TY - CHAP
A1 - Unger, Jörg F.
A1 - Könke, Carsten
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - DISCRETE CRACK SIMULATION OF CONCRETE USING THE EXTENDED FINITE ELEMENTMETHOD
N2 - The extended finite element method (XFEM) offers an elegant tool to model material discontinuities and cracks within a regular mesh, so that the element edges do not necessarily coincide with the discontinuities. This allows the modeling of propagating cracks without the requirement to adapt the mesh incrementally. Using a regular mesh offers the advantage, that simple refinement strategies based on the quadtree data structure can be used to refine the mesh in regions, that require a high mesh density. An additional benefit of the XFEM is, that the transmission of cohesive forces through a crack can be modeled in a straightforward way without introducing additional interface elements. Finally different criteria for the determination of the crack propagation angle are investigated and applied to numerical tests of cracked concrete specimens, which are compared with experimental results.
KW - Architektur
KW - CAD
KW - Computerunterstütztes Verfahren
Y1 - 2006
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-30303
UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html
ER -
TY - CHAP
A1 - Unger, Jörg F.
A1 - Könke, Carsten
T1 - Simulation of concrete using the extended finite element method
N2 - Simulation of concrete using the extended finite element method
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2006
ER -
TY - CHAP
A1 - Luther, Torsten
A1 - Könke, Carsten
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - INVESTIGATION OF CRACK GROWTH IN POLYCRYSTALLINE MESOSTRUCTURES
N2 - The design and application of high performance materials demands extensive knowledge of the materials damage behavior, which significantly depends on the meso- and microstructural complexity. Numerical simulations of crack growth on multiple length scales are promising tools to understand the damage phenomena in complex materials. In polycrystalline materials it has been observed that the grain boundary decohesion is one important mechanism that leads to micro crack initiation. Following this observation the paper presents a polycrystal mesoscale model consisting of grains with orthotropic material behavior and cohesive interfaces along grain boundaries, which is able to reproduce the crack initiation and propagation along grain boundaries in polycrystalline materials. With respect to the importance of modeling the geometry of the grain structure an advanced Voronoi algorithm is proposed to generate realistic polycrystalline material structures based on measured grain size distribution. The polycrystal model is applied to investigate the crack initiation and propagation in statically loaded representative volume elements of aluminum on the mesoscale without the necessity of initial damage definition. Future research work is planned to include the mesoscale model into a multiscale model for the damage analysis in polycrystalline materials.
KW - Architektur
KW - CAD
KW - Computerunterstütztes Verfahren
Y1 - 2006
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29886
UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html
ER -
TY - CHAP
A1 - Luther, Torsten
A1 - Könke, Carsten
T1 - Analysis of crack initiation and propagation in polyctystalline meso- and microstructures of metal materials
N2 - Analysis of crack initiation and propagation in polyctystalline meso- and microstructures of metal materials
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2006
ER -
TY - CHAP
A1 - Luther, Torsten
A1 - Könke, Carsten
T1 - Investigation of crack growth in polycrystalline mesostructures
N2 - Investigation of crack growth in polycrystalline mesostructures
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2006
ER -
TY - CHAP
A1 - Könke, Carsten
A1 - Eckardt, Stefan
A1 - Häfner, Stefan
T1 - Spatial and temporal multiscale simulations of damage processes for concrete
N2 - Spatial and temporal multiscale simulations of damage processes for concrete
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2006
ER -
TY - CHAP
A1 - Könke, Carsten
T1 - Damage tolerant design
N2 - Damage tolerant design
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2006
ER -
TY - CHAP
A1 - Häfner, Stefan
A1 - Könke, Carsten
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - MULTIGRID PRECONDITIONED CONJUGATE GRADIENT METHOD IN THE MECHANICAL ANALYSIS OF HETEROGENEOUS SOLIDS
N2 - A fast solver method called the multigrid preconditioned conjugate gradient method is proposed for the mechanical analysis of heterogeneous materials on the mesoscale. Even small samples of a heterogeneous material such as concrete show a complex geometry of different phases. These materials can be modelled by projection onto a uniform, orthogonal grid of elements. As one major problem the possible resolution of the concrete specimen is generally restricted due to (a) computation times and even more critical (b) memory demand. Iterative solvers can be based on a local element-based formulation while orthogonal grids consist of geometrical identical elements. The element-based formulation is short and transparent, and therefore efficient in implementation. A variation of the material properties in elements or integration points is possible. The multigrid method is a fast iterative solver method, where ideally the computational effort only increases linear with problem size. This is an optimal property which is almost reached in the implementation presented here. In fact no other method is known which scales better than linear. Therefore the multigrid method gains in importance the larger the problem becomes. But for heterogeneous models with very large ratios of Young's moduli the multigrid method considerably slows down by a constant factor. Such large ratios occur in certain heterogeneous solids, as well as in the damage analysis of solids. As solution to this problem the multigrid preconditioned conjugate gradient method is proposed. A benchmark highlights the multigrid preconditioned conjugate gradient method as the method of choice for very large ratio's of Young's modulus. A proposed modified multigrid cycle shows good results, in the application as stand-alone solver or as preconditioner.
KW - Architektur
KW - CAD
KW - Computerunterstütztes Verfahren
Y1 - 2006
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29626
UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html
ER -
TY - CHAP
A1 - Häfner, Stefan
A1 - Könke, Carsten
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - DAMAGE SIMULATION OF HETEROGENEOUS SOLIDS BY NONLOCAL FORMULATIONS ON ORTHOGONAL GRIDS
N2 - The present paper is part of a comprehensive approach of grid-based modelling. This approach includes geometrical modelling by pixel or voxel models, advanced multiphase B-spline finite elements of variable order and fast iterative solver methods based on the multigrid method. So far, we have only presented these grid-based methods in connection with linear elastic analysis of heterogeneous materials. Damage simulation demands further considerations. The direct stress solution of standard bilinear finite elements is severly defective, especially along material interfaces. Besides achieving objective constitutive modelling, various nonlocal formulations are applied to improve the stress solution. Such a corrective data processing can either refer to input data in terms of Young's modulus or to the attained finite element stress solution, as well as to a combination of both. A damage-controlled sequentially linear analysis is applied in connection with an isotropic damage law. Essentially by a high resolution of the heterogeneous solid, local isotropic damage on the material subscale allows to simulate complex damage topologies such as cracks. Therefore anisotropic degradation of a material sample can be simulated. Based on an effectively secantial global stiffness the analysis is numerically stable. The iteration step size is controlled for an adequate simulation of the damage path. This requires many steps, but in the iterative solution process each new step starts with the solution of the prior step. Therefore this method is quite effective. The present paper provides an introduction of the proposed concept for a stable simulation of damage in heterogeneous solids.
KW - Architektur
KW - CAD
KW - Computerunterstütztes Verfahren
Y1 - 2006
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170327-29638
UR - http://euklid.bauing.uni-weimar.de/ikm2006/index.php_lang=de&what=papers.html
ER -
TY - CHAP
A1 - Häfner, Stefan
A1 - Könke, Carsten
T1 - Multigrid preconditioned conjugate gradient method in the mechanical analysis of heterogeneous solids
N2 - Multigrid preconditioned conjugate gradient method in the mechanical analysis of heterogeneous solids
KW - Angewandte Mathematik
KW - Strukturmechanik
Y1 - 2006
ER -