<p>There have been considerable requirements for improved products of sheet metal in automobile industry. A quick and economical route to new products is to design novel surface textures of varying scales for improved product enhancement in better optical appearance and formability. The critical deformation in the surface texturing is on the order of only a few microns, and can not be accurately predicted by the classical plasticity due to the size effect. The theory of strain gradient plasticity has been developed to capture the size effect based on the concept of geometrically necessary dislocations (GNDs). A selected strain gradient theory has been implemented into the finite element (FE) model to simulate the surface texturing process. A 3D FE model was developed to simulate the rolling process of sheet metal which has band-type feature on the original surface. The numerical results show that a textured roller can efficiently modify the band-type feature without changing the whole mechanical property of the sheet. Size effect has significant contribution to the magnitude of the rolling force. A FE model was developed to simulate the tensile test of the sheet with textured surface. A textured surface of the sheet is prepared through the indention on the sheet surface. The results show that the textured surface becomes harder due to the strain gradient effect, and finally improves the formability of the sheet.</p> / Master of Applied Science (MASc)

At micrometer length scales of material removal, size effect is observed in mechanical micro-cutting where the energy per unit volume i.e. specific cutting energy increases nonlinearly as the uncut chip thickness is reduced from several hundred microns to a few microns (or less). There is no consensus in the literature on the cutting mechanism that causes this size effect. Noticeable discrepancy is also observed in the surface roughness produced at small feeds in micro-turning between the theoretical and the measured roughness. To date, there has been little effort made to develop a detailed process model for micro-cutting to accurately predict the size effect in specific cutting energy, and to develop a fundamental understanding of surface generation at the low feeds typical of micro-cutting processes. The main objective of this thesis is therefore to develop a predictive process model of micro-cutting of ductile metals that is capable of accurately predicting the size effect in specific cutting energy based on strain gradient based material strengthening considerations. In addition, this thesis attempts to explain the discrepancy between the theoretical and measured surface roughness at small feeds in micro-turning via a model that accounts for the size effect due to material strengthening. A coupled thermo-mechanical finite element model formulation incorporating strain gradient plasticity is developed to simulate orthogonal micro-cutting process. The thermo-mechanical model is experimentally validated in orthogonal micro-cutting of a strain rate insensitive aluminum alloy Al5083-H116. The model is then used to analyze the contributions of two major material strengthening factors to the size effect in specific cutting energy: strain gradient and temperature. The effects of cutting edge radius on the specific cutting energy and its role relative to the material length scale arising from strain gradient plasticity are also examined. A surface roughness model for micro-turning that incorporates the effects of kinematic roughness, cutting edge roughness and surface roughening due to plastic side flow is developed and shown to explain the observed discrepancy between the theoretical and measured surface roughness in micro-cutting. In addition, the model is found to accurately capture the increase in surface roughness at very low feeds.

Quartzite samples taken in the east part of Krkonoše-Jizera Massif belong to metasedimentary cover of paraautochtonous unit. Rocks underwent a polyphase deformation which established a strong shape preffered orientation (SPO) of quartz grains. In folded quartz veins, deformation overprint mechanisms and microstructure, CPO and SPO relations were studied. For determination of crystal preffered orientations (CPO) the method of computer integrated polarization microscopy (CIP) was used. Microstructural analysis was focused on grain sizes, aspect ratios, long axis orientations and their relation to the deformation overprint grade. Results implies that dominant mechanism of quartz grain recrystallization is grain boundary migration. Folds were created by simple shear in microscale. The deformation overprint grade is strongest in the top of the fold hinge, where grains achieve highest aspect ratios and sizes. In the lower parts of the fold hinge the original CPO is preserved in small grains and SPO has similar orientation to original CPO. During folding CPO and SPO rotated with shear direction in dependance on deformation overprint grade.

Background Running is a popular form of exercise that more than 55 million Americans actively participate. Endurance running like marathon and half- marathon is getting increasingly popular among active runners. Although the effect of running is considered beneficial to bone health, the direct relationship between strains and strain gradients occurred during long distance running and bone changes is still not clear. Especially, given a high rate of injury associated with the first-time marathon, understanding the direct effect of strain stimuli on bone health is an important issue. Based on the previous studies, we hypothesized that the higher values of strain will induce bone adaptation more effectively and will lead to higher bone osteogenic changes. Since osteocytes sense shear stress caused by the interstitial fluid flow, which is created by the deformations, and regulate activities of osteoblasts and osteoclast that govern bone adaptation, we also hypothesized that the local strain gradient will create pressure differences within the interstitial fluid network and will increase fluid flow. Furthermore, due to that increased fluid flow, the regions with the higher strain gradient will experience a higher amount of bone adaptation. Thus, in this study, our purpose was to define the effect of the strains and strain gradients on bone changes within distal tibia, which is the most prone anatomical site to low risk stress fracture, during training for first-time marathon. Methods High-resolution and low-resolution computed tomographic (CT) images of the distal tibia were obtained before and after a self-selected training from runners who were actively training to participate in their first-time marathon in the next calendar year. The low resolution scan covered a 69.864 mm length of the distal end of the tibia while the high resolution CT scan covered a 9.02 mm region of the distal tibia. Using low resolution CT image based subject specific finite element (FE) models, the strains and strain gradients of the distal tibia at the instance of the peak ground reaction force (GRF) were calculated. The baseline and follow-up high resolution CT scans were used in high resolution peripheral quantitative CT (HRpQCT) analysis and the estimation of bone changes over the training period. Finally, the effect of strains and strain gradients on the distal tibia bone changes was estimated based on the FE model driven strain values and HRpQCT analysis driven bone changes. We used a linear mixed model to define the relationship between strain values and bone changes in the distal tibia. Results The strain values that occurred during marathon training had significant effects on bone changes in the distal tibia. Particularly, the strain gradients showed a higher effect than the strains. In the cortical compartment, the strain gradients, which were calculated as a strain difference of a node from the surrounding nodes (Strain Gradient-1), affected the bone mineral density (BMD) negatively, and per 1000 µε increase resulted in 2.123% decrease in the cortical BMD. The strain gradients, which were calculated as a strain difference of a node from the surrounding nodes normalized to distance to surrounding nodes (Strain Gradient-2), presented a positive effect on the cortical bone volume with a slope of 4.335% / 1000 µε. In the trabecular compartment, the strain gradient-1 showed negative effects on the percent change in BMD and bone mineral density (BMC), whereas the strain gradient-2 showed positive effects on the percent change in BMD and BMC. Conclusion The linear mixed model analysis revealed a statistically significant (p < 0.05) relationship between strain gradients that occurred during running and distal tibia bone changes. The strains, biometrics, and initial parameters of bone did not show any significant effect on the bone changes. The connection between local strain environment and bone changes in the distal tibia investigated in this study is an important step to understand the mechanism of mechanically induced bone adaptation.

Eshelby-type inclusion problems of an infinite or a finite homogeneous isotropic elastic body containing an arbitrary-shape inclusion prescribed with an eigenstrain and an eigenstrain gradient are analytically solved. The solutions are based on a simplified strain gradient elasticity theory (SSGET) that includes one material length scale parameter in addition to two classical elastic constants. For the infinite-domain inclusion problem, the Eshelby tensor is derived in a general form by using the Green’s function in the SSGET. This Eshelby tensor captures the inclusion size effect and recovers the classical Eshelby tensor when the strain gradient effect is ignored. By applying the general form, the explicit expressions of the Eshelby tensor for the special cases of a spherical inclusion, a cylindrical inclusion of infinite length and an ellipsoidal inclusion are obtained. Also, the volume average of the new Eshelby tensor over the inclusion in each case is analytically derived. It is quantitatively shown that the new Eshelby tensor and its average can explain the inclusion size effect, unlike its counterpart based on classical elasticity. To solve the finite-domain inclusion problem, an extended Betti’s reciprocal theorem and an extended Somigliana’s identity based on the SSGET are proposed and utilized. The solution for the disturbed displacement field incorporates the boundary effect and recovers that for the infinite-domain inclusion problem. The problem of a spherical inclusion embedded concentrically in a finite spherical body is analytically solved by applying the general solution, with the Eshelby tensor and its volume average obtained in closed forms. It is demonstrated through numerical results that the newly obtained Eshelby tensor can capture the inclusion size and boundary effects, unlike existing ones. Finally, a homogenization method is developed to predict the effective elastic properties of a heterogeneous material using the SSGET. An effective elastic stiffness tensor is analytically derived for the heterogeneous material by applying the Mori-Tanaka and Eshelby’s equivalent inclusion methods. This tensor depends on the inhomogeneity size, unlike what is predicted by existing homogenization methods based on classical elasticity. Numerical results for a two-phase composite reveal that the composite becomes stiffer when the inhomogeneities get smaller.

The Eshelby-type problems of an arbitrary-shape polygonal or polyhedral inclusion embedded in an infinite homogeneous isotropic elastic material are analytically solved using a simplified strain gradient elasticity theory (SSGET) that contains a material length scale parameter. The Eshelby tensors for a plane strain inclusion with an arbitrary polygonal cross section and for an arbitrary-shape polyhedral inclusion are analytically derived in general forms in terms of three potential functions. These potential functions, as area integrals over the polygonal cross section and volume integrals over the polyhedral inclusion, are evaluated. For the polygonal inclusion problem, the three area integrals are first transformed to three line integrals using the Green's theorem, which are then evaluated analytically by direct integration. In the polyhedral inclusion case, each of the three volume integrals is first transformed to a surface integral by applying the divergence theorem, which is then transformed to a contour (line) integral based on Stokes' theorem and using an inverse approach. In addition, the Eshelby tensor for an anti-plane strain inclusion with an arbitrary polygonal cross section embedded in an infinite homogeneous isotropic elastic material is analytically solved. Each of the newly derived Eshelby tensors is separated into a classical part and a gradient part. The latter includes the material length scale parameter additionally, thereby enabling the interpretation of the inclusion size effect. For homogenization applications, the area or volume average of each newly derived Eshelby tensor over the polygonal cross section or the polyhedral inclusion domain is also provided in a general form. To illustrate the newly obtained Eshelby tensors and their area or volume averages, different types of polygonal and polyhedral inclusions are quantitatively studied by directly using the general formulas derived. The numerical results show that the components of the each SSGET-based Eshelby tensor for all inclusion shapes considered vary with both the position and the inclusion size. It is also observed that the components of each averaged Eshelby tensor based on the SSGET change with the inclusion size.

Size-dependent material responses observed at fine length scales are receiving growing attention due to the need in the modeling of very small sized mechanical structures. The conventional continuum theories do not suffice for accurate descriptions of the exact material behaviors in the fine-scale regime due to the lack of inherent material lengths. A number of new theories/models have been propounded so far to interpret such novel phenomena. In this dissertation a few enriched-continuum theories - the adhesive contact mechanics, surface elasticity and strain gradient elasticity - are employed to study the mechanical behaviors of a semi-infinite solid induced by the boundary forces. A unified treatment of axisymmetric adhesive contact problems is developed using the harmonic functions. The generalized solution applies to the adhesive contact problems involving an axisymmetric rigid punch of arbitrary shape and an adhesive interaction force distribution of any profile, and it links existing solutions/models for axisymmetric non-adhesive and adhesive contact problems like the Hertz solution, Sneddon's solution, the JKR model, the DMT model and the M-D model. The generalized Boussinesq and Flamant problems are examined in the context of the surface elasticity of Gurtin and Murdoch (1975, 1978), which treats the surface as a negligibly thin membrane with material properties differing from those of the bulk. Analytical solution is derived based on integral transforms and use of potential functions. The newly derived solution applies to the problems of an elastic half-space (half-plane as well) subjected to prescribed surface tractions with consideration of surface effects. The newly derived results exhibit substantial deviations from the classical predictions near the loading points and converge to the classical ones at a distance far away from those points. The size-dependency of material responses is clearly demonstrated and material hardening effects are predicted. The half-space contact problems are also studied using the simplified strain gradient elasticity theory which incorporates material microstructural effects. The solution is obtained by taking advantage of the displacement functions of Mindlin (1964) and integral transforms. Significant discrepancy between the current and the classical solutions is seen to exist in the immediate vicinity of the loading area. The discontinuity and singularity exist in classical solution are removed, and the stress and displacement components change smoothly through the solid body.

Cells in living organisms are constantly experiencing a variety of mechanical cues. From the stiffness of the extra cellular matrix to its topography, not to mention the presence of shear stress and tension, the physical characteristics of the microenvironment shape the cells’ fate. A rapidly growing body of work shows that cellular responses to these stimuli constitute regulatory mechanisms in many fundamental biological functions. Substrate strains were previously shown to be sensed by cells and activate diverse biochemical signaling pathways, leading to major remodeling and reorganization of cellular structures. The majority of studies had focused on the stretching avoidance response in near-uniform strain fields. Prior to this work, the cellular responses to complex planar strain fields were largely unknown. In this thesis, we uncover various aspects of strain sensing and response by first developing a tailored lab-on-a-chip platform that mimics the non-uniformity and complexity of physiological strains. These microfluidic cell stretchers allow independent biaxial control, generate cyclic stretching profiles with biologically relevant strain and strain gradient amplitudes, and enable high resolution imaging of on-chip cell cultures. Using these microdevices, we reveal that strain gradients are potent mechanical cues by uncovering the phenomenon of cell gradient avoidance. This work establishes that the cellular mechanosensing machinery can sense and localize changes in strain amplitude, which orchestrate a coordinated cellular response. Subsequently, we investigate the effect of multiple changes in stretching directions to further explore mechanosensing subtleties. The evolution of the cellular response shed light on the interplay of the strain avoidance and the newly demonstrated strain gradient avoidance, which were found to occur on two different time scales. Finally, we extend our work to study the influence of cyclic strains on the early stages of cancer development in epithelial tissues (using MDCK-RasV12 system), which was previously largely unexplored. This work reveals that external mechanical forces impede the healthy cells’ ability to eliminate newly transformed cells and greatly promote invasive protrusions, as a result of their different mechanoresponsiveness. Overall, not only does our work reveal new insights regarding the long-range organization in population of cells, but it may also contribute to paving the way towards new approaches in cancer prevention treatments.

Being able to predict the evolution of plastic deformation at the microstructural scale is of paramount importance in the engineering of materials for advanced applications. However, this is not straightforward because of the multiscale nature of deformation heterogeneity, both in space and time . The present thesis combines four related studies in a coherent work, which is aimed to develop experimental methods for studying crystal plasticity at the micro and mesoscale. A novel methodology for gold remodelling is initially proposed and used to apply high-density speckle patterns on the surface of stainless steel specimens. The unique proprieties of the speckle pattern enabled plastic deformation mapping with submicron resolution using digital image correlation (HDIC). It was therefore possible to study the concomitant evolution of microbands and transgranular deformation bands in such alloy. High-resolution deformation mapping also enabled comparison with high-resolution electron backscatter diffraction (EBSD) observations. The only partial correspondence of results proved the limits of EBSD in characterizing plastic deformation. The cause of such limitation is later identified in the reduced sensitivity to lattice slip of the EBSD technique. Hence, a novel method of HDIC data analysis is proposed to separate the contributions of lattice slip and lattice rotation from the deformation mapping. The method is adopted to characterize plasticity in austenitic stainless steel and at the plastic deformation zone (PDZ) around a silicon particle embedded in a softer aluminum matrix. Results show that the proposed experimental methodology has the unique capability of providing a complete description of the micro and mesoscale mechanics of crystal plasticity. HDIC therefore emerges as a key technique in the development of accurate physical-based multiscale crystal plasticity models.

Background Running is a popular form of exercise that more than 55 million Americans actively participate. Endurance running like marathon and half- marathon is getting increasingly popular among active runners. Although the effect of running is considered beneficial to bone health, the direct relationship between strains and strain gradients occurred during long distance running and bone changes is still not clear. Especially, given a high rate of injury associated with the first-time marathon, understanding the direct effect of strain stimuli on bone health is an important issue. Based on the previous studies, we hypothesized that the higher values of strain will induce bone adaptation more effectively and will lead to higher bone osteogenic changes. Since osteocytes sense shear stress caused by the interstitial fluid flow, which is created by the deformations, and regulate activities of osteoblasts and osteoclast that govern bone adaptation, we also hypothesized that the local strain gradient will create pressure differences within the interstitial fluid network and will increase fluid flow. Furthermore, due to that increased fluid flow, the regions with the higher strain gradient will experience a higher amount of bone adaptation. Thus, in this study, our purpose was to define the effect of the strains and strain gradients on bone changes within distal tibia, which is the most prone anatomical site to low risk stress fracture, during training for first-time marathon. Methods High-resolution and low-resolution computed tomographic (CT) images of the distal tibia were obtained before and after a self-selected training from runners who were actively training to participate in their first-time marathon in the next calendar year. The low resolution scan covered a 69.864 mm length of the distal end of the tibia while the high resolution CT scan covered a 9.02 mm region of the distal tibia. Using low resolution CT image based subject specific finite element (FE) models, the strains and strain gradients of the distal tibia at the instance of the peak ground reaction force (GRF) were calculated. The baseline and follow-up high resolution CT scans were used in high resolution peripheral quantitative CT (HRpQCT) analysis and the estimation of bone changes over the training period. Finally, the effect of strains and strain gradients on the distal tibia bone changes was estimated based on the FE model driven strain values and HRpQCT analysis driven bone changes. We used a linear mixed model to define the relationship between strain values and bone changes in the distal tibia. Results The strain values that occurred during marathon training had significant effects on bone changes in the distal tibia. Particularly, the strain gradients showed a higher effect than the strains. In the cortical compartment, the strain gradients, which were calculated as a strain difference of a node from the surrounding nodes (Strain Gradient-1), affected the bone mineral density (BMD) negatively, and per 1000 µε increase resulted in 2.123% decrease in the cortical BMD. The strain gradients, which were calculated as a strain difference of a node from the surrounding nodes normalized to distance to surrounding nodes (Strain Gradient-2), presented a positive effect on the cortical bone volume with a slope of 4.335% / 1000 µε. In the trabecular compartment, the strain gradient-1 showed negative effects on the percent change in BMD and bone mineral density (BMC), whereas the strain gradient-2 showed positive effects on the percent change in BMD and BMC. Conclusion The linear mixed model analysis revealed a statistically significant (p < 0.05) relationship between strain gradients that occurred during running and distal tibia bone changes. The strains, biometrics, and initial parameters of bone did not show any significant effect on the bone changes. The connection between local strain environment and bone changes in the distal tibia investigated in this study is an important step to understand the mechanism of mechanically induced bone adaptation.