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Book
256 p. : ill. ; 20 cm.
SAL3 (off-campus storage)
Book
422 pages : illustrations (some color) ; 22 cm
Green Library
Book
616 p. : ill. ; 23 cm.
Green Library
Book
255, [1] p. ; 19 cm.
SAL3 (off-campus storage)

5. Böll [1978]

Book
224 p. : ill. ; 19 cm.
SAL3 (off-campus storage)
Book
115 p. illus. 18cm.
SAL3 (off-campus storage)
Book
144 p. illus. 18 cm.
SAL3 (off-campus storage)
Book
176 p. : ill. ; 18 cm.
SAL3 (off-campus storage)
Book
1 online resource.
The thesis presents the development, the mathematical analysis, as well as applications of a computational framework for the simulation of curvilinear crack propagation. At the core of the computational framework lies a novel finite element method, named the Mapped Finite Element Method (MFEM), for the optimal convergence of singular solutions. The main challenges in solving numerically the mathematical description of a propagating fracture can be identified in: the continuously evolving (cracked) domain, the singular nature of the elasticity fields, and the computation of the stress intensity factors for the prediction of crack growth. Current state-of-the-art methods are plagued by low order of accuracy, high computational cost, and complex data structures. The work herein addresses the aforementioned challenges by developing a computationally efficient, rapidly convergent, and non-intrusive algorithm consisting of three key ingredients: Universal Meshes, Mapped Finite Element Methods, and Interaction Integrals. First, Universal Meshes are introduced as a computationally efficient and robust meshing algorithm for the generation of conforming subdivisions of the evolving domain. Second, Mapped Finite Element Methods (MFEM) will be developed for the solution of the singular elasticity fields. The methods are shown to converge with optimal order for the same computational cost, preserving well conditioning and sparsity properties, and with no alteration to the data structure of standard Lagrange finite element methods (known to converge sub-optimally for this class of problems). The optimality of convergence is supported by mathematical analysis and applications of MFEM are showcased beyond brittle fracture (e.g. the resolution of boundary layers in flows around moving obstacle, real-space Kohn-Sham density functional theory calculations, etc). Third, the thesis presents the construct of a family of linear and affine functionals, named Interaction Integral functionals, for the rapidly convergent computation of the stress intensity factors (SIFs) for curvilinear fractures. The distinct feature of the Interaction Integral functionals is their ability to double the rate of convergence of the energy norm of the solution in the evaluation of the SIFs. Sketches of the mathematical analysis are provided to support the observed rapid rates of convergence. The propagation algorithm that combines the developed tools (Universal Meshes, Mapped Finite Element Methods, and Interaction Integrals) is presented and shown to be consistent (in the sense of being able to replicate observed experimental results) and predictive (in the sense of yielding crack paths that converge to a unique solution with refinement of the discretization). Lastly, the capabilities of the developed algorithm are exploited to study the formation of wavy crack patterns when brittle heat conductors are rapidly cooled.
Book
1 online resource.
Shale formations contain large oil and gas resources that have recently been exploited by hydraulic fracturing, and serve also as a typical caprock for CO2 storage reservoirs. Developing our understanding of, and predictive modeling capability for, the mechanical behavior of shale is therefore an important aspect of addressing pressing energy related social and sustainability issues, such as energy resilience, environmental safety, and climate change mitigation. The deformation and fracture properties of shale depend on the mechanical properties of its basic constituents, including nano- to micrometer sized organic, clay, and hard-mineral particles, as well as nanoscale porosity. A great deal of understanding of the overall mechanical properties of shales can be gained by studying the deformation and fracture properties of these constituents and how they behave as a composite material at nano- to micrometer length scales, informing the development of constitutive theory consistent with the nanomechanical origins of the shale's exhibited macromechanical behavior. This work describes a combined experimental and computational approach to the development of constitutive theory for shale. The experimental part of this work consisted of nanoindentation testing spanning nano- to micro-length scales coupled with FIB-SEM imaging and EDX spectroscopy. The FIB-SEM imaging and EDX spectroscopy were utilized to characterize the shale at the scale of the nanoindentation testing in both pre- and post-indented regions. The experiments reveal the mechanical properties of the relatively homogeneous constituent materials as well as those of the heterogeneous composite material, and provide insight into the shale's nanomechanical nature. Qualitative and quantitative interpretations of these measurements have motivated the development of material-appropriate constitutive modeling for organic and clay rich shales. A novel finite deformation elastoplastic constitutive framework for geomaterials is presented that makes use of Eshelby's stress tensor to reckon thermodynamic principles with the large inelastic volume strains that these materials are observed to exhibit. This constitutive framework is further extended to couple critical-state plasticity and continuum ductile-damage (CS-DD) theory in order to account for the extensive microfracture and changes in porosity observed through FIB-SEM imaging of post-indented regions. An important outcome of this work is to show that traditional finite deformation elastoplasticity models typically used for geomaterials are not consistent with the second law of thermodynamics, and may actually violate the second law under certain loading conditions. A novel stress measure for the spatial representation of hyperelastic constitutive laws is introduced as an alternative to traditional Kirchhoff stress formulations that are shown to satisfy the second law but give rise to spurious stresses under inelastic volumetric deformation. The thermodynamically consistent CS-DD framework is developed in the form of novel Modified Cam-Clay/Damage and Drucker-Prager/Damage material models incorporating continuum damage mechanics, and is implemented in 2D and 3D finite element simulations of laboratory and in-situ measurements.
Book
1 online resource.
Deformation mechanisms at the pore scale are responsible for producing large strains in porous rocks. They include cataclastic flow, dislocation creep, dynamic recrystallization, diffusive mass transfer, and grain boundary sliding, among others. In this work, we focus on two dominant pore-scale mechanisms resulting from purely mechanical, isothermal loading: crystal plasticity and micro-fracturing. We examine the contributions of each mechanism to the overall behavior at a scale larger than the grains but smaller than the specimen, which is commonly referred to as the mesoscale. Crystal plasticity is assumed to occur as dislocations along the many crystallographic slip planes, whereas micro-fracturing entails slip and frictional sliding on microcracks. It is observed that under combined shear and tensile loading, micro-fracturing generates a softer response compared to crystal plasticity alone, which is attributed to slip weakening where the shear stress drops to a residual level determined by the frictional strength. For compressive loading, however, micro-fracturing produces a stiffer response than crystal plasticity due to the presence of frictional resistance on the slip surface. Behaviors under tensile, compressive, and shear loading invariably show that porosity plays a critical role in the initiation of the deformation mechanisms. Both crystal plasticity and micro-fracturing are observed to initiate at the peripheries of the pores, consistent with results of experimental studies. We next develop a computational framework that captures the microfracture processes triggering shear band bifurcation in porous crystalline rocks. The framework consists of computational homogenization on a representative elementary volume (REV) that upscales the pore-scale microfracture processes to the continuum scale. The assumed enhanced strain (AES) finite element approach is used to capture the discontinuous displacement field generated by the microfractures. Homogenization at the continuum scale results in incrementally nonlinear material response, in which the overall constitutive tangent tensor varies with the stress state as well as with the loading direction. Continuum bifurcation detects the formation of a shear band on the REV level; 3D strain probes, necessitated by the incremental nonlinearity of the overall constitutive response, determine the most critical orientation for shear band bifurcation. Numerical simulations focus on microfracturing at the pore scale with either predominant interface separation or predominant interface contact modes. Results suggest a non-associative overall plastic flow and shear band bifurcation that depends on the microfracture length and the characteristic sliding distance related to slip weakening.
Book
1 online resource.
In this study we present a framework for the stress-strain analysis of polycrystalline materials subjected to quasistatic and isothermal loading conditions. We focus on rate-independent crystal plasticity as the primary micro-mechanism in the plastic deformation of crystalline aggregates. This deformation mechanism is modeled by a nonlinear stress-strain relationship and multiple linearly dependent yield constraints. Convergence problems induced by linear dependency of constraints is one of the challenges in modeling rate-independent crystal plasticity. Failure to converge at a single crystal level can cause numerical stability problems when modeling larger scales such as boundary value problems. In this work we first build a stress point model based on the `ultimate' algorithm in the infinitesimal deformation range. Since this algorithm solves the stress-strain response analytically, the model is unconditionally convergent. Numerical examples are presented to demonstrate the numerical stability of the algorithm and the significance of considering crystal microstructure in modeling the plastic deformation of single crystals. To investigate the overall elasto-plastic behavior of crystalline solids at scales larger than a single crystal, the stress point model at the infinitesimal deformation range is implemented in a nonlinear finite element code. Several boundary value problems are presented to demonstrate the numerical stability of the finite element model and also the effect of considering crystal microstructure on predicting the macro-scale elasto-plastic behavior of crystalline solids. We next formulate crystal plasticity in the finite deformation range. This formulation, which is based on the theory of distribution and strong discontinuity concepts, considers both material and geometric nonlinearity in the plastic deformation of crystals. We propose exact and approximate stress point algorithms to solve the presented framework. To find the set of linearly independent slip systems, we follow the same idea as the `ultimate' algorithm. The presented numerical examples demonstrate that the simplified approximate algorithm is accurate. The examples also indicate the significant impact of geometric nonlinearity on the stress-strain response of single crystals. We derive a framework to analyze the onset and configuration of localization in crystalline solids at infinitesimal and finite deformation ranges. The presented examples demonstrate that geometric nonlinearity has a significant impact on the localization analyses of crystalline solids.
Special Collections
Book
1 online resource.
Hydromechanical interactions between fluid flow and deformation in porous geomaterials give rise to a wide range of societally important problems such as landslides, ground subsidence, and injection-induced earthquakes. Many geomaterials in these problems possess two-scale porous structures due to fractures, particle aggregation, or other reasons. However, coupled hydromechanical processes in these multiscale porous materials, such as ground deformation caused by preferential flow, are beyond the modeling capabilities of classical frameworks. This thesis develops theoretical and computational frameworks for fully coupled hydromechanical modeling of geomaterials with two-scale porous structures. Adopting the concept of double porosity, we treat these materials as a multiscale continuum in which two pore regions of different scales interact within the same continuum. Three major developments are presented. First, we build a mathematical framework for thermodynamically consistent modeling of unsaturated porous media with double porosity. Conservation laws are formulated incorporating an effective stress tensor that is energy-conjugate to the rate of deformation tensor of the solid matrix. Based on energy-conjugate pairs identified in the first law of thermodynamics, we develop a constitutive framework for hydrological and mechanical processes coupled at two scales. Second, we introduce a novel constitutive framework for elastoplastic materials with evolving internal structures. By partitioning the thermodynamically consistent effective stress into two individual, single-scale effective stresses, this framework uniquely distinguishes proportional volume changes in the two pore regions under finite deformations. This framework accommodates the impact of pore pressure difference between the two scales on the solid deformation, which was predicted by thermodynamic principles. We show that the proposed framework not only improves the prediction of deformation of two-scale geomaterials, but also simulates secondary compression effects due to delayed pressure dissipation in the less permeable pore region. Third, we develop a finite element framework that enables the use of computationally efficient equal-order elements for solving coupled fluid flow and deformation problems in double-porosity media. At the core of the finite element formulation is a new method that stabilizes twofold saddle point problems arising in the undrained condition. The stabilized finite elements allow for equal-order linear interpolations of three primary variables—the displacement field and two pore pressure variables—throughout the entire range of drainage conditions.

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