Browsing by Author "Dolbow, John Everett"
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Item Open Access A Computational Framework for Fracture Modeling in Coupled Field Problems(2018) Liu, YingjieThis dissertation proposes a family of computational frameworks for fracture modeling in coupled field problems. Fracture mechanics has been a topic of considerable interest for several decades due to the wide existence of fracture in different engineering structures and the important applications of fracture in multiple industries.
The present study first develops a continuum-discrete approach to model the fluid-driven fracture of granular media. This approach avoids remeshing by representing the particles as moving interfaces on a fixed background mesh. The effect of particle movement on the flow is characterized by a non-slip boundary condition. A boundary split scheme is proposed to ensure the coercivity of the method. The fluid-driven force on particles is represented by a boundary integral of the viscous drag force around the particles. The corresponding initial-boundary value problem is constructed for the invading fluid and is spatially discretized with the finite element method. A novel quadrature method is developed to handle partial elements that arise due to the mismatch between the mesh and the physical domain. The conditioning issue of partial elements is also addressed in the present study.
The present study also aims at developing a general and robust computational approach for the fracture modeling of conventional materials within coupled field problems. We follow the framework of a phase field regularization because of its strength in handling complex fracture patterns. The first application we consider is the fracture simulation of kidney stones during shock wave lithotripsy (SWL), an acoustic-solid-fracture coupling problem. The present study develops a novel computational framework for simulating SWL.
The propagation of acoustic pressure is modeled by a wave equation and the deformation of the phantom stone is modeled by the elasto-dynamics equations. The interactions between the acoustic wave and kidney stone is enforced via the continuity condition. The initialization and propagation of fracture within the stone is implicitly represented by the evolution of the phase field.
Traditional phase field is designed to model the brittle fracture of homogeneous materials. The present study develops a phase field framework to model fracture propagation in anisotropic and heterogeneous solids. The present model is distinguished from the traditional phase field approach by the fact that it converges to a cohesive type model instead of a Griffith model. A mathematically self-consistent strain energy density functional is proposed that is valid for any anisotropic linear elastic materials. Anisotropy in both the bulk moduli and the crack surface energy are characterized. The model employs multiple phase fields to capture the fracture behavior of the material with more than one preferential cleavage plane. The model develops a novel degradation function which relaxes the strong constraint between the regularization length l and the material properties. The convergence of the model with reducing l and the energy conservation properties of the framework are demonstrated through numerical examples. A robust adaptivity strategy is developed to increase the efficiency of the model. The present framework is applied to model fracture in heterogeneous and anisotropic materials. Coupled with a fine scale analysis, the present model is also used to model the fracture of functionally graded materials.
Item Open Access A Dynamic Fracture Simulation Based on Embedded Finite Element Methods(2012) Zhao, BingxiaoIn this thesis, a hybrid numerical approach is proposed for modeling dynamic fracture in brittle materials. This method is based on a combination of embedded finite element methods and extrinsic cohesive zone models. The effect of different methods to enforce the kinematics at the embedded interface for crack initiation and propagation are investigated and numerically compared. Finally, Nitsche's method is suggested within the hybrid numerical schemes to simulate dynamic fracture. In the pre-failure stage, terms for consistency and stabilization are introduced into the finite element framework with Nitsche's method. When the fracture criterion is met, the extrinsic cohesive law governs the behavior of the opening surfaces by a simple change of framework without modifications of the mesh. This traction and separation law is directly implemented at the interface through an interface approach. Upon closure of the crack surfaces in compression, Nitsche's method is suggested to weakly enforce contact conditions at crack surfaces.
The applicability of the proposed hybrid method is investigated in numerical examples. By using Nitsche's method, the main advantage of the hybrid method for modeling dynamic crack propagation is to avoid unphysical initial slopes in the numerical implementation of extrinsic cohesive laws, which affords us more accurate crack initiation than with the penalty method. Another advantage is that the consistency and stability at unfractured interfaces during crack propagation are maintained and hence the issues caused by the penalty method in explicit dynamic schemes are avoided. Importantly, Nitsche's method performs better than the penalty method conventionally used to prevent interpenetration under compressive loadings.
Item Open Access A New Method for Modeling Free Surface Flows and Fluid-structure Interaction with Ocean Applications(2016) Lee, CurtisThe computational modeling of ocean waves and ocean-faring devices poses numerous challenges. Among these are the need to stably and accurately represent both the fluid-fluid interface between water and air as well as the fluid-structure interfaces arising between solid devices and one or more fluids. As techniques are developed to stably and accurately balance the interactions between fluid and structural solvers at these boundaries, a similarly pressing challenge is the development of algorithms that are massively scalable and capable of performing large-scale three-dimensional simulations on reasonable time scales. This dissertation introduces two separate methods for approaching this problem, with the first focusing on the development of sophisticated fluid-fluid interface representations and the second focusing primarily on scalability and extensibility to higher-order methods.
We begin by introducing the narrow-band gradient-augmented level set method (GALSM) for incompressible multiphase Navier-Stokes flow. This is the first use of the high-order GALSM for a fluid flow application, and its reliability and accuracy in modeling ocean environments is tested extensively. The method demonstrates numerous advantages over the traditional level set method, among these a heightened conservation of fluid volume and the representation of subgrid structures.
Next, we present a finite-volume algorithm for solving the incompressible Euler equations in two and three dimensions in the presence of a flow-driven free surface and a dynamic rigid body. In this development, the chief concerns are efficiency, scalability, and extensibility (to higher-order and truly conservative methods). These priorities informed a number of important choices: The air phase is substituted by a pressure boundary condition in order to greatly reduce the size of the computational domain, a cut-cell finite-volume approach is chosen in order to minimize fluid volume loss and open the door to higher-order methods, and adaptive mesh refinement (AMR) is employed to focus computational effort and make large-scale 3D simulations possible. This algorithm is shown to produce robust and accurate results that are well-suited for the study of ocean waves and the development of wave energy conversion (WEC) devices.
Item Open Access A Variational Framework for Phase-Field Fracture Modeling with Applications to Fragmentation, Desiccation, Ductile Failure, and Spallation(2021) Hu, TianchenFracture is a common phenomenon in engineering applications. Many types of fracture exist, including, but not limited to, brittle fracture, quasi-brittle fracture, cohesive fracture, and ductile fracture. Predicting fracture has been one of the most challenging research topics in computational mechanics. The variational treatment of fracture and its associated phase-field regularization have been employed with great success for modeling fracture in brittle materials. Extending the variational statement to describe other types of fracture and coupled field phenomena has proven less straightforward. Main challenges that remain include how to best construct a total potential that is both mathematically sound and physically admissible, and how to properly describe the coupling between fracture and other phenomena.
The research presented in this dissertation aims at addressing the aforementioned challenges. A variational framework is proposed to describe fracture in general dissipative solids. In essence, the variational statement is extended to account for large deformation kinematics, inelastic deformation, dissipation mechanisms, dynamic effects, and thermal effects. The proposed variational framework is shown to be consistent with conservations and laws of thermodynamics, and it provides guidance and imposes restrictions on the construction of models for coupled field problems. Within the proposed variational framework, several models are instantiated to address practical engineering problems. A brittle and quasi-brittle fracture model is used to investigate fracture evolution in polycrystalline materials; a cohesive fracture model is applied to revisit soil desiccation; a novel ductile fracture model is proposed and successfully applied to simulate some challenging benchmark problems; and a creep fracture model is developed to simulate the spallation of oxide scale on high temperature heat exchangers.
Item Open Access Adaptive Spline-based Finite Element Method with Application to Phase-field Models of Biomembranes(2015) Jiang, WenInterfaces play a dominant role in governing the response of many biological systems and they pose many challenges to traditional finite element. For sharp-interface model, traditional finite element methods necessitate the finite element mesh to align with surfaces of discontinuities. Diffuse-interface model replaces the sharp interface with continuous variations of an order parameter resulting in significant computational effort. To overcome these difficulties, we focus on developing a computationally efficient spline-based finite element method for interface problems.
A key challenge while employing B-spline basis functions in finite-element methods is the robust imposition of Dirichlet boundary conditions. We begin by examining weak enforcement of such conditions for B-spline basis functions, with application to both second- and fourth-order problems based on Nitsche's approach. The use of spline-based finite elements is further examined along with a Nitsche technique for enforcing constraints on an embedded interface. We show that how the choice of weights and stabilization parameters in the Nitsche consistency terms has a great influence on the accuracy and robustness of the method. In the presence of curved interface, to obtain optimal rates of convergence we employ a hierarchical local refinement approach to improve the geometrical representation of interface.
In multiple dimensions, a spline basis is obtained as a tensor product of the one-dimensional basis. This necessitates a rectangular grid that cannot be refined locally in regions of embedded interfaces. To address this issue, we develop an adaptive spline-based finite element method that employs hierarchical refinement and coarsening techniques. The process of refinement and coarsening guarantees linear independence and remains the regularity of the basis functions. We further propose an efficient data transfer algorithm during both refinement and coarsening which yields to accurate results.
The adaptive approach is applied to vesicle modeling which allows three-dimensional simulation to proceed efficiently. In this work, we employ a continuum approach to model the evolution of microdomains on the surface of Giant Unilamellar Vesicles. The chemical energy is described by a Cahn-Hilliard type density functional that characterizes the line energy between domains of different species. The generalized Canham-Helfrich-Evans model provides a description of the mechanical energy of the vesicle membrane. This coupled model is cast in a diffuse-interface form using the phase-field framework. The effect of coupling is seen through several numerical examples of domain formation coupled to vesicle shape changes.
Item Open Access An efficient finite element method for embedded interface problems(2013) Annavarapu, ChandrasekharWe focus on developing a computationally efficient finite element method for interface problems. Finite element methods are severely constrained in their ability to resolve interfaces. Many of these limitations stem from their inability in independently representing interface geometry from the underlying discretization. We propose an approach that facilitates such an independent representation by embedding interfaces in the underlying finite element mesh. This embedding, however, raises stability concerns for existing algorithms used to enforce interfacial kinematic constraints. To address these stability concerns, we develop robust methods to enforce interfacial kinematics over embedded interfaces. We begin by examining embedded Dirichlet problems – a simpler class of embedded constraints. We develop both stable methods, based on Lagrange multipliers,and stabilized methods, based on Nitsche’s approach, for enforcing Dirichlet constraints over three-dimensional embedded surfaces and compare and contrast their performance. We then extend these methods to enforce perfectly-tied kinematics for elastodynamics with explicit time integration. In particular, we examine the coupled aspects of spatial and temporal stability for Nitsche’s approach.We address the incompatibility of Nitsche’s method for explicit time integration by (a) proposing a modified weighted stress variational form, and (b) proposing a novel mass-lumpingprocedure.We revisit Nitsche’s method and inspect the effect of this modified variational form on the interfacial quantities of interest. We establish that the performance of this method, with respect to recovery of interfacial quantities, is governed significantly by the choice for the various method parameters viz.stabilization and weighting. We establish a relationship between these parameters and propose an optimal choice for the weighting. We further extend this approach to handle non-linear,frictional sliding constraints at the interface. The naturally non-symmetric nature of these problems motivates us to omit the symmetry term arising in Nitsche’s method.We contrast the performance of the proposed approach with the more commonly used penalty method. Through several numerical examples, we show that with the pro-posed choice of weighting and stabilization parameters, Nitsche’s method achieves the right balance between accurate constraint enforcement and flux recovery - a balance hard to achieve with existing methods. Finally, we extend the proposed approach to intersecting interfaces and conduct numerical studies on problems with junctions and complex topologies.Item Open Access Analysis of the Elastica with Applications to Vibration Isolation(2007-05-02T17:38:28Z) Santillan, Sophia TeresaLinear theory is useful in determining small static and dynamic deflections. However, to characterize large static and dynamic deflections, it is no longer useful or accurate, and more sophisticated analysis methods are necessary. In the case of beam deflections, linear beam theory makes use of an approximate curvature expression. Here, the exact curvature expression is used to derive the governing partial differential equations that describe the in-plane equilibrium and dynamics of a long, thin, inextensible beam, where the self-weight of the beam is included in the analysis. These beam equations are expressed in terms of arclength, and the resulting equilibrium shape is called the elastica. The analysis gives solutions that are accurate for any deflection size, and the method can be used to characterize the behavior of many structural systems. Numerical and analytical methods are used to solve or to approximate solutions to the governing equations. Both a shooting method and a finite difference, time-stepping algorithm are developed and implemented to find numerical solutions and these solutions are compared with some analytical approximation method results. The elastica equations are first used to determine both linear and nonlinear equilibrium configurations for a number of boundary conditions and loading types. In the case of a beam with a significant self-weight, the system can exhibit nonlinear static behavior even in the absence of external loading, and the elastica equations are used to determine the weight corresponding to the onset of instability (or self-weight buckling). The equations are also used to characterize linear and nonlinear vibrations of some structural systems, and experimental tests are conducted to verify the numerical results. The linear vibration analysis is applied to a vibration isolator system, where a postbuckled clamped-clamped beam or otherwise highly-deformed structure is used (in place of a conventional spring) to reduce system motion. The method is also used to characterize nonlinear dynamic behavior, and the resulting frequency-response curves are compared with those in the literature. Finally, the method is used to investigate the dynamics of subsea risers, where the effects of gravity, buoyancy, and the current velocity are considered.Item Open Access Application of Numerical Methods to Study Arrangement and Fracture of Lithium-Ion Microstructure(2016) Stershic, Andrew JosephThe focus of this work is to develop and employ numerical methods that provide characterization of granular microstructures, dynamic fragmentation of brittle materials, and dynamic fracture of three-dimensional bodies.
We first propose the fabric tensor formalism to describe the structure and evolution of lithium-ion electrode microstructure during the calendaring process. Fabric tensors are directional measures of particulate assemblies based on inter-particle connectivity, relating to the structural and transport properties of the electrode. Applying this technique to X-ray computed tomography of cathode microstructure, we show that fabric tensors capture the evolution of the inter-particle contact distribution and are therefore good measures for the internal state of and electronic transport within the electrode.
We then shift focus to the development and analysis of fracture models within finite element simulations. A difficult problem to characterize in the realm of fracture modeling is that of fragmentation, wherein brittle materials subjected to a uniform tensile loading break apart into a large number of smaller pieces. We explore the effect of numerical precision in the results of dynamic fragmentation simulations using the cohesive element approach on a one-dimensional domain. By introducing random and non-random field variations, we discern that round-off error plays a significant role in establishing a mesh-convergent solution for uniform fragmentation problems. Further, by using differing magnitudes of randomized material properties and mesh discretizations, we find that employing randomness can improve convergence behavior and provide a computational savings.
The Thick Level-Set model is implemented to describe brittle media undergoing dynamic fragmentation as an alternative to the cohesive element approach. This non-local damage model features a level-set function that defines the extent and severity of degradation and uses a length scale to limit the damage gradient. In terms of energy dissipated by fracture and mean fragment size, we find that the proposed model reproduces the rate-dependent observations of analytical approaches, cohesive element simulations, and experimental studies.
Lastly, the Thick Level-Set model is implemented in three dimensions to describe the dynamic failure of brittle media, such as the active material particles in the battery cathode during manufacturing. The proposed model matches expected behavior from physical experiments, analytical approaches, and numerical models, and mesh convergence is established. We find that the use of an asymmetrical damage model to represent tensile damage is important to producing the expected results for brittle fracture problems.
The impact of this work is that designers of lithium-ion battery components can employ the numerical methods presented herein to analyze the evolving electrode microstructure during manufacturing, operational, and extraordinary loadings. This allows for enhanced designs and manufacturing methods that advance the state of battery technology. Further, these numerical tools have applicability in a broad range of fields, from geotechnical analysis to ice-sheet modeling to armor design to hydraulic fracturing.
Item Open Access Crack Nucleation and Branching in the eXtended Finite Element Method(2013) Merewether, Mark ThomasThe eXtended Finite Element Method (X-FEM) has proven to be a robust method for simulating crack propagation, but relatively little work has focused on the important problem of crack initiation or nucleation. In this work, we examine various options for nucleating cracks within a cohesive framework and the X-FEM. Attention is confined to shell problems. We discuss the details of the methods and their strengths and weaknesses. With the introduction of such nucleation algorithms, the need to model more complex crack growth topologies also arises. In particular, we examine algorithms for enabling crack branching, focusing on both the mechanics and element kinematic considerations. The results of various benchmark problems for the nucleation and branching algorithms are also presented and discussed.
Item Open Access Data Transfer between Meshes for Large Deformation Frictional Contact Problems(2013) Kindo, Temesgen MarkosIn the finite element simulation of problems with contact there arises
the need to change the mesh and continue the simulation on a new mesh.
This is encountered when the mesh has to be changed because the original mesh experiences severe distortion or the mesh is adapted to minimize errors in the solution. In such instances a crucial component is the transfer of data from the old mesh to the new one.
This work proposes a strategy by which such remeshing can be accomplished in the presence of mortar-discretized contact,
focusing in particular on the remapping of contact variables which must occur to make the method robust and efficient.
By splitting the contact stress into normal and tangential components and transferring the normal component as a scalar and the tangential component by parallel transporting on the contact surface an accurate and consistent transfer scheme is obtained. Penalty and augmented Lagrangian formulations are considered. The approach is demonstrated by a number of two and three dimensional numerical examples.
Item Open Access Finite Element Methods for Interface Problems with Mesh Adaptivity(2015) Zhang, ZiyuThis dissertation addresses interface problems simulated with the finite element method (FEM) with mesh adaptivity. More specifically, we concentrate on the strategies that adaptively modify the mesh and the associated data transfer issues.
In finite element simulations there often arises the need to change the mesh and continue the simulation on a new mesh. Analysts encounter such an issue when they adaptively refine the mesh to reduce the computational cost, smooth distorted elements to improve system conditioning, or introduce new surfaces and change the domain in simulations of fracture problems. In such circumstances, the transfer of data from the old mesh to the new one is of crucial importance, especially for nonlinear problems. We are concerned in this work with contact problems with adaptive re-meshing and fracture problems modeled with the eXtended finite element method (X-FEM). For the former ones, the transfer of surface data is built upon the technique of parallel transport, and the error of such a transfer strategy is investigated through classic benchmark tests. A transfer scheme based on a least squares problem is also proposed to transfer the bulk data when nearly incompressible hyperelastic materials are employed. For the latter type of problems, we facilitate the transfer of internal variables by making partial elements utilize the same quadrature points from the uncut parent elements and meanwhile adjusting the quadrature weights via the solution of moment fitting equations. The proposed scheme helps avoid the complicated remapping procedure of internal variables between two different sets of quadrature points. A number of numerical examples are presented to demonstrate the robustness and accuracy of our proposed approaches.
Another renowned technique to simulate fracture problems is based upon the phase-field formulation, where a set of coupled mechanics and phase-field equations are solved via FEM without modeling crack geometries. However, losing the ability to model distinct surfaces in the phase-field formulation has drawbacks, such as difficulties simulating contact on crack surfaces and poorly-conditioned stiffness matrices. On the other hand, using the pure X-FEM in fracture simulations mandates the calculation of the direction and increment of crack surfaces at each step, introducing intricacies of tracing crack evolution. Thus, we propose combining phase-field and X-FEM approaches to utilize their individual benefits based on a novel medial-axis algorithm. Consequently, we can still capture complex crack geometries while having crack surfaces explicitly modeled by modifying the mesh with the X-FEM.
Item Open Access Imposing a Speed Limit to Crack Propagation in Phase Field for Fracture(2021) Versteeg, CasperHigh-speed fracture is typically a strain-rate dependent phenomenon, and it isgenerally accepted that the fracture energy is a function of the speed at which a crack propagates. Importantly, most experimental observations seem to indicate that crack tip speed limits are lower than the bulk wave speed for a given material. This means the coupling between fracture and elastodynamics is dependent on the limiting speed, and developing models that capture this limit accurately is desirable.
This thesis presents a thermodynamically consistent modification to the popularphase field for fracture framework, which includes a dissipative term that is intended to impose a limiting speed on propagating cracks. Additionally, it highlights the extent to which modifications to the existing theory are permissible.
Item Open Access Influence of Material Properties and Fracture Properties on the Crack Nucleation and Growth(2021) Zeng, BoIn this thesis, we studied the influence of spatial variations in the fracture property and the elastic property on the resulting crack patterns during soil desiccation. Young's modulus is selected as the representative elastic property and the fracture toughness is selected as that for the fracture property. Their well-defined spatially fluctuated random fields are the input of the phase-field fracture simulation, and the resulting damage field is the output. Various postprocessing of the damage field were carried out to analyze the resulting fields. After comparing the morphology of the cracks and fragment size distributions, a preliminary guess was that the two inputs have very close influence on the output. Then the Pearson correlation coefficient, as a first try of sensitivity analysis, also gave an indistinguishable correlation number between the two. A more rigorous approach with highly isolated sensitivity quantity was needed, which brought us to the Sobol' indice based on polynomial chaos expansion, a global sensitivity analysis measure which accounts for the variation of output into the variation of each input and any combination of input.
Item Open Access Modeling Microdomain Evolution on Giant Unilamellar Vesicles using a Phase-Field Approach(2013) Embar, Anand SrinivasanThe surface of cell membranes can display a high degree of lateral heterogeneity. This non-uniform distribution of constituents is characterized by mobile nanodomain clusters called rafts. Enriched by saturated phospholipids, cholesterol and proteins, rafts are considered to be vital for several important cellular functions such as signalling and trafficking, morphological transformations associated with exocytosis and endocytosis and even as sites for the replication of viruses. Understanding the evolving distribution of these domains can provide significant insight into the regulation of cell function. Giant vesicles are simple prototypes of cell membranes. Microdomains on vesicles can be considered as simple analogues of rafts on cell membranes and offer a means to study various features of cellular processes in isolation.
In this work, we employ a continuum approach to model the evolution of microdomains on the surface of Giant Unilamellar Vesicles (GUVs). The interplay of species transport on the vesicle surface and the mechanics of vesicle shape change is captured using a chemo-mechanical model. Specifically, the approach focuses on the regime of vesicle dynamics where shape change occurs on a much faster time scale in comparison to species transport, as has been observed in several experimental studies on GUVs. In this study, shape changes are assumed to be instantaneous, while species transport, which is modeled by phase separation and domain coarsening, follows a natural time scale described by the Cahn--Hilliard dynamics.
The curvature energy of the vesicle membrane is defined by the classical Canham--Helfrich--Evans model. Dependence of flexural rigidity and spontaneous curvature on the lipid species is built into the energy functional. The chemical energy is characterized by a Cahn--Hilliard type density function that intrinsically captures the line energy of interfaces between two phases. Both curvature and chemical contributions to the vesicle energetics are consistently non-dimensionalized.
The coupled model is cast in a diffuse-interface form using the phase-field framework. The phase-field form of the governing equations describing shape equilibrium and species transport are both fourth-order and nonlinear. The system of equations is discretized using the finite element method with a uniform cubic-spline basis that satisfies global higher-order continuity. For shape equilibrium, geometric constraints of constant internal volume and constant surface area of the vesicle are imposed weakly using the penalty approach. A time-stepping scheme based on the unconditionally gradient-stable convexity-splitting technique is employed for explicit time integration of nonlocal integrals arising from the geometric constraints.
Numerical examples of axisymmetric stationary shapes of uniform vesicles are presented. Further, two- and three-dimensional numerical examples of domain formation and growth coupled to vesicle shape changes are discussed. Simulations qualitatively depicting curvature-dependent domain sorting and shape changes to minimize line tension are presented. The effect of capturing the difference in time scales is also brought out in a few numerical simulations that predict a starkly different pathway to equilibrium.
Item Open Access Multiphase Flow in a Hele-Shaw Cell(2018) Rhea, Carter LeeThe primary goal of this thesis is to explore the capabilities of MOOSE (Multiphysics
Object Oriented Simulation Environment) and LAMMPS (Large-scale Atomic/Molecular
Massively Parallel Simulator) and their potential to be coupled in order to simulate
multiphase flow in a Hele-Shaw cell. After formulating the Darcy-Richards multi-
phase flow equations for a finite element method application, I synthesized the nec-
essary particle-particle interactions from existing literature and implemented them
in LAMMPS. In addition, I created a parallelized C++ program to calculate the
particle packing field through the heavy employ of OpenMP. With the conclusion
of extensive testing suites for both LAMMPS and MOOSE, I developed a python
program which was used to mesh LAMMPS and MOOSE by acting as a translation
and book-keeping program. While the coupling scheme appears to function properly
in test cases, it fails to capture the full impact of the particles on the fluid system and
thus allows for penetration of the invading fluid into regions which ought to remain
unsaturated.
Item Open Access The Ductile to Brittle Transition in Polycarbonate(2011) Pogacnik, JustinAn advanced bulk constitutive model is used with a new cohesive zone model that is stress state and rate-dependent in order to simulate the ductile to brittle failure transition in polycarbonate. The cohesive zone model is motivated by experimental evidence that two different critical energies per unit area of crack growth exist in glassy polymers. A higher energy state is associated with ductile failure (slow crack growth), while a lower energy state is associated with brittle failure (fast crack growth). The model is formulated so that as rate or stress state changes within a simulation, the fracture energy and thus fracture mode may also change appropriately. The ductile to brittle transition occurs when the cohesive opening rate is over a threshold opening rate and when the stress state is close to plane strain in a fracture specimen. These effects are coupled. The principal contribution of this work is that this is the first time a single set of material input parameters can predict the transition from slow to fast crack growth as test loading rate and sample thickness are varied. This result enlisted the use of an advanced constitutive model and the new cohesive zone model with rate and stress-state dependencies in three-dimensional finite element analysis.
Item Open Access Towards Accurate and Robust Modeling of Fluid-Driven Fracture(2023) Costa, AndreThis work advances a phase-field method for fluid-driven fractures and proposes arobust and efficient discretization framework. It begins by addressing a modeling challenge related to the application of pressure loads on diffuse crack surfaces. Along the way, a new J-Integral for pressurized fractures in a regularized context is devel- oped.
Then, the focus turns to a hybrid method to model fluid-driven fracture propaga-tion. A so-called multi-resolution method is presented that uses a combination of en- richment schemes with the phase-field method to address the complex fluid-fracture interaction that occurs during hydraulic fracture. On one hand, the phase-field method alleviates some of the difficulties associated with the geometric evolution of the fracture, which are usually the limiting aspect of purely enrichment-based schemes. On the other hand, the discrete representation allows for a better treat- ment of the fluid loads and crack apertures, which are the main challenges associated with phase-field approaches.
The multi-resolution method is first presented in a simplified scheme to treat two-dimensional problems. Various benchmark problems are used to verify the framework against well-known analytical solutions. The method is then extended to three- dimensions. A robust algorithm to handle planar cracks in 3D is developed and its extension to non-planar cases is discussed. Finally, opportunities for improvements and extensions are discussed, paving the road for future work in this area.
Item Open Access Towards Simulations of Pervasive Fracture Across Structural Scales(2020) Geelen, RudyFracture is a fundamental mechanism of material and structural failure and remains one of the most long-standing research topics within computational solid mechanics. Propagating cracks exhibit a rich behavior governed by the delicate interplay between macroscopic elasticity and microscopic failure mechanisms in the neighborhood of the crack tip. This dissertation takes a closer look at enabling the computational modeling of pervasive fracture and material failure across disparate spatial scales. While the search for a generally applicable approach is a continuous effort, variational fracture models have established themselves as the dominant numerical analysis method for the simulation of these processes. The main appeal of variational approaches to fracture mechanics is that they diminish the need for an a priori knowledge of the crack path or ad hoc assumptions in the form of crack path selection laws and completely eliminate the need for interface tracking.
The research presented in this dissertation aims at remedying some of the most vexing issues surrounding the variational modeling of fracture. A variational description of dynamic fracture tailored for cohesive fracture mechanics is postulated. The model applies beyond the well-known Griffith regime where both the maximum stress and the critical strain become infinite as the regularization length scale vanishes. Another distinct issue lies in the identification of a sharp crack surface when a strict "smeared crack" point-of-view is embraced. This issue is revisited through the lens of optimization, where the notion of the auxiliary damage field plays an important role. Additionally, this dissertation discusses the development of a scalable and performant implementation of a scale-bridging extended/generalized finite element method to resolve the disparate physical and geometric length scales and provide some relief to the sheer computational expense of variational fracture problems. Several numerical experiments are conducted to substantiate the proposed theories and methodologies.