SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

Advanced BEM-based methodologies to identify and simulate wave fields in complex geostructures

To enhance the applicability of BEM for geomechanical modeling numerically optimized BEM models, hybrid FEM-BEM models, and parallel computation of seismic Full Waveform Inversion (FWI) in GPU are implemented. Inverse modeling of seismic wave propagation in inhomogeneous and heterogeneous half-plane is implemented in Boundary Element Method (BEM) using Particle Swarm Optimization (PSO). The Boundary Integral Equations (BIE) based on the fundamental solutions for homogeneous elastic isotropic continuum are modified by introducing mesh-dependent variables. The variables are optimized to obtain the site-specific impedance functions. The PSO-optimized BEM models have significantly improved the efficiency of BEM for seismic wave propagation in arbitrarily inhomogeneous and heterogeneous media. Similarly, a hybrid BEM-FEM approach is developed to evaluate the seismic response of a complex poroelastic soil region containing underground structures. The far-field semi-infinite geological region is modeled via BEM, while the near-field finite geological region is modeled via FEM. The BEM region is integrated into the global FEM system using an equivalent macro-finite-element. The model describes the entire wave path from the seismic source to the local site in a single hybrid model. Additionally, the computational efficiency of time domain FWI algorithm is enhanced by parallel computation in CPU and GPU

Simulation of Hydraulic Stimulation: Acoustic Wave Emission in Fractured Porous Media Using Local and Global Partition-of-Unity Finite Element

Hydraulic Fracturing (HF) is an effective stimulation process for extracting oil and gas from unconventional low-permeable reservoirs. The process is conducted by injecting high-pressure fluids into the ground to generate fracture networks in rock masses and stimulate natural fractures to increase the permeability of formation and extract oil and gas. Due to the multiple and coupled-physics involved, hydraulic fracturing is a complex engineering process. The extent of the induced fractures and stimulated volume and reactivation of natural faults and fractures are some of the practical issues associated with hydraulic fracturing. Acoustic Emission (AE) monitoring and analysis are used to probe the behaviour of solid materials in such applications. The process of elastic wave propagation induced by an abrupt local release of stored strain energy is known as acoustic, microseismic, and seismic emission (depending on the context and the magnitude of the event). These emissions can be triggered by material bifurcation-instabilities like slope slipping, fault-reactivation, pore collapsing, and cracking - processes that are all categorized as localization phenomena. The microseismic monitoring industry attempts to relate acoustic emissions measured by geophones to the nature of the stimulated volume created during hydraulic fracturing. This process is full of uncertainties and researchers have not yet focused on both explicitly modeling the process of fracture reactivation and the accurate simulation of acoustic wave propagations resulting from the localization. The biggest gap in the modeling literature is that most of the previous works fail to accurately simulate the process of transient acoustic wave propagation through the fractured porous media following the elastic energy release. Instead of explicitly modeling fracturing and acoustic emission, most previous studies have aimed to relate energy release to seismic moment. To overcome some of the existing shortcomings in the numerical modeling of the coupled problem of interface localization-acoustic emission, this thesis is focused on developing new computational methods and programs for the simulation of microseismic wave emissions induced by interface slip instability in fractured porous media. As a coupled nonlinear mixed multi-physics problem, simulation of hydraulic stimulation involves several mathematical and computational complexities and difficulties in terms of modeling, stability, and convergence, such as the inf-sup stability problems that arise from mixed formulations due to the hydro-mechanical couplings and contact conditions. In AE modeling, due to the high-frequency transient nature of the problem, additional numerical problems emerging from the Gibbs phenomenon and artificial period elongation and amplitude decay are also involved. The thesis has three main objectives. The first objective is to develop a numerical model for simulation of wave propagation in discontinuous media, which is fulfilled in Chapter 2 of the thesis. In this chapter a new enriched finite element method is developed for simulation of wave propagation in fractured media. The method combines the advantages of the global Partition-of-Unity Method (PUM) with harmonic enrichment functions via the Generalized Finite Element Method (GFEM) with the local PUM via the Phantom Node Method (PNM). The GFEM enrichments suppress the spurious oscillations that can appear in regular Finite Element Method (FEM) analysis of dynamic/wave propagations due to numerical dispersions and Gibbs phenomenon. The PNM models arbitrary fractures independently of the original mesh. Through several numerical examples it has been demonstrated that the spurious oscillations that appear in propagation pattern of high-frequency waves in PNM simulations can be effectively suppressed by employing the enriched model. This is observed to be especially important in fractured media where both primary waves and the secondary reflected waves are present. The second objective of the thesis is to develop a mixed numerical model for simulation of wave propagation in discontinuous porous media and interface modeling. This objective is realized in Chapter 3 of the thesis. In this chapter, a new enriched mixed finite element model is introduced for simulation of wave propagation in fractured porous media, based on an extension of the developed numerical method in Chapter 2. Moreover, frictional contact at interfaces is modeled and realized using an augmented Lagrange multiplier scheme. Through various numerical examples, the effectiveness of the developed enriched FE model over conventional approaches is demonstrated. Moreover, it is shown that the most accurate wave results with the least amount of spurious oscillations are achieved when both the displacement and pore pressure fields are enriched with appropriate trigonometric functions. The third objective of the thesis is to develop computational models for the simulation of acoustic emissions induced by fracture reactivation and shear slip. This objective is realized in Chapter 4 of the thesis. In this chapter, an enriched mixed finite element model (introduced in Chapter 3) is developed to simulate the interface slip instability and the associated induced acoustic wave propagation processes, concurrently. Acoustic events are triggered through a sudden release of strain energy at the fracture interfaces due to shear slip instability. The shear slip is induced via hydraulic stimulation that switches the interface behaviour from a stick to slip condition. The superior capability of the proposed enriched mixed finite element model (i.e., PNM-GFEM-M) in comparison with regular finite element models in inhibiting the spurious oscillations and numerical dispersions of acoustic signals in both velocity and pore pressure fields is demonstrated through several numerical studies. Moreover, the effects of different characteristics of the system, such as permeability, viscous damping, and friction coefficient at the interface are investigated in various examples

Hybrid-Trefftz finite elements for elastostatic and elastodynamic problems in porous media

The displacement and stress models of the hybrid-Trefftz finite element formulation are applied to the elastostatic and elastodynamic analysis of two-dimensional saturated and unsaturated porous media problems. The formulation develops from the classical separation of variables in time and space, but it leads to two time integration strategies. The first is applied to periodic problems, which are discretized in time using Fourier analysis. A mixed finite element approach is used in the second strategy for discretization in time of non-periodic/transient problems. These strategies lead to a series of uncoupled problems in the space dimension, which is subsequently discretized using either the displacement or the stress model of the hybrid-Trefftz finite element formulation. The main distinction between the two models is in the way that the interelement continuity is enforced. The displacement model enforces the interelement compatibility, while the stress model enforces the interelement equilibrium. As is typical of Trefftz methods, for both models, the approximation bases are constrained to satisfy locally the homogeneous form of the domain (Navier) equations. The free-field solutions of these equations are derived in cylindrical coordinates and used to construct the domain approximations of the hybrid-Trefftz displacement and stress elements. If the original equations are non-homogeneous, the influence of the source terms is modelled using Trefftz-compliant solutions of the corresponding static problem. For saturated porous media, the finite element models are based on the Biot's theory. It assumes an elastic solid phase fully permeated by a compressible liquid phase obeying the Darcy's law. For the modelling of unsaturated porous media, the finite elements are formulated using the theory of mixtures with interfaces. The model is thermodynamically consistent and considers the full coupling between the solid, fluid and gas phases, including the effects of relative (seepage) accelerations. Small displacements and linear-elastic material behaviour are assumed for all models

Parallel simulation of volume-coupled multi-field problems with special application to soil dynamics

Zur Lösung vieler ingenieur- und naturwissenschaftlichen Problemstellungen sind numerische Simulationen ein wichtiges Hilfsmittel. Sie dienen beispielsweise der Wettervorhersage in der Meteorologie oder der Strukturanalyse und Strukturoptimierung im Maschinenbau. In vielen Aufgabenstellungen kann das untersuchte Problem, aufgrund seiner starken Wechselwirkung mit den angrenzenden Systemen, nicht losgelöst betrachtet werden, so dass eine gesamtheitliche Betrachtungsweise notwendig wird. Diese Systeme werden in der Literatur als gekoppelte Probleme bezeichnet. Aufgrund der Komplexität der betrachteten Probleme sind zur effizienten Lösung der zugrunde liegenden Gleichungen parallele Lösungsstrategien von Vorteil. Hierbei wird das Gesamtproblem in kleinere Teilprobleme zerlegt, die gleichzeitig auf verschiedenen Rechnern oder Prozessoren gelöst werden. Um die Vorteile dieses Lösungsverfahrens bestmöglich nutzen zu können, sind erhebliche Anstrengungen zunächst für die initiale Entwicklung und Umsetzung eines effizienten Lösungsverfahrens sowie anschließend für dessen kontinuierliche Weiterentwicklung notwendig. Die vorliegende Monographie beschreibt einen Ansatz zur Kosimulation numerischer Probleme zwischen dem kommerziellen auf der Finite-Elemente-Methode (FEM) basierenden Programmpaket Abaqus und dem für die Forschung entwickelten Löser PANDAS. Durch die Entwicklung einer allgemeinen Schnittstelle können die Materialmodelle von PANDAS direkt, ohne eine langwierige und fehleranfällige Reimplementierung, in eine für die industrielle Anwendung wichtige Simulationsumgebung überführt werden. Hierbei kann direkt auf die umfangreiche Materialmodellbibliothek von PANDAS zurückgegriffen werden. Zur Illustration der Anwendungsmöglichkeiten der Abaqus-PANDAS-Kopplung wird diese exemplarisch zur Simulation verschiedener volumengekoppelter Mehrfeldprobleme herangezogen. Als bodenmechanisches Anwendungsbeispiel wird die Tragfähigkeit eines flüssigkeitgesättigten granularen Materials unter quasi-statischen und dynamischen zyklischen Belastungen untersucht. Weiterhin werden mehrphasige Strömungsprozesse, wie sie z. B. im Produktionsprozess von faserverstärkten Kunststoffen auftreten, numerisch simuliert. Im sogenannten Vaccum-Assisted-Resin-Transfer-Moulding (VARTM), wird ein zunächst trockenes (gasgesättigtes) Fasergewebe kontinuierlich mit Harz getränkt, wobei für die praktische Anwendung insbesondere die Zeit bis zur vollständigen Sättigung und der sich einstellende Faservolumenanteil im fertigen Bauteil von großem Interesse sind. Weiterhin werden die Effizienz und die parallele Skalierbarkeit des vorgeschlagenen Kosimulationsansatzes untersucht