TY - JOUR A1 - Legatiuk, Dmitrii A1 - Weisz-Patrault, Daniel T1 - Coupling of Complex Function Theory and Finite Element Method for Crack Propagation Through Energetic Formulation: Conformal Mapping Approach and Reduction to a Riemann–Hilbert Problem JF - Computational Methods and Function Theory N2 - In this paper we present a theoretical background for a coupled analytical–numerical approach to model a crack propagation process in two-dimensional bounded domains. The goal of the coupled analytical–numerical approach is to obtain the correct solution behaviour near the crack tip by help of the analytical solution constructed by using tools of complex function theory and couple it continuously with the finite element solution in the region far from the singularity. In this way, crack propagation could be modelled without using remeshing. Possible directions of crack growth can be calculated through the minimization of the total energy composed of the potential energy and the dissipated energy based on the energy release rate. Within this setting, an analytical solution of a mixed boundary value problem based on complex analysis and conformal mapping techniques is presented in a circular region containing an arbitrary crack path. More precisely, the linear elastic problem is transformed into a Riemann–Hilbert problem in the unit disk for holomorphic functions. Utilising advantages of the analytical solution in the region near the crack tip, the total energy could be evaluated within short computation times for various crack kink angles and lengths leading to a potentially efficient way of computing the minimization procedure. To this end, the paper presents a general strategy of the new coupled approach for crack propagation modelling. Additionally, we also discuss obstacles in the way of practical realisation of this strategy. KW - Angewandte Mathematik KW - Finite-Elemente-Methode KW - Rissausbreitung KW - Modellierung KW - Bruchmechanik KW - fracture mechanics KW - crack propagation KW - coupling KW - energetic approach Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210805-44763 UR - https://link.springer.com/article/10.1007/s40315-021-00403-7 VL - 2021 SP - 1 EP - 23 PB - Springer CY - Heidelberg ER - TY - THES A1 - Hollerbuhl, Lutz T1 - Simulation der Schädigung der Kölnbreintalsperre während des Ersteinstaus 1978 T1 - Crack propagation simulations for the Koelnbrein-Dam N2 - Die Arbeit befasst sich mit der österreichischen Bogenstaumauer Kölnbrein, die während des Ersteinstaus geschädigt wurde. Diese Schäden, sowie mögliche Ursachen sind anhand von Literaturquellen dokumentiert. Nach Erstellung eines Rechenmodells wurden, durch ein Randelementeprogramm, Rissfortschrittsberechnungen durchgeführt und mit dem realen Bauwerk verglichen. Zum Einsatz kamen die Anwendungen „OSM“, „FRANC3D“ und „BES“ der Cornell-University. KW - Rissausbreitung KW - Talsperre KW - Bogenstaumauer KW - Staumauer KW - Kölnbrein KW - Koelnbrein KW - Crack Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-5877 N1 - Der Volltext-Zugang wurde im Zusammenhang mit der Klärung urheberrechtlicher Fragen mit sofortiger Wirkung gesperrt. ER - TY - JOUR A1 - Hanna, John T1 - Computational Modelling for the Effects of Capsular Clustering on Fracture of Encapsulation-Based Self-Healing Concrete Using XFEM and Cohesive Surface Technique JF - Applied Sciences N2 - The fracture of microcapsules is an important issue to release the healing agent for healing the cracks in encapsulation-based self-healing concrete. The capsular clustering generated from the concrete mixing process is considered one of the critical factors in the fracture mechanism. Since there is a lack of studies in the literature regarding this issue, the design of self-healing concrete cannot be made without an appropriate modelling strategy. In this paper, the effects of microcapsule size and clustering on the fractured microcapsules are studied computationally. A simple 2D computational modelling approach is developed based on the eXtended Finite Element Method (XFEM) and cohesive surface technique. The proposed model shows that the microcapsule size and clustering have significant roles in governing the load-carrying capacity and the crack propagation pattern and determines whether the microcapsule will be fractured or debonded from the concrete matrix. The higher the microcapsule circumferential contact length, the higher the load-carrying capacity. When it is lower than 25% of the microcapsule circumference, it will result in a greater possibility for the debonding of the microcapsule from the concrete. The greater the core/shell ratio (smaller shell thickness), the greater the likelihood of microcapsules being fractured. KW - Beton KW - Mikrokapsel KW - Rissausbreitung KW - Tragfähigkeit KW - self-healing concrete KW - microcapsule KW - capsular clustering KW - circumferential contact length KW - OA-Publikationsfonds2022 Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20220721-46717 UR - https://www.mdpi.com/2076-3417/12/10/5112 VL - 2022 IS - Volume 12, issue 10, article 5112 SP - 1 EP - 17 PB - MDPI CY - Basel ER - TY - THES A1 - Hamdia, Khader T1 - On the fracture toughness of polymeric nanocomposites: Comprehensive stochastic and numerical studies N2 - Polymeric nanocomposites (PNCs) are considered for numerous nanotechnology such as: nano-biotechnology, nano-systems, nanoelectronics, and nano-structured materials. Commonly , they are formed by polymer (epoxy) matrix reinforced with a nanosized filler. The addition of rigid nanofillers to the epoxy matrix has offered great improvements in the fracture toughness without sacrificing other important thermo-mechanical properties. The physics of the fracture in PNCs is rather complicated and is influenced by different parameters. The presence of uncertainty in the predicted output is expected as a result of stochastic variance in the factors affecting the fracture mechanism. Consequently, evaluating the improved fracture toughness in PNCs is a challenging problem. Artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) have been employed to predict the fracture energy of polymer/particle nanocomposites. The ANN and ANFIS models were constructed, trained, and tested based on a collection of 115 experimental datasets gathered from the literature. The performance evaluation indices of the developed ANN and ANFIS showed relatively small error, with high coefficients of determination (R2), and low root mean square error and mean absolute percentage error. In the framework for uncertainty quantification of PNCs, a sensitivity analysis (SA) has been conducted to examine the influence of uncertain input parameters on the fracture toughness of polymer/clay nanocomposites (PNCs). The phase-field approach is employed to predict the macroscopic properties of the composite considering six uncertain input parameters. The efficiency, robustness, and repeatability are compared and evaluated comprehensively for five different SA methods. The Bayesian method is applied to develop a methodology in order to evaluate the performance of different analytical models used in predicting the fracture toughness of polymeric particles nanocomposites. The developed method have considered the model and parameters uncertainties based on different reference data (experimental measurements) gained from the literature. Three analytical models differing in theory and assumptions were examined. The coefficients of variation of the model predictions to the measurements are calculated using the approximated optimal parameter sets. Then, the model selection probability is obtained with respect to the different reference data. Stochastic finite element modeling is implemented to predict the fracture toughness of polymer/particle nanocomposites. For this purpose, 2D finite element model containing an epoxy matrix and rigid nanoparticles surrounded by an interphase zone is generated. The crack propagation is simulated by the cohesive segments method and phantom nodes. Considering the uncertainties in the input parameters, a polynomial chaos expansion (PCE) surrogate model is construed followed by a sensitivity analysis. T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2018,4 KW - Bruch KW - Unsicherheit KW - Rissausbreitung KW - Bayes KW - Sensitivitätsanalyse KW - Fracture mechanics KW - Uncertainty analysis KW - Polymer nanocomposites KW - Bayesian method KW - Phase-field modeling Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20180712-37652 ER -