A microscopically motivated continuum model for cellular materials. Issue 1 (December 2014)

• Record Type: Journal Article
• Authors: Diebels, Stefan; Grammes, Thilo; Goldschmidt, Florian; Jung, Anne
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 14:Issue 1(2014)
• Page Start: 421
• Page End: 422
• Publication Date: 2014-12
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201410198
• Languages: English
• ISSNs: 1617-7061

Abstract

<abstract abstract-type="main" xml:lang="en"> <title>Abstract</title> <p>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 &amp; Co. KGaA, Weinheim)</p> </abstract>