Determining Cosserat constants of 2D cellular solids from beam models
Abstract We present results of a two-scale model of disordered cellular materials where we describe the microstructure in an idealized manner using a beam network model and then make a transition to a Cosserat-type continuum model describing the same material on the macroscopic scale. In such scale...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2018-01-01
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| Series: | Materials Theory |
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| Online Access: | http://link.springer.com/article/10.1186/s41313-017-0009-x |
| _version_ | 1819077042633703424 |
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| author | Stefan Liebenstein Michael Zaiser |
| author_facet | Stefan Liebenstein Michael Zaiser |
| author_sort | Stefan Liebenstein |
| collection | DOAJ |
| description | Abstract We present results of a two-scale model of disordered cellular materials where we describe the microstructure in an idealized manner using a beam network model and then make a transition to a Cosserat-type continuum model describing the same material on the macroscopic scale. In such scale transitions, normally either bottom-up homogenization approaches or top-down reverse modeling strategies are used in order to match the macro-scale Cosserat continuum to the micro-scale beam network. Here we use a different approach that is based on an energetically consistent continuization scheme that uses data from the beam network model in order to determine continuous stress and strain variables in a set of control volumes defined on the scale of the individual microstructure elements (cells) in such a manner that they form a continuous tessellation of the material domain. Stresses and strains are determined independently in all control volumes, and constitutive parameters are obtained from the ensemble of control volume data using a least-square error criterion. We show that this approach yields material parameters that are for regular honeycomb structures in close agreement with analytical results. For strongly disordered cellular structures, the thus parametrized Cosserat continuum produces results that reproduce the behavior of the micro-scale beam models both in view of the observed strain patterns and in view of the macroscopic response, including its size dependence. |
| first_indexed | 2024-12-21T18:50:55Z |
| format | Article |
| id | doaj.art-ffd9fc8a14974566b0fdc740f61fe46a |
| institution | Directory Open Access Journal |
| issn | 2509-8012 |
| language | English |
| last_indexed | 2024-12-21T18:50:55Z |
| publishDate | 2018-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Materials Theory |
| spelling | doaj.art-ffd9fc8a14974566b0fdc740f61fe46a2022-12-21T18:53:45ZengSpringerOpenMaterials Theory2509-80122018-01-012112010.1186/s41313-017-0009-xDetermining Cosserat constants of 2D cellular solids from beam modelsStefan Liebenstein0Michael Zaiser1Institute of Materials Simulation (WW8), Friedrich-Alexander University Erlangen-Nürnberg (FAU)Institute of Materials Simulation (WW8), Friedrich-Alexander University Erlangen-Nürnberg (FAU)Abstract We present results of a two-scale model of disordered cellular materials where we describe the microstructure in an idealized manner using a beam network model and then make a transition to a Cosserat-type continuum model describing the same material on the macroscopic scale. In such scale transitions, normally either bottom-up homogenization approaches or top-down reverse modeling strategies are used in order to match the macro-scale Cosserat continuum to the micro-scale beam network. Here we use a different approach that is based on an energetically consistent continuization scheme that uses data from the beam network model in order to determine continuous stress and strain variables in a set of control volumes defined on the scale of the individual microstructure elements (cells) in such a manner that they form a continuous tessellation of the material domain. Stresses and strains are determined independently in all control volumes, and constitutive parameters are obtained from the ensemble of control volume data using a least-square error criterion. We show that this approach yields material parameters that are for regular honeycomb structures in close agreement with analytical results. For strongly disordered cellular structures, the thus parametrized Cosserat continuum produces results that reproduce the behavior of the micro-scale beam models both in view of the observed strain patterns and in view of the macroscopic response, including its size dependence.http://link.springer.com/article/10.1186/s41313-017-0009-xCellular materialsDisorderMicro-to-macro transitionCosserat continuum |
| spellingShingle | Stefan Liebenstein Michael Zaiser Determining Cosserat constants of 2D cellular solids from beam models Materials Theory Cellular materials Disorder Micro-to-macro transition Cosserat continuum |
| title | Determining Cosserat constants of 2D cellular solids from beam models |
| title_full | Determining Cosserat constants of 2D cellular solids from beam models |
| title_fullStr | Determining Cosserat constants of 2D cellular solids from beam models |
| title_full_unstemmed | Determining Cosserat constants of 2D cellular solids from beam models |
| title_short | Determining Cosserat constants of 2D cellular solids from beam models |
| title_sort | determining cosserat constants of 2d cellular solids from beam models |
| topic | Cellular materials Disorder Micro-to-macro transition Cosserat continuum |
| url | http://link.springer.com/article/10.1186/s41313-017-0009-x |
| work_keys_str_mv | AT stefanliebenstein determiningcosseratconstantsof2dcellularsolidsfrombeammodels AT michaelzaiser determiningcosseratconstantsof2dcellularsolidsfrombeammodels |