TY - THES A1 - Goswami, Somdatta T1 - Phase field modeling of fracture with isogeometric analysis and machine learning methods N2 - This thesis presents the advances and applications of phase field modeling in fracture analysis. In this approach, the sharp crack surface topology in a solid is approximated by a diffusive crack zone governed by a scalar auxiliary variable. The uniqueness of phase field modeling is that the crack paths are automatically determined as part of the solution and no interface tracking is required. The damage parameter varies continuously over the domain. But this flexibility comes with associated difficulties: (1) a very fine spatial discretization is required to represent sharp local gradients correctly; (2) fine discretization results in high computational cost; (3) computation of higher-order derivatives for improved convergence rates and (4) curse of dimensionality in conventional numerical integration techniques. As a consequence, the practical applicability of phase field models is severely limited. The research presented in this thesis addresses the difficulties of the conventional numerical integration techniques for phase field modeling in quasi-static brittle fracture analysis. The first method relies on polynomial splines over hierarchical T-meshes (PHT-splines) in the framework of isogeometric analysis (IGA). An adaptive h-refinement scheme is developed based on the variational energy formulation of phase field modeling. The fourth-order phase field model provides increased regularity in the exact solution of the phase field equation and improved convergence rates for numerical solutions on a coarser discretization, compared to the second-order model. However, second-order derivatives of the phase field are required in the fourth-order model. Hence, at least a minimum of C1 continuous basis functions are essential, which is achieved using hierarchical cubic B-splines in IGA. PHT-splines enable the refinement to remain local at singularities and high gradients, consequently reducing the computational cost greatly. Unfortunately, when modeling complex geometries, multiple parameter spaces (patches) are joined together to describe the physical domain and there is typically a loss of continuity at the patch boundaries. This decrease of smoothness is dictated by the geometry description, where C0 parameterizations are normally used to deal with kinks and corners in the domain. Hence, the application of the fourth-order model is severely restricted. To overcome the high computational cost for the second-order model, we develop a dual-mesh adaptive h-refinement approach. This approach uses a coarser discretization for the elastic field and a finer discretization for the phase field. Independent refinement strategies have been used for each field. The next contribution is based on physics informed deep neural networks. The network is trained based on the minimization of the variational energy of the system described by general non-linear partial differential equations while respecting any given law of physics, hence the name physics informed neural network (PINN). The developed approach needs only a set of points to define the geometry, contrary to the conventional mesh-based discretization techniques. The concept of `transfer learning' is integrated with the developed PINN approach to improve the computational efficiency of the network at each displacement step. This approach allows a numerically stable crack growth even with larger displacement steps. An adaptive h-refinement scheme based on the generation of more quadrature points in the damage zone is developed in this framework. For all the developed methods, displacement-controlled loading is considered. The accuracy and the efficiency of both methods are studied numerically showing that the developed methods are powerful and computationally efficient tools for accurately predicting fractures. T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2021,1 KW - Phasenfeldmodell KW - Neuronales Netz KW - Sprödbruch KW - Isogeometric Analysis KW - Physics informed neural network KW - phase field KW - deep neural network KW - brittle fracture Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210304-43841 ER - TY - THES A1 - Unger, Jörg F. T1 - Neural networks in a multiscale approach for concrete N2 - From a macroscopic point of view, failure within concrete structures is characterized by the initiation and propagation of cracks. In the first part of the thesis, a methodology for macroscopic crack growth simulations for concrete structures using a cohesive discrete crack approach based on the extended finite element method is introduced. Particular attention is turned to the investigation of criteria for crack initiation and crack growth. A drawback of the macroscopic simulation is that the real physical phenomena leading to the nonlinear behavior are only modeled phenomenologically. For concrete, the nonlinear behavior is characterized by the initiation of microcracks which coalesce into macroscopic cracks. In order to obtain a higher resolution of this failure zones, a mesoscale model for concrete is developed that models particles, mortar matrix and the interfacial transition zone (ITZ) explicitly. The essential features are a representation of particles using a prescribed grading curve, a material formulation based on a cohesive approach for the ITZ and a combined model with damage and plasticity for the mortar matrix. Compared to numerical simulations, the response of real structures exhibits a stochastic scatter. This is e.g. due to the intrinsic heterogeneities of the structure. For mesoscale models, these intrinsic heterogeneities are simulated by using a random distribution of particles and by a simulation of spatially variable material parameters using random fields. There are two major problems related to numerical simulations on the mesoscale. First of all, the material parameters for the constitutive description of the materials are often difficult to measure directly. In order to estimate material parameters from macroscopic experiments, a parameter identification procedure based on Bayesian neural networks is developed which is universally applicable to any parameter identification problem in numerical simulations based on experimental results. This approach offers information about the most probable set of material parameters based on experimental data and information about the accuracy of the estimate. Consequently, this approach can be used a priori to determine a set of experiments to be carried out in order to fit the parameters of a numerical model to experimental data. The second problem is the computational effort required for mesoscale simulations of a full macroscopic structure. For this purpose, a coupling between mesoscale and macroscale model is developed. Representative mesoscale simulations are used to train a metamodel that is finally used as a constitutive model in a macroscopic simulation. Special focus is placed on the ability of appropriately simulating unloading. N2 - Makroskopisch betrachtet kann das Versagen von Beton durch die Entstehung und das Wachstum von Rissen beschrieben werden. Im ersten Teil der Arbeit wird eine Methode zur Simulation der makroskopischen Rissentwicklung von Beton unter Verwendung von kohäsiven diskreten Rissen basierend auf der erweiterten Finiten Elemente Methode vorgestellt. Besondere Bedeutung liegt dabei auf der Untersuchung von Kriterien zur Rissentstehung und zum Risswachstum. Ein Nachteil von makroskopischen Simulationen liegt in der nur phänomenologischen Berücksichtigung der tatsächlichen Vorgänge. Nichtlineares Verhalten von Beton ist durch die Entstehung von Mikrorissen gekennzeichnet, die bei weiterer Belastung zu makroskopischen Rissen zusammenwachsen. Um die Versagenszone realitätsnah abbilden zu können, wurde ein Mesoskalenmodell von Beton entwickelt, welches Zuschläge, Matrix und Übergangszone zwischen beiden Materialien (ITZ) direkt abbildet. Hauptmerkmal sind die Simulation der Zuschläge nach einer Sieblinie, eine kohäsive Materialformulierung der ITZ und ein kombiniertes Model aus Schädigung und Plastizität für das Matrixmaterial. Im Gegensatz zu numerischen Simulationen ist die Systemantwort reeller Strukturen eine unscharfe Größe. Dies liegt u.a. an Heterogenitäten innerhalb der Struktur, die im Rahmen der Arbeit durch eine zufällige Verteilung der Zuschläge und über räumlich variierende Materialparameter unter Verwendung von Zufallsfeldern simuliert werden. Zwei Hauptprobleme sind bei den Mesoskalensimulationen aufgetreten. Einerseits sind Materialparameter auf der Mesoskala oft schwer zu bestimmen. Deswegen wurde eine Methode basierend auf Bayes neuronalen Netzen entwickelt, die eine Parameteridentifikation unter Verwendung von makroskopischen Versuchen erlaubt. Diese Methode ist aber universell anwendbar auf alle Parameteridentifikationsprobleme in numerischen Simulationen basierend auf experimentellen Daten. Der Ansatz liefert sowohl Informationen über den wahrscheinlichsten Parametersatz des Models zur numerischen Simulation eines Experiments als auch eine Einschätzung der Genauigkeit dieses Schätzers. Die Methode kann auch verwendet werden, um a priori einen Satz von Experimenten auszuwählen der notwendig ist, um die Parameter eines numerischen Modells zu bestimmen. Ein zweites Problem ist der numerische Aufwand von Mesoskalensimulationen für makroskopische Strukturen. Aus diesem Grund wurde eine Kopplungsstrategie zwischen Meso- und Makromodell entwickelt, bei dem repräsentative Simulationen auf der Mesoebene verwendet werden, um ein Metamodell zu generieren, welches dann die Materialformulierung in einer makroskopischen Simulation darstellt. Ein Fokus liegt dabei auf der korrekten Abbildung von Entlastungen. T2 - Neuronale Netze in einem Multiskalenansatz für Beton T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2009,1 KW - Beton KW - Mehrskalenmodell KW - Mehrskalenanalyse KW - Neuronales Netz KW - Monte-Carlo-Simulation KW - Simulation KW - Monte-Carlo-Integration KW - Kontinuierliche Simul KW - Bayes neuronale Netze KW - Parameteridentification KW - Bayesian neural networks KW - parameter identification Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20090626-14763 ER -