Browsing by Subject "Elasticity"

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Domain decomposition methods in geomechanics
(2012-08) Florez Guzman, Horacio Antonio; Wheeler, Mary F. (Mary Fanett); Delshad, Mojdeh; Mear, Mark; Landis, Chad; Rodriguez, Adolfo
Hydrocarbon production or injection of fluids in the reservoir can produce changes in the rock stresses and in-situ geomechanics, potentially leading to compaction and subsidence with harmful effects in wells, cap-rock, faults, and the surrounding environment as well. In order to tackle these changes and their impact, accurate simulations are essential. The Mortar Finite Element Method (MFEM) has been demonstrated to be a powerful technique in order to formulate a weak continuity condition at the interface of sub-domains in which different meshes, i.e. non-conforming or hybrid, and / or variational approximations are used. This is particularly suitable when coupling different physics on different domains, such as elasticity and poroelasticity, in the context of coupled flow and geomechanics. In this dissertation, popular Domain Decomposition Methods (DDM) are implemented in order to carry large simulations by taking full advantage of current parallel computer architectures. Different solution schemes can be defined depending upon the way information is exchanged between sub-domain interfaces. Three different schemes, i.e. Dirichlet-Neumann (DN), Neumann-Neumann (NN) and MFEM, are tested and the advantages and disadvantages of each of them are identified. As a first contribution, the MFEM is extended to deal with curve interfaces represented by Non-Uniform Rational B-Splines (NURBS) curves and surfaces. The goal is to have a more robust geometrical representation for mortar spaces, which allows gluing non-conforming interfaces on realistic geometries. The resulting mortar saddle-point problem will be decoupled by means of the DN- and NN-DDM. Additionally, a reservoir geometry reconstruction procedure based on NURBS surfaces is presented as well. The technique builds a robust piecewise continuous geometrical representation that can be exploited by MFEM in order to tackle realistic problems, which is a second contribution. Tensor product meshes are usually propagated from the reservoir in a conforming way into its surroundings, which makes non-matching interfaces highly attractive in this case. In the context of reservoir compaction and subsidence estimation, it is common to deal with serial legacy codes for flow. Indeed, major reservoir simulators such as compositional codes lack parallelism. Another issue is the fact that, generally speaking, flow and mechanics domains are different. To overcome this limitation, a serial-parallel approach is proposed in order to couple serial flow codes with our parallel mechanics code by means of iterative coupling. Concrete results in loosely coupling are presented as a third contribution. As a final contribution, the DN-DDM is applied to couple elasticity and plasticity, which seems very promising in order to speed up computations involving poroplasticity. Several examples of coupling of elasticity, poroelasticity, and plasticity ranging from near-wellbore applications to field level subsidence computations help to show that the proposed methodology can handle problems of practical interest. In order to facilitate the implementation of complex workflows, an advanced Python wrapper interface that allows programming capabilities have been implemented. The proposed serial-parallel approach seems to be appropriate to handle geomechanical problems involving different meshes for flow and mechanics as well as coupling parallel mechanistic codes with legacy flow simulators.
The effects of pressure variations and chemical reactions on the elasticity of the Lower Tuscaloosa sandstone of the Cranfield Field, Mississippi
(2011-08) Joy, Corey Anthony; Sen, Mrinal K.; Tatham, Robert; Spikes, Kyle
Compliance with current and evolving federal and commercial regulations require the monitoring of injected carbon dioxide for geological sequestration. The goal of this project is to provide geophysicists with tools to quantitatively interpret seismic data for the amount of carbon dioxide retained in subsurface reservoirs. Rock physics can be used to predict the effects on the seismic response of injecting carbon dioxide on the reservoir. However, classical rock physics models fail when chemical reactions alter the microstructure of the host rock. These chemically induced changes can stiffen or soften the rock frame by precipitation or dissolution, respectively, of minerals in the pore space. Increasing pore pressure is another effect of sequestering carbon dioxide. The amount of change in the microstructure due to chemical reactions and pressure variations depends on the reservoir into which the fluid is injected. Therefore, measuring velocities on site-specific subsurface core samples may provide the ability to differentiate between chemical reactions and pressure variations on the elastic properties of the reservoir rock. Core samples come from the Lower Tuscaloosa Sandstone of the Cranfield study area in Mississippi. The experiments consisted of injecting core plugs with carbon dioxide rich brine and measuring compressional and shear velocities at different effective pressures. The elastic moduli of the rock frame are calculated from the measured elastic wave propagation velocities at specific injected pore volumes and effective pressures. Injecting carbon dioxide rich brine into sandstone core samples, which are composed on average of 80% quartz and 20% clay minerals, resulted in softening of the rock frame due to the dissolution of iron bearing minerals. The moduli exponentially decreased with injected pore volumes and were linearly proportional to effective pressure. The bulk modulus and rigidity of the more quartz rich sample decreased by 13% and 6.5%, respectively, due to a combined effect of changing differential pressure from 35 MPa to 27 MPa and injecting CO₂-rich brine. For the more clay rich sample, the moduli decreased by even larger percentages (39.0% and 20.1%, respectively), which could have significant implications on time-lapse seismic data and subsequent estimations of injected CO₂ volumes.
Feasibility of isotropic inversion in orthorhombic media : the Barrett unconventional model
(2016-05) Yanke, Andrew James; Spikes, Kyle; Sen, Mrinal K; Fomel, Sergey B
Geophysicists often relegate shale reservoirs as having higher symmetries (e.g., transversely isotropic (TI) or isotropic) than what reality demonstrates. Routine application of TI (or even isotropic) algorithms to orthorhombic media neglects the associated errors because we never know the true model in practice. This thesis evaluates the viability of isotropic post-stack and pre-stack seismic inversion to orthorhombic media using the SEAM Barrett Unconventional Model, the most realistic depositional model to date. The Barrett Model contains buried topography, simulated stratigraphy, and designated reservoir zones with orthorhombic anisotropy. I inverted the Barrett data volume for isotropic elastic property cubes, which I compared to the model volume in each symmetry-plane of an orthorhombic medium. If the stacked seismic data contained only the near offsets, post-stack inversion resolved acoustic impedances that closely matched the true model both within and outside of the reservoir zones at all well locations. Anisotropy most affected the far offsets, so muting them predictably enhanced the post-stack inversion. I maintained all offsets for pre-stack inversion, but a parabolic radon filter eliminated nonhyperbolic behavior (rather than nonhyperbolic moveout analysis) at far offsets. The pre-stack impedance attributes adequately described the vertical heterogeneity of the true model at a cross-validation well, but the inverted values increasingly relied on the initial model with depth. The inverted density estimates experienced notable oscillations relative to the initial model, particularly where steep contrasts in elastic properties occurred. Mismatch of the inverted elastic properties at the well locations can be attributed to noise, thin layering effects, band limitation, steep contrasts in elastic properties, AVO behavior stacked into the data, an inaccurate starting model, and the effects of anisotropy. The most significant sources of error include small-scale reflectivity and comprehensive filtering of nonhyperbolic phenomena. Away from the well locations, the isotropic inversion gave no visual indication of reservoir geobodies, but it sufficiently described the elastic property variations near reservoir mid-sections. Moreover, I showed that the inverted elastic properties differ from their orthorhombic models by no more than 35%. The greatest misfits occurred near reservoir contacts and geobody locations. The computed impedance models in each symmetry-plane have distinctive differences, but isotropic inversion dismisses these variations entirely. I conclude that isotropic inversion should not be a surrogate for orthorhombic methods in data preconditioning and quantitative reservoir characterization.
Finite element methods in linear poroelasticity: theoretical and computational results
(2005) Phillips, Phillip Joseph; Wheeler, Mary F. (Mary Fanett)
Linear Poroelasticity refers to fluid flow within a deformable porous medium under the assumption of relatively small deformations. Some of the areas that are being modeled with the equations of linear poroelasticity include reservoir engineering, soil mechanics and, more recently, biomedical engineering. The purpose of this dissertation is to present original results for the development, analysis and application of numerical finite element algorithms in the field of linear poroelasticity. A fully coupled finite element method involving continuous elements for displacements and a mixed space for flow is developed (CG/Mixed). Existence, uniqueness and optimality results are provided. The norm measuring the pressure error, however, depends on the value of the constrained specific storage coefficient. For degenerate values, this leads to a slightly weaker optimality result. For the not untypical case of a null constrained specific storage coef- ficient, the solution produced by the CG/Mixed scheme sometimes produces non-physical pressure oscillations, a phenomenon referred to as locking. One potential remedy is to eliminate the continuity requirement for the elements approximating displacements. Therefore, a family of schemes which couples discontinuous elements for displacements and a mixed space for flow is introduced (DG/Mixed). Existence and uniqueness are established, optimal a priori error estimates are provided, and some success in the removal of locking is shown. Direct verification of several benchmark analytical solutions shows that solutions in linear poroelasticity can lack regularity. This sometimes manifests in pressure boundary layers which might degrade the rate of convergence of numerical solutions. The situation can often be ameliorated with the development of adaptive grid refinement strategies. This motivates a posteriori estimates in terms of computable residual quantities. Interestingly, it is also shown that the CG/Mixed method can be combined with adaptive grid refinement as an alternative means to eliminate locking. The produced algorithms are then applied to some interesting application areas. In one instance, they are used to analyze the deformation and pressure dynamics in a cantilever bracket. Additionally, a variety of miscellaneous problems ranging from subsidence and well placement to scuba suit design highlight intriguing applications.
A hybrid-stress finite element approach for stress and vibration analysis in linear anisotropic elasticity
(1987) Mahadevan, L. (Lakshminarayanan); Oden, J. Tinsley (John Tinsley), 1936-
A hybrid-stress finite element method is developed for accurate stress and vibration analysis of problems in linear anisotropic elasticity. A modified form of the Hellinger-Reissner principle is formulated for dynamic analysis and an algorithm for the determination of the anisotropic elastic and compliance constants from experimental data is developed. These schemes have been implemented in a finite element program for static and dynamic analysis of linear anisotropic two-dimensional elasticity problems. Specific numerical examples are considered to verify the accuracy of the hybrid-stress approach and compare it with that of the standard displacement method, especially for highly anisotropic materials. It is that the hybrid-stress approach gives significantly better results than the displacement method. Preliminary work on extensions of this method to three-dimensional elasticity is discussed, and the stress shape functions necessary for this extension are included
Integrated system for ultrasonic, elasticity and photoacoustic imaging
(2008-08) Park, Suhyun, 1977-; Emelianov, Stanislav Y.
By integrating three complementary imaging techniques - ultrasound, elasticity and photoacoustic imaging, a hybrid imaging system utilizing an array transducer is proposed for various biomedical imaging applications including cancer detection, diagnosis and therapy monitoring. Simultaneous imaging of the anatomy (ultrasound imaging), changes in biomechanical properties (elasticity imaging) and cancer-induced angiogenesis (photoacoustic imaging) of tissue is based on many synergistic features of these modalities and may result in a unique and important imaging tool. In this study, numerical analysis and experimental studies are presented to demonstrate the feasibility, to evaluate the performance, and also to improve the quality of the combined array-based ultrasound, elasticity and photoacoustic imaging system. To estimate spatial resolution, a point source was imaged using ultrasound and photoacoustic imaging modes. Then, several tissue mimicking phantoms were examined using ultrasound, photoacoustic and elasticity imaging. In elasticity imaging, ultrasound frames were acquired during deformation of the tissue. To reduce the data acquisition time of the system, high frame rate imaging was used. High frame rate imaging is possible by transmitting a broader and less focused ultrasound beam but the image quality is sacrificed. Thus, we compared the quality of the high frame rate and conventional ultrasound images. In photoacoustic imaging, acoustic transients are generated simultaneously in the entire volume of the laser irradiated tissue. Hence, image formation (beamforming) algorithms were developed based on the characteristics of the photoacoustic signals. Then, adaptive beamforming method is suggested to improve the image quality of the photoacoustic imaging. The results of the numerical analyses and experimental studies clearly indicate that ultrasound, elasticity and photoacoustic imaging techniques complement each other and together provide critical information needed for the reliable detection and diagnosis of diseases.
Mechanics and applications of stretchable serpentine structures
(2016-05) Yang, Shixuan; Lu, Nanshu; Ravi-Chandar, K; Liechti, Kenneth M; Huang, Rui; Sun, Nan
Stretchable structures have been developed for various applications, including expandable coronary stents, deployable sensor networks and stretchable bio-mimetic and bio-integrated electronics. High-performance, stretchable electronics have to utilize high-quality and long-lasting inorganic electronic materials such as silicon, oxide dielectrics and metals, which are intrinsically stiff and often brittle. It is therefore an interdisciplinary challenge to make inorganic electronics stretchable while retaining their electronic functionality. Patterning stiff materials into serpentine-shaped wavy ribbons has become a popular strategy for fabricating stretchable inorganic electronics. However due to a lack of mechanics understanding, design of serpentine structures is still largely empirical, whether for freestanding or substrate supported serpentines. This dissertation systematically investigates the mechanics of serpentine structures with emphasis on the effects of serpentine geometry and substrate stiffness, which involves theoretical analysis, numerical simulation, and experimental validation. Our theory has successfully predicted the stretchability and stiffness of various serpentine shapes and has been applied to the optimization of serpentine designs under practical constraints. We are also the first to point out that not all geometric effects are monotonic and serpentines are not always more stretchable than linear ribbons. To manufacture high quality serpentine ribbons with high throughput and low cost, we have invented a “cut-and-paste” method to fabricate both metallic and ceramic serpentines. As a demonstration of our method, a noninvasive, tattoo-like multifunctional epidermal sensor system has been built for the measurement of electrophysiological signals, skin temperature, skin hydration, and respiratory rate. Engineering of epidermal stretchable antenna for wireless communication is also detailed and rationalized.
Mixed hp-adaptive finite element methods for elasticity and coupled problems
(2010-08) Qiu, Weifeng, 1978-; Demkowicz, Leszek; Prudhomme, Serge M.
In my dissertation, I developed mixed hp-finite element methods for linear elasticity with weakly imposed symmetry, which is based on Arnold-Falk-Winther's stable mixed finite elements. I have proved the h-stability of my method for meshes with arbitrary variable orders. In order to show the h-stability, I need an upper limit of the highest order of meshes, which can be an arbitrary nonnegative integer.
Simulation and analysis of the multiphase flow and stability of co-extruded layered polymeric films
(2011-08) Chabert, Erwan; Bonnecaze, R. T. (Roger T.); Paul, Don R.
The flow and stability of co-extruded layers of different polymers in a forced assembly process is studied computationally to determine the extent of the stable process window and the types of instabilities that occur. Recent advances in layer-multiplying co-extrusion of incompatible polymers have made possible the fabrication of multilayered nanostructures with improved barrier, thermal and mechanical behavior. However, existing layering techniques are very sensitive to mismatches in viscosity and elasticity of the co-extruded polymers which often give rise to layer non-uniformity and flow instabilities, such as encapsulation. Simulations of the flows inside the feedblock and the successive multiplier dies of the multi-layering system are used to track the interface and predict instabilities and degrees of encapsulation as a function of process parameters, primarily the flow rates and rheology of the polymers. Encapsulation is found to be negligible in practice in the feedblock even for large viscosity contrasts and differences in elasticity between the two co-extruded polymers. Encapsulation or pinch-off of interfaces is more severe in the multiplier dies when there the rheologies of the polymers differ. A secondary flow due to the second normal stress differences for non-Newtonian fluids is primarily responsible for the encapsulation. A new multiplier design is proposed and simulated. The pressure drop in the proposed design is half that of the current design, which is useful for extruding highly elastic materials. Further, the degree of encapsulation is also reduced. The results of the simulations are validated with experimental measurements of pressure drop and flow visualization provided by research collaborators.
Size effects in out-of-plane bending in elastic honeycombs fabricated using additive manufacturing : modeling and experimental results
(2011-12) Mikulak, James Kevin; Kovar, Desiderio; Taleff, Eric M.; Rodin, Gregory J.; Bourell, David L.; Haberman, Michael R.
Size effects in out-of-plane bending stiffness of honeycomb cellular materials were studied using analytical mechanics of solids modeling, fabrication of samples and mechanical testing. Analysis predicts a positive size-effect relative to continuum model predictions in the flexure stiffness of a honeycombed beam loaded in out-of-plane bending. A method of determining the magnitude of that effect for several different methods of constructing or assembling square-celled and hexagonal-celled materials, using both single-walled and doubled-walled construction methods is presented. Hexagonal and square-celled honeycombs, with varying volume fractions were fabricated in Nylon 12 using Selective Laser Sintering. The samples were mechanically tested in three-point and four point-bending to measure flexure stiffness. The results from standard three-point flexure tests, did not agree with predictions based on a mechanics of solids model for either square or hexagonal-celled samples. Results for four-point bending agreed with the mechanics of solids model for the square-celled geometries but not for the hexagonal-celled geometries. A closed form solution of an elasticity model for the response of the four-point bending configuration was developed, which allows interpretation of recorded displacement data at two points and allows separation the elastic bending from the localized, elastic/plastic deformation that occurs between the loading rollers and the specimen’s surface. This localized deformation was significant in the materials tested. With this analysis, the four-point bending data agreed well with the mechanics of solids predictions.
Thermomechanical and interfacial properties of monolayer graphene
(2014-08) Gao, Wei, active 21st century; Huang, Rui, doctor of civil and environmental engineering
The thermomechanical properties of monolayer graphene and the interfacial interactions between graphene and an SiO₂ substrate are investigated in this dissertation using a multiscale approach. The temperature dependent mechanical behavior of graphene with thermal fluctuations is studied by statistical mechanics analysis under harmonic approximation, which is then compared to molecular dynamics simulations. It is found that the amplitude of thermal fluctuation depends nonlinearly on the graphene size due to anharmonic interactions between bending and stretching modes, but a small positive pre-strain could suppress fluctuation amplitude considerably and results in very different scaling behavior. The thermal expansion of graphene depends on two competing effects: positive expansion due to in-plane modes and negative expansion due to out-of-plane fluctuations. The in-plane stress-strain relation of graphene becomes nonlinear even at infinitesimal strain due to the entropic contribution. Consequently, the modulus of graphene depends on strain non-monotonically, with strain stiffening followed by intrinsic softening. Moreover, it is found that the thermomechnical behavior of graphene is dependent on its interactions with environment such as supporting substrate. The interfacial interactions between graphene and SiO₂ substrate is investigated in terms of three perspectives. Firstly, the interaction mechanisms between graphene and SiO₂ substrate are studied by density functional theory (DFT). The dispersion interaction is found to be the predominant mechanism, and the interaction strength is strongly influenced by changes of SiO₂ surface structures due to surface reactions with water. The adhesion energy is reduced when the reconstructed SiO₂ surface is hydroxylated, and further reduced when covered by a monolayer of adsorbed water molecules. Next, we study the interfacial interactions between graphene and a wet substrate that is covered by a liquid-like water film. During the separation of graphene from the wet substrate, MD simulations show evolution of the water from a continuous film to discrete islands. The water bridging effects are further described by continuum models. Finally, a continuum model is developed to predict how the surface roughness may affect the adhesion between graphene membranes and their substrate.