash / dimensional spatial variation in the modulus of elasticity. Poisson&rsquo / s ratio is assumed to be constant due to its insignificant effect on the contact stress distribution [30]. In the formulation of the problem it is assumed that the functionally graded surface is in frictional sliding contact with a rigid flat stamp. Using elasticity theory and semi-infinite plane approximation for the graded medium, the problem is reduced to a singular integral equation of the second kind. Integral equation is solved numerically by expanding the unknown contact stress distribution into a series of Jacobi polynomials and using suitable collocation points. The developed method is validated by providing comparisons to a closed form solution derived for homogeneous materials. Main numerical results consist of the effects of the material nonhomogeneity parameters, coefficient of friction and stamp size and location on the contact stress distribution.

Univ., Habil.-Schr.--Hannover, 2002. / Literaturverz. S. [174] - 183. Originally publ. as vol. 3 of the series "Lecture notes in applied mechanics", Springer- Verl., Berlin 2002.

Thesis (Ph. D.)--Ohio State University, 2008. / Title from first page of PDF file. Includes bibliographical references (p. 189-198).

Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2008. / Committee Chair: Rick Neu; Committee Member: Itzhak Green; Committee Member: Jeffrey Streator

This Thesis develops a mathematical model for predicting the thermal response in the surgical drilling of bone. The model accounts for the bone, chip and drill bit interactions by providing a detailed account of events within a cylindrical control volume enveloping the drill, the cut bone chip within the drill bit flute and the solid bone. Lumped parameter approach divides the control volume into a number of cells and cells within the sub-volumes representing the drill solid, the bone chip and the bone solid are allowed to interact. The contact mechanics of rough surfaces is used to model chip-flute and chip-bone frictional interaction. In this way not only the quantification of friction due to sliding contact of chip-flute and chip-bone rough surface contact are treated, but also the contact thermal resistances between the rubbing surfaces are included in the model. A mixed combination of constant and adaptive mesh is employed to permit the simulation of the heat transfer as the drill bit penetrates deeper into the bone during a drilling process. Using the model the effect of various parameters on the temperature rise in bone, drill and the chip are investigated. It is found that maximum temperature within the bone occurs at the location adjacent to the corner of the drill-tip and drill body. The results of the model are found to agree favorably with the experimental measurements reported in the existing literature on surgical drilling.

Doctor of Philosophy / Department of Mechanical and Nuclear Engineering / Kevin B. Lease / The overall goal of this study was to assess the effects of surface chemistry on adhesion of polymeric systems underwater. The adhesion is quantified by the thermodynamic work of adhesion (W) when two surfaces are approached and the energy release rate (G) when the surfaces are separated. For some polymeric systems there is a difference between W and G, referred to as adhesion hysteresis. For this study an experimental approach based upon Johnson-Kendall-Roberts (JKR) theory of contact mechanics was utilized to evaluate how surface chemistry affects the adhesion behavior (both W and adhesion hysteresis) in the presence of water. The interfacial interactions were also studied in air and contrasted to those obtained underwater. To accomplish the overall goal of this research, this study was divided into two phases where smooth model surfaces with disparate surface chemistries were used. The model surfaces in the first part included poly(dimethysiloxane) (PDMS), glass surfaces chemically functionalized to display hydrophilic to medium to hydrophobic characteristics, and thin films of wood-based biopolymers. The functionalities used to modify glass surfaces included polyethylene oxide (PEO) with hydrophilic nature; amine, carbomethoxy, and mercapto (thiol) with intermediate characteristics; cyclohexyl, fluorocarbon, and methyl with hydrophobic behavior. In addition to these surfaces, flat PDMS and clean glass surfaces were also used for means of comparison. The wood-derived polymers included two different cellulose types (natural cellulose and regenerated cellulose) as well as one lignin surface (from hardwood milled lignin). These surfaces were probed with native PDMS hemispheres, which are hydrophobic. The results showed that in air the value of W for all model surfaces was independent of the surface chemistry, except fluorocarbon which was lower. Underwater W was significantly affected by the surface hydrophilicity/ hydrophobicity. The adhesion hysteresis both in air and underwater was significantly dependent on the structure of the probed surface. For the second phase PDMS hemispheres were chemically modified with amine functionality to probe model surfaces with hydrophilic and intermediate behavior. These surfaces included glass surfaces functionalized with PEO and amine as well as PDMS sheets that were functionalized with amine. Native PDMS flat surfaces were also used for means of comparison. The results showed that for the selected surfaces both W and hysteresis were affected by the surface chemistry in both media.