TY - JOUR A1 - Könke, Carsten A1 - Eckardt, Stefan A1 - Häfner, Stefan A1 - Luther, Torsten A1 - Unger, Jörg F. T1 - Multiscale simulation methods in damage prediction of brittle and ductile materials JF - International Journal for Multiscale Computational Engineering N2 - Multiscale simulation methods in damage prediction of brittle and ductile materials KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2010 SP - 17 EP - 36 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 - TY - CHAP A1 - Häfner, Stefan A1 - Vogel, Frank A1 - Könke, Carsten ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - FINITE ELEMENT ANALYSIS OF TORSION FOR ARBITRARY CROSS-SECTIONS N2 - The present article proposes an alternative way to compute the torsional stiffness based on three-dimensional continuum mechanics instead of applying a specific theory of torsion. A thin, representative beam slice is discretized by solid finite elements. Adequate boundary conditions and coupling conditions are integrated into the numerical model to obtain a proper answer on the torsion behaviour, thus on shear center, shear stress and torsional stiffness. This finite element approach only includes general assumptions of beam torsion which are independent of cross-section geometry. These assumptions essentially are: no in-plane deformation, constant torsion and free warping. Thus it is possible to achieve numerical solutions of high accuracy for arbitrary cross-sections. Due to the direct link to three-dimensional continuum mechanics, it is possible to extend the range of torsion analysis to sections which are composed of different materials or even to heterogeneous beams on a high scale of resolution. A brief study follows to validate the implementation and results are compared to analytical solutions. 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:wim2-20170314-28483 UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html SN - 1611-4086 ER - TY - CHAP A1 - Eckardt, Stefan A1 - Könke, Carsten ED - Gürlebeck, Klaus ED - Könke, Carsten T1 - ENERGY RELEASE CONTROL FOR NONLINEAR MESOSCALE SIMULATIONS N2 - In nonlinear simulations the loading is, in general, applied in an incremental way. Path-following algorithms are used to trace the equilibrium path during the failure process. Standard displacement controlled solution strategies fail if snap-back phenomena occur. In this contribution, a path-following algorithm based on the dissipation of the inelastic energy is presented which allows for the simulation of snap-backs. Since the constraint is defined in terms of the internal energy, the algorithm is not restricted to continuum damage models. Furthermore, no a priori knowledge about the final damage distribution is required. The performance of the proposed algorithm is illustrated using nonlinear mesoscale simulations. 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:wim2-20170314-28414 UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html SN - 1611-4086 ER - TY - JOUR A1 - Nasser, Mourad A1 - Schwedler, Michael A1 - Wuttke, Frank A1 - Könke, Carsten T1 - Seismic analysis of structural response using simplified soil-structure interaction models JF - Bauingenieur, D-A-CH-Mitteilungsblatt N2 - Seismic analysis of structural response using simplified soil-structure interaction models KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2010 ER - TY - JOUR A1 - Luther, Torsten A1 - Könke, Carsten T1 - Polycrystal models for the analysis of intergranular crack growth in metallic materials JF - Engineering Fracture Mechanics N2 - Polycrystal models for the analysis of intergranular crack growth in metallic materials KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2009 SP - 2332 EP - 2343 ER - TY - JOUR A1 - Eckardt, Stefan A1 - Könke, Carsten T1 - Adaptive damage simulation of concrete using heterogeneous multiscale models JF - Journal of Algorithms & Computational Technology N2 - Adaptive damage simulation of concrete using heterogeneous multiscale models KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2008 SP - 275 EP - 297 ER - TY - JOUR A1 - Unger, Jörg F. A1 - Könke, Carsten T1 - Coupling of scales in a multiscale simulation using neural networks JF - Computers & Structures N2 - Coupling of scales in a multiscale simulation using neural networks KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2008 ER - TY - JOUR A1 - Unger, Jörg F. A1 - Eckardt, Stefan A1 - Könke, Carsten T1 - Modelling of cohesive crack growth in concrete structures with the extended finite element method JF - Computer Methods in Applied Mechanics and Engineering N2 - Modelling of cohesive crack growth in concrete structures with the extended finite element method KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2007 SP - 4087 EP - 4100 ER - TY - JOUR A1 - Häfner, Stefan A1 - Eckardt, Stefan A1 - Luther, Torsten A1 - Könke, Carsten T1 - Mesoscale modeling of concrete: Geometry and numerics JF - Computers and Structures N2 - Mesoscale modeling of concrete: Geometry and numerics KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2006 SP - 450 EP - 461 ER -