%0 Thesis %1 hund2007hierarchische %A Hund, Andrea S. %D 2007 %I Doktorarbeit, Bericht Nr. 48, Institut für Baustatik und Baudynamik, Universität Stuttgart %K MAT MS from:maltevonscheven ibb phdthesis %R 10.18419/opus-262 %T Hierarchische Mehrskalenmodellierung des Versagens von Werkstoffen mit Mikrostruktur. %X The present study is concerned with the analysis of the behavior of structures, made up of micro- heterogeneous materials like composites. Models, which directly resolve the material structure are too expensive, since the characteristic length of material components is much smaller than the characteristic length of the structure. On the other hand, macroscopic models capturing the local material behavior only in phenomenological sense are too inaccurate for a reliable analysis of the structural behavior within the post-failure range. An alternative are methods, which take care of the physical behavior on the scale of material heterogeneities in a detailed manner and include them on the structural scale by means of a multiscale model. The aim of this thesis is the development of an appropriate multiscale concept to solve problems of structural mechanics with multiscale characteristics for softening material behavior. In this connection an efficient and robust solution algorithm is of particular importance. The proposed multiscale method is based on a volume coupled scale transition, which is realized via a hierarchical refinement of the large scale solution. With this volume coupled scale transition, the multiscale model remains valid in the stage of softening, where the differences between scales become small due to localized material behavior. With respect to the efficiency of this method, hierarchical refinement is restricted to regions with nonlinear material behavior. Therefore a strain-based criterion for the adaptive adjustment of the multiscale region is proposed. Additionaly a local carrier is introduced for the fine scale variables, which allows a very efficient solution of the small scale equations. A simultaneous solution algorithm accounts for the strong coupling between the scales. In the context of the locality assumption for the small scale variables, different possibilities to formulate constraint conditions are presented and introduced. Using adequate test cases these possibilities are investigated and compared with respect to their pros and cons within the multiscale method. The potential of the proposed multiscale concept with respect to accuracy and efficiency is examplified by means of various applications.

@phdthesis{hund2007hierarchische, abstract = {The present study is concerned with the analysis of the behavior of structures, made up of micro- heterogeneous materials like composites. Models, which directly resolve the material structure are too expensive, since the characteristic length of material components is much smaller than the characteristic length of the structure. On the other hand, macroscopic models capturing the local material behavior only in phenomenological sense are too inaccurate for a reliable analysis of the structural behavior within the post-failure range. An alternative are methods, which take care of the physical behavior on the scale of material heterogeneities in a detailed manner and include them on the structural scale by means of a multiscale model. The aim of this thesis is the development of an appropriate multiscale concept to solve problems of structural mechanics with multiscale characteristics for softening material behavior. In this connection an efficient and robust solution algorithm is of particular importance. The proposed multiscale method is based on a volume coupled scale transition, which is realized via a hierarchical refinement of the large scale solution. With this volume coupled scale transition, the multiscale model remains valid in the stage of softening, where the differences between scales become small due to localized material behavior. With respect to the efficiency of this method, hierarchical refinement is restricted to regions with nonlinear material behavior. Therefore a strain-based criterion for the adaptive adjustment of the multiscale region is proposed. Additionaly a local carrier is introduced for the fine scale variables, which allows a very efficient solution of the small scale equations. A simultaneous solution algorithm accounts for the strong coupling between the scales. In the context of the locality assumption for the small scale variables, different possibilities to formulate constraint conditions are presented and introduced. Using adequate test cases these possibilities are investigated and compared with respect to their pros and cons within the multiscale method. The potential of the proposed multiscale concept with respect to accuracy and efficiency is examplified by means of various applications.}, added-at = {2021-03-09T13:40:57.000+0100}, author = {Hund, Andrea S.}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2f6c910116bfc667693f4f64cd102ffe3/ibb-publication}, doi = {10.18419/opus-262}, interhash = {935db2b6cc32ee64fa186eeea1220be1}, intrahash = {f6c910116bfc667693f4f64cd102ffe3}, keywords = {MAT MS from:maltevonscheven ibb phdthesis}, publisher = {Doktorarbeit, Bericht Nr. 48, Institut für Baustatik und Baudynamik, Universität Stuttgart}, timestamp = {2021-03-24T14:38:56.000+0100}, title = {Hierarchische Mehrskalenmodellierung des Versagens von Werkstoffen mit Mikrostruktur.}, year = 2007 }