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A microscopically motivated continuum model for cellular materials
Author(s) -
Diebels Stefan,
Grammes Thilo,
Goldschmidt Florian,
Jung Anne
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410198
Subject(s) - rheology , materials science , constitutive equation , compressibility , phenomenological model , mechanics , deformation (meteorology) , elasticity (physics) , digital image correlation , continuum mechanics , statistical physics , composite material , physics , thermodynamics , finite element method , condensed matter physics
Cellular materials like metal foams exhibit localised deformation expressed in deformation bands under inelastic strain conditions. According to the compressible behaviour of metal foams, there is localised damage in crushing zones with a thickness of several pores. In the present contribution, a new phenomenological modelling approach has been developed, which allows the explicit consideration of micro structural effects. The model accounts for micro structural effects by a rheological model offering the possibility to reflect the macroscopic stress fluctuations. Connecting a micro structural size with the rheological spring model results in a modified elasticity law and allows the description of localisation effects. By introducing a rheological model, the constitutive equations still contain fundamental parameters, but these are motivated by the micro structure, whereas the continuum model is able to account for size effects. The model is experimentally validated and its microstructurally motivated parameters are experimentally identified in quasi‐static compression tests with unloading. Using digital image correlation (DIC), it was possible to connect the micro structural deformation to the global macroscopic stress‐strain behaviour. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)