The purpose of this study is to investigate the plastic deformation behavior of a round bar at the roll-gap during the rolling process of a three-roll planetary mill. The analysis is carried out with the aid of a finite element program MARC adopting the large deformation - large strain theory and the updated lagrangian formulation (ULF). A mesh rezoning procedure is also adopted to improve the uncontrollable running error of elements turning inside out. The mesh system of the whole bar billet is created by using three-dimensional brick elements, and the three-dimensional elastic-plastic finite element model in MARC is chosen to perform the simulations of three-roll planetary rolling processes. The simulation examples consist of three groups. Firstly, three different friction coefficients are adopted to investigate the rolling process. Secondly, totally five different offset angles are used during the simulation of the rolling process. Finally, five different profiles of the roller are used to study the simulation of the rolling process. The successfully obtained numerical results, including equivalent von-Mises stress and plastic strain distributions, rolling force, rolling moment, billet speeds at the entrance and exit planes of the roll-gap are useful in designing the pass schedules of the three-roll planetary rolling processes.

The continuum theory of large deformation elasto-plasticity is summarized as far as it is necessary for the numerical treatment with the Finite-Element-Method. Using the calculus of modern differential geometry and functional analysis, the fundamental equations are derived and the proof of most of them is shortly outlined. It was not our aim to give a contribution to the development of the theory, rather to show the theoretical background and the assumptions to be made in state of the art elasto-plasticity.

Many studies have previously been done on moisture-induced strains in wood. An in- finitesimal/engineering strain model has been used for most of these studies, which is often an accurate approximation for small rotations. However, if large deformations oc- cur, then fictive strains are obtained resulting from the simplified engineering strain.  This work aims to develop a finite element formulation for problems of moisture- induced strains in orthotropic materials based on the total Lagrangian approach, where large displacements and rotations are considered. This model is then used to examine static drying deformations and their effect on dynamic vibrations. A dynamic vibration test was also done to estimate the modulus of elasticity in the fibre direction. The pur- pose is to increase the understanding of moisture-induced strains in wood and also to emphasize the advantages of using a large deformation model.  To facilitate the understanding of large deformation theory, the implementation is first done for a 2D isotropic beam where static and dynamic simulations are made. Re- sults will be compared with a standard model based on engineering strains. For the static part, two types of wooden species are studied, radiata pine and Norway spruce, and com- pared with a previous research study [32] where engineering strain theory is used. The dynamical considerations are divided into a theoretical and an experimental part. The theoretical part analyzes the vibration of radiata pine and Norway spruce samples from a study by Cown and Ormarsson 2005 [32]. In the experimental part, three Norway spruce boards were analyzed.  The results from the numerical implementation showed, among other things, that by taking moisture-induced strains into account two additional properties, the matrix Gm and the vector Emf appear in the finite element formulation. It was concluded that by using a large deformation model the accuracy will increase without causing any extra computational costs.  The transient numerical mass flow analysis showed reasonable results although the sorption exchange rate has to be slightly higher than indicated by comparable measure- ments. For the dynamic part, the performed experiment showed a difference in response between the three Norway spruce species. It was shown that the frequency increases with distance from the pith and also with lower moisture content. The difference in vibration response between Norway spruce and radiata pine was analyzed based on boards from a study by Cown and Ormarsson 2005 [32]. The response for Norway spruce tends to show a higher frequency compared to radiata pine for the test performed in this investigation. This is mainly due to a higher modulus of elasticity and lower density for Norway spruce compared to radiata pine.

The boundary value problems (BVPs) of geomechanics are challenging due to the complexity in modeling soil behavior and difficulties in modeling large deformations. While traditional numerical schemes have struggled in realistically simulating geomechanical BVPs, new numerical methods –such as the material point method (MPM)–are increasingly being used to tackle these problems. However, algorithms in MPM have not yet been sufficiently developed, scrutinized, and validated. This thesis focuses on the development, verification, and validation of MPM for use in geomechanical BVPs. In particular, the thesis focuses on simulation of cone penetration tests in both controlled environments and in field conditions.<div><br></div><div>To efficiently simulate cone penetration, a silent boundary scheme, known as a cone boundary, was proposed in the generalized interpolation material point method (GIMP), a variant of MPM. The implementation of the cone boundary in GIMP was discussed, and the boundaries were validated by comparison against several benchmark problems. The cone boundaries were shown to be suitable in transmitting energy at the boundary. In addition, the implementation of traction boundaries in GIMP was analyzed. In GIMP, traction boundaries may be implemented either at the centroid of the material point, or at the edge of the material point domain. It was shown that the implementation of traction boundaries at the edge of the domain led to stress oscillations near the boundary, which were minimized when the traction boundaries were implemented at the edge of the domain.<br></div><div><br></div><div>During cone penetration, the soil near the cone-soil interface is pushed to large strains. At large strains, soils reach critical state, a state in which the soil shears at constant volume. Simulation of incompressible materials using low-order shape functions commonly used in GIMP leads to stiffer solutions and stress oscillations. To mitigate the constraints imposed by incompressibility, the non-linear B-bar method was implemented in GIMP. The modifications required for the implementation of the B-bar method in GIMP were discussed, and the efficacy of the method in mitigating incompressibility was demonstrated by analyzing several benchmark problems.<br></div><div><br></div><div>To simulate cone penetration in saturated soil, a coupled formulation was proposed in GIMP.A single material point was used to represent both the soil matrix and water. The governing equations were solved using an explicit scheme with the velocity of the soil matrix and the velocity of water as the primary variables. The formulation was validated through problems for which analytical or numerical solutions are available.<br></div><div><br></div><div>Finally, cone penetration analyses were performed both in dry sand and saturated clays. Two bounding surface models –one for sand and one for clay –were used for accurately capturing the soil response. Cone penetration tests were performed on Ottawa 20-30 sand under a variety of loading conditions at a large calibration chamber. The penetration resistances were measured, and the displacement fields were captured using the digital image correlation technique(DIC). The cone penetration resistances predicted by MPM were within 25% of the measured values, and the displacement fields computed using MPM were similar to those captured using DIC. For saturated clays, cone penetration test results reported in the literature for a Boston Blue Clay (BBC) test site were used. The simulated cone resistance of 650 kPa lied within the CPT resistance range of 580-730 kPa reported in the field. The results demonstrate the capability of MPM in simulating cone penetration in both sands and clays provided that sufficiently accurate algorithms and advanced constitutive models capable of reproducing realistic soil behavior are used in the analyses.<br></div>

No description available.

Mechanical instabilities such as wrinkling and buckling-driven delamination in thin film-substrate systems have historically been considered as one of structural failure mechanisms, which should be avoided. The past decade has witnesssed rapid growth in harnessing such surface instabilities for a wide range of tunable surface related properties and functionalities, especially in soft materials on small scales. Compared to extensively studied wrinkling on soft substrates and localized buckling driven delamination on stiff substrates, the fundamental mechanics underpinning ordered buckle-delamination on soft substrate over large area and its guidance for potential implications in engineering innovation remain largely to be explored. This thesis aims to partially bridging such a knowledge gap. In this thesis, I exploit how to generate the controllable and globally periodic delaminated buckling patterns in thin films on highly prestrained elastomeric substrates, and then explore the fundamental mechanics of this spontaneous extreme buckling driven periodic delamination, as well as its implications in design of extremely stretchable electronics and interfacial mechanical properties measurement. Compared to wrinkling, one of the benefits of extremely buckling driven delamination is the extraordinarily high aspect ratio of buckles. The large surface roughness and high local curvature could potentially enable extreme surface topographies related properties, such as adhesion, wetting, friction, and optics, as well as augment the extreme stretchability in stretchable optical and electronic devices. In the aim of harnessing this extreme buckling driven delamination, I first explore the formation and evolution of extraordinarily high-aspect-ratio delaminated buckles of thin films on 400% pre-strained elastomers, as well as uncovered the underlying deformation mechanism through combining quantitative theoretical analysis and experimental and numerical approaches. A theoretical framework is developed to describe the formation and evolution process of periodic delaminated buckles, which includes three deformation stages, i.e. onset of localized blisters (Stage I), growth and propagation of delamination (Stage II), and post-buckling after delamination arrest (Stage III). I show that under extreme large compressive strain, the profile of periodic blisters changes from sinusoidal shape to jig-saw-like shape with relative high aspect ratio, which have potential applications for design of extremely stretchable electronics. Equipped with the fundamental mechanics of buckle-delamination in thin films, I then exploit harnessing the spontaneous buckling driven periodic delamination to achieve high stretchability in both metal and silicon films. Experimentally I observe periodic buckle-delaminated patterns over large area, accompanied by highly ordered transversely cracking patterns, which can be theoretically predicted by simple crack fragments model. I hypothesize that when the width of ribbons is set to be equal or smaller than the theoretically predicted crack fragment width, there would be no cracking fragmentation. This criteria for designing crack-free micro-ribbons is further validated by related experiments. Guided by the validated criteria, I successfully design crack-free and spontaneous delaminated ribbons on highly prestrained elastomer substrates, which provides a high stretchability of about 120% and 400% in Si and Au ribbons, respectively. I further extend the buckling instability-based metrology to systematically measure the mechanical properties of 2D organic conjugated polymer nano-films, which have tremendous promising applications in organic integrated circuits, solar cells, and stretchable devices. I develop a new fabrication strategy to generate buckle-delaminated free-standing organic conjugated polymeric (P3BT/C60) nanosheets. Through both experiments and theoretical analysis, I show that the free-standing buckle-delaminated organic P3BT/C60 nanosheets have significant advantages over the traditional spin-coated wrinkled nanosheets, including the enhanced mechanical properties, a higher level of stretchability with lower electrical resistance, and a wider range of controllable wettability modulation. / Mechanical Engineering

A high-order hybrid discontinuous Galerkin finite element method (DG-FEM) is developed for multi-layered curved panels having large deformation and finite strain. The kinematics of the multi-layered shells is presented at first. The Jacobian matrix and its determinant are also calculated. The weak form of the DG-FEM is next presented. In this case, the discontinuous basis functions can be employed for the displacement basis functions. The implementation details of the nonlinear FEM are next presented. Then, the Consistent Orthogonal Basis Function Space is developed. Given the boundary conditions and structure configurations, there will be a unique basis function space, such that the mass matrix is an accurate diagonal matrix. Moreover, the Consistent Orthogonal Basis Functions are very similar to mode shape functions. Based on the DG-FEM, three dedicated finite elements are developed for the multi-layered pipes, curved stiffeners and multi-layered stiffened hydrofoils. The kinematics of these three structures are presented. The smooth configuration is also obtained, which is very important for the buckling analysis with large deformation and finite strain. Finally, five problems are solved, including sandwich plates, 2-D multi-layered pipes, 3-D multi-layered pipes, stiffened plates and stiffened multi-layered hydrofoils. Material and geometric nonlinearities are both considered. The results are verified by other papers' results or ANSYS. / Master of Science

The research carried out in this thesis has concentrated on the application of numerical solutions to geotechnical penetration problems in offshore engineering. Several important issues closely relevant to deep-water oil and gas developments were investigated, covering installation of suction caisson foundations, interpretation of fullflow penetrometers and shallow penetration of a cylindrical object (submarine pipeline or T-bar), all in clayey sediments such as are often encountered in deep-water sites. These problems are commonly characterised by large vertical movements of structural elements relative to the seabed. A large deformation finite element method was adopted and further developed to simulate these challenging problems, referred to as Remeshing and Interpolation Technique with Small Strain. In this approach, a sequence of small strain Lagrangian increments, remeshing and interpolation of stresses and material properties are repeated until the required displacement has been reached. This technique is able to model relative motion between the penetrating objects and the soil, which is critical for evaluating soil heave inside the caissons, the effect of penetration-induced remoulding on the resistance of full-flow penetrometers, and influence of soil surface heave on the embedment of pipelines. '...' Simple expressions were presented allowing the resistance factors for the T-bar and ball penetrometers to be expressed as a function of the rate and strain-softening parameters. By considering average strength conditions during penetration and extraction of these full-flow penetrometers, an approximate expression was derived that allowed estimation of the hypothetical resistance factor with no strain-softening, and hence an initial estimate of the stain-rate dependency of the soil. Further simulations of cyclic penetration tests showed that a cyclic range of three diameters of the penetrometers was sufficient to avoid overlap of the failure mechanism at the extremes and mid-point of the cyclic range. The ball had higher resistance factors compared with the T-bar, but with similar cyclic resistance degradation curves, which could be fitted accurately by simple expressions consistent with the strain-softening soil model adopted. Based on the curve fitting, more accurate equations were proposed to deduce the resistance factor with no strain-softening, compared with that suggested previously based on the resistances measured in the first cycle of penetration and extraction. The strain-rate dependency was similar in intact or post-cyclic soil for a given rate parameter. The resistance factor for the post-cyclic condition was higher than that for the initial conditions, to some degree depending upon soil sensitivity and brittleness parameter. For the shallow penetration of a cylindrical object, the penetration resistance profile observed from centrifuge model tests was very well captured by the numerical simulation. The mechanism of shear band shedding was reproduced by the numerical technique, although the frequency of the shear band generation and the exact shape of the heave profile were not correctly captured, which were limited by the simple strainsoftening soil model adopted.

The mechanical behavior of the arterial wall is determined by the composition and structure of its internal constituents as well as the applied traction-forces, such as pressure and axial stretch. The purpose of this work is to develop new theoretical frameworks and experimental methodologies to further the understanding of arterial mechanics and role of the various intrinsic and extrinsic mechanically motivating factors. Specifically, residual deformation, matrix organization, and perivascular support are investigated in the context of their effects on the overall and local mechanical behavior of the artery. We propose new kinematic frameworks to determine the displacement field due to residual deformations previously unknown, which include longitudinal and shearing residual deformations. This allows for improved predictions of the local, intramural stresses of the artery. We found distinct microstructural differences between the femoral and carotid arteries from non-human primates. These arteries are functionally and mechanically different, but are geometrically and compositionally similar, thereby suggesting differences in their microstructural alignments, particularly of their collagen fibers. Finally, we quantified the mechanical constraint of perivascular support on the coronary artery by mechanically testing the artery in-situ before and after surgical exposure.

In this thesis a theory for large deformation of plates is presented. Herein aspects of the common 3D-theory for large deformation with the Kirchhoff hypothesis for reducing the dimension from 3D to 2D is combined. Even though the Kirchhoff assumption was developed for small strain and linear material laws, the deformation of thin plates made of isotropic non-linear material was investigated in a numerical experiment. Finally a heavily deformed shell without any change in thickness arises. This way of modeling leads to a two-dimensional strain tensor essentially depending on the first two fundamental forms of the deformed mid surface. Minimizing the resulting deformation energy one ends up with a nonlinear equation system defining the unknown displacement vector U. The aim of this thesis was to apply the incremental Newton technique with a conformal, C^1-continuous finite element discretization. For this the computation of the second derivative of the energy functional is the key difficulty and the most time consuming part of the algorithm. The practicability and fast convergence are demonstrated by different numerical experiments.