{"id":{"repo_id":"aachen","oai_identifier":"oai:publications.rwth-aachen.de:62893"},"canonical_url":"https://search.dev.ndltd.org/etd/aachen/oai:publications.rwth-aachen.de:62893","repository":{"repo_id":"aachen","name":"RWTH Aachen University","base_url":"https://publications.rwth-aachen.de/oai2d"},"display":{"title":"Einspieluntersuchungen von Verbundwerkstoffen mit periodischer Mikrostruktur","abstract":"In the present work, the shakedown behaviour of composite materials with periodic microstructure is investigated. For this, a general static shakedown theorem is given and proven taking into account the effects of limited linear kinematical hardening and plastic ductile damage. A general procedure is proposed to determine the admissible domains of macroscopic stresses. The methodology is based on the finite element method and a nonlinear mathematical programme to determine the safety factor against failure for large scale nonlinear problems. For this, an idealised class of composite material with a periodic microstructure is considered, allowing the determination of the macroscopic behaviour from microscopic information by means of the homogenisation theory. To this end, the concept of a representative volume element is introduced, which may be viewed as a heterogeneous structure under prescribed boundary conditions, corresponding to the uniform local continuum fields. To predict the life-time of such materials, several illustrative examples are given to show the applicability of the presented method with regards to the special case of metal-matrix composites with continuous fibers.","abstract_html":"In the present work, the shakedown behaviour of composite materials with periodic microstructure is investigated. For this, a general static shakedown theorem is given and proven taking into account the effects of limited linear kinematical hardening and plastic ductile damage. A general procedure is proposed to determine the admissible domains of macroscopic stresses. The methodology is based on the finite element method and a nonlinear mathematical programme to determine the safety factor against failure for large scale nonlinear problems. For this, an idealised class of composite material with a periodic microstructure is considered, allowing the determination of the macroscopic behaviour from microscopic information by means of the homogenisation theory. To this end, the concept of a representative volume element is introduced, which may be viewed as a heterogeneous structure under prescribed boundary conditions, corresponding to the uniform local continuum fields. 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For this, a general static shakedown theorem is given and proven taking into account the effects of limited linear kinematical hardening and plastic ductile damage. A general procedure is proposed to determine the admissible domains of macroscopic stresses. The methodology is based on the finite element method and a nonlinear mathematical programme to determine the safety factor against failure for large scale nonlinear problems. For this, an idealised class of composite material with a periodic microstructure is considered, allowing the determination of the macroscopic behaviour from microscopic information by means of the homogenisation theory. To this end, the concept of a representative volume element is introduced, which may be viewed as a heterogeneous structure under prescribed boundary conditions, corresponding to the uniform local continuum fields. 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