TY - THES
A1 - Schrader, Kai
T1 - Algorithmische Umsetzung eines elasto-plastischen Kontakt-Materialgesetzes zur Abbildung der Rissflächen-Degradation bei kohäsiven Rissen
N2 - Entwicklung eines Algorithmus für ein nichtlineares Materialgesetz für die vollautomatische Rissentwicklungssimulation unter Verwendung der am Institut für Strukturmechanik entwickelten netzfreien Verfahren. In Anlehnung an die Kontinuumsplastizität wird unter Verwendung einer arbeitsbasierten Formulierung mit Kombination der Mode I und Mode IIa Bruchenergien für sensitive Strukturen und eines nicht-assoziierten Fließgesetzes werden die Rissweggrößen (Rissöffnungsweite und Rissgleitungen) iterativ ermittelt. Dadurch ist es möglich, den Dilatanzeffekt sowie die verzahnte Kontaktfläche und die daraus resultierenden erhöhten Schubwiderstände abzubilden. Umsetzung mit Hilfe des sehr effizienten impliziten Closest Point Projection Iterationsverfahren auf Basis einer 3-D Kontaktformulierung (Kontakt-Elemente). 2-D Implementation in die Forschungssoftware SLang des Instituts für Strukturmechanik der Bauhaus-Universität Weimar. Verifikation der Modellcharakteristik mit signifikanten Belastungszuständen. Zwei Anwendungsbeispiele zur Rissfortschrittsberechnung sind unter Verwendung des umgesetzten Materialgesetzes zum Einsatz gekommen. Untersuchungen hinsichtlich der Materialparameter wurden vorgenommen.
N2 - In this documentation a general model for combined normal/shear cracking will be presented. Basically it is defined of the normal and shear stresses of a cohesive crack with the corresponding displacements in normal and tangential direction. For the load state there can be considered three cases of loading: pure tension, shear-tension and shear-compression. In the softening state of quasi-brittle materials like concrete there are be mould physical effects like dilatancy by shearing deformations, nevertheless no dilatancy under very high compression can be performed. By this way it is additionally possible to simulate extended roughness at the contact surface besides the coulomb criteria as it exists in real cracking deformations of structures characterized by sensitive material behavior. To enable this goal in context of smeared crack analysis a special feature in combined activating Mode I and Mode II fracture energies (mixed mode cracking) is used. \\ After presenting this model a direct way for implementation as a constitutive law based for interface elements will be realized. Integrating this to the stochastic FE software SLang - The Structural Language some tests for verificating the interface model (by comparing the numerical results with existing experimental data) will be performed as well as discussing the cracking model with regard to practical aspects.
KW - Dilatanz
KW - Bruchzone
KW - Rissbildung
KW - plastische Formänderungsarbeit
KW - nicht-assoziierte Fließfläche
KW - Kontaktformulierung
KW - Rissfortschrittsberechnung
KW - dilatancy
KW - mixed mode cracking
KW - mode I
KW - mode IIa
KW - closest point projection
Y1 - 2005
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20111215-6195
N1 - Der Volltext-Zugang wurde im Zusammenhang mit der Klärung urheberrechtlicher Fragen mit sofortiger Wirkung gesperrt.
ER -
TY - THES
A1 - Schrader, Kai
T1 - Hybrid 3D simulation methods for the damage analysis of multiphase composites
T1 - Hybride 3D Simulationsmethoden zur Abbildung der Schädigungsvorgänge in Mehrphasen-Verbundwerkstoffen
N2 - Modern digital material approaches for the visualization and simulation of heterogeneous materials allow to investigate the behavior of complex multiphase materials with their physical nonlinear material response at various scales. However, these computational techniques require extensive hardware resources with respect to computing power and main memory to solve numerically large-scale discretized models in 3D. Due to a very high number of degrees of freedom, which may rapidly be increased to the two-digit million range, the limited hardware ressources are to be utilized in a most efficient way to enable an execution of the numerical algorithms in minimal computation time. Hence, in the field of computational mechanics, various methods and algorithms can lead to an optimized runtime behavior of nonlinear simulation models, where several approaches are proposed and investigated in this thesis.
Today, the numerical simulation of damage effects in heterogeneous materials is performed by the adaption of multiscale methods. A consistent modeling in the three-dimensional space with an appropriate discretization resolution on each scale (based on a hierarchical or concurrent multiscale model), however, still contains computational challenges in respect to the convergence behavior, the scale transition or the solver performance of the weak coupled problems. The computational efficiency and the distribution among available hardware resources (often based on a parallel hardware architecture) can significantly be improved. In the past years, high-performance computing (HPC) and graphics processing unit (GPU) based computation techniques were established for the investigationof scientific objectives. Their application results in the modification of existing and the development of new computational methods for the numerical implementation, which enables to take advantage of massively clustered computer hardware resources. In the field of numerical simulation in material science, e.g. within the investigation of damage effects in multiphase composites, the suitability of such models is often restricted by the number of degrees of freedom (d.o.f.s) in the three-dimensional spatial discretization. This proves to be difficult for the type of implementation method used for the nonlinear simulation procedure and, simultaneously has a great influence on memory demand and computational time.
In this thesis, a hybrid discretization technique has been developed for the three-dimensional discretization of a three-phase material, which is respecting the numerical efficiency of nonlinear (damage) simulations of these materials. The increase of the computational efficiency is enabled by the improved scalability of the numerical algorithms. Consequently, substructuring methods for partitioning the hybrid mesh were implemented, tested and adapted to the HPC computing framework using several hundred CPU (central processing units) nodes for building the finite element assembly. A memory-efficient iterative and parallelized equation solver combined with a special preconditioning technique for solving the underlying equation system was modified and adapted to enable combined CPU and GPU based computations.
Hence, it is recommended by the author to apply the substructuring method for hybrid meshes, which respects different material phases and their mechanical behavior and which enables to split the structure in elastic and inelastic parts. However, the consideration of the nonlinear material behavior, specified for the corresponding phase, is limited to the inelastic domains only, and by that causes a decreased computing time for the nonlinear procedure. Due to the high numerical effort for such simulations, an alternative approach for the nonlinear finite element analysis, based on the sequential linear analysis, was implemented in respect to scalable HPC. The incremental-iterative procedure in finite element analysis (FEA) during the nonlinear step was then replaced by a sequence of linear FE analysis when damage in critical regions occured, known in literature as saw-tooth approach. As a result, qualitative (smeared) crack initiation in 3D multiphase specimens has efficiently been simulated.
T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2013,2
KW - high-performance computing
KW - finite element method
KW - heterogeneous material
KW - domain decomposition
KW - scalable smeared crack analysis
KW - FEM
KW - multiphase
KW - damage
KW - HPC
KW - solver
Y1 - 2012
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20131021-20595
ER -
TY - JOUR
A1 - Schrader, Kai
A1 - Könke, Carsten
T1 - Hybrid computing models for large-scale heterogeneous 3d microstructures
JF - International Journal for Multiscale Computational Engineering
N2 - Hybrid computing models for large-scale heterogeneous 3d microstructures
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2011
SP - 365
EP - 377
ER -
TY - JOUR
A1 - Schrader, Kai
A1 - Könke, Carsten
T1 - Distributed computing for the nonlinear analysis of multiphase composites
JF - Advances in Engineering Software
N2 - Distributed computing for the nonlinear analysis of multiphase composites
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2013
SP - 20
EP - 32
ER -
TY - CHAP
A1 - Most, Thomas
A1 - Eckardt, Stefan
A1 - Schrader, Kai
A1 - Deckner, T.
T1 - An improved cohesive crack model for combined crack opening and sliding under cyclic loading
N2 - An improved cohesive crack model for combined crack opening and sliding under cyclic loading
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2006
ER -
TY - CHAP
A1 - Most, Thomas
A1 - Eckardt, Stefan
A1 - Schrader, Kai
A1 - Deckner, T.
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - AN IMPROVED COHESIVE CRACK MODEL FOR COMBINED CRACK OPENING AND SLIDING UNDER CYCLIC LOADING
N2 - The modeling of crack propagation in plain and reinforced concrete structures is still a field for many researchers. If a macroscopic description of the cohesive cracking process of concrete is applied, generally the Fictitious Crack Model is utilized, where a force transmission over micro cracks is assumed. In the most applications of this concept the cohesive model represents the relation between the normal crack opening and the normal stress, which is mostly defined as an exponential softening function, independently from the shear stresses in tangential direction. The cohesive forces are then calculated only from the normal stresses. By Carol et al. 1997 an improved model was developed using a coupled relation between the normal and shear damage based on an elasto-plastic constitutive formulation. This model is based on a hyperbolic yield surface depending on the normal and the shear stresses and on the tensile and shear strength. This model also represents the effect of shear traction induced crack opening. Due to the elasto-plastic formulation, where the inelastic crack opening is represented by plastic strains, this model is limited for applications with monotonic loading. In order to enable the application for cases with un- and reloading the existing model is extended in this study using a combined plastic-damage formulation, which enables the modeling of crack opening and crack closure. Furthermore the corresponding algorithmic implementation using a return mapping approach is presented and the model is verified by means of several numerical examples. Finally an investigation concerning the identification of the model parameters by means of neural networks is presented. In this analysis an inverse approximation of the model parameters is performed by using a given set of points of the load displacement curves as input values and the model parameters as output terms. It will be shown, that the elasto-plastic model parameters could be identified well with this approach, but require a huge number of simulations.
KW - Architektur
KW - CAD
KW - Computerunterstütztes Verfahren
Y1 - 2006
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29933
UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html
ER -
TY - CHAP
A1 - Schrader, Kai
A1 - Könke, Carsten
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - SPARSE APPROXIMATE COMPUTATION OF SADDLE POINT PROBLEMS ARISING FROM FETI-DP DISCRETIZATION
N2 - The numerical simulation of microstructure models in 3D requires, due to enormous d.o.f., significant resources of memory as well as parallel computational power. Compared to homogeneous materials, the material hetrogeneity on microscale induced by different material phases demand for adequate computational methods for discretization and solution process of the resulting highly nonlinear problem. To enable an efficient/scalable solution process of the linearized equation systems the heterogeneous FE problem will be described by a FETI-DP (Finite Element Tearing and Interconnecting - Dual Primal) discretization. The fundamental FETI-DP equation can be solved by a number of different approaches. In our approach the FETI-DP problem will be reformulated as Saddle Point system, by eliminating the primal and Lagrangian variables. For the reduced Saddle Point system, only defined by interior and dual variables, special Uzawa algorithms can be adapted for iteratively solving the FETI-DP saddle-point equation system (FETI-DP SPE). A conjugate gradient version of the Uzawa algorithm will be shown as well as some numerical tests regarding to FETI-DP discretization of small examples using the presented solution technique. Furthermore the inversion of the interior-dual Schur complement operator can be approximated using different techniques building an adequate preconditioning matrix and therewith leading to substantial gains in computing time efficiency.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Architektur
KW - Computerunterstütztes Verfahren
KW - Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing
Y1 - 2010
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28874
UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN - 1611-4086
ER -