Higher Order Continuum Modelling for Predicting the Mechanical Behaviour of Solid Foams

Liebenstein, Stefan; Sandfeld, Stefan; Zaiser, Michael

doi:10.1002/pamm.201410145

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“…Unlike most top-down attempts, where one takes the (size-dependent) macroscopic system response of the beam model and then tries to fit the parameters of the higher order continuum (see e.g. Diebels and Steeb, 2002;Tekoglu and Onck, 2005;Mora and Waas, 2007;Liebenstein et al, 2014) our approach allows to directly take the information of the microstructure into account. We showed this in an accompanying paper by Liebenstein and Zaiser (2017) where we identified constitutive parameters of a Cosserat continuum.…”

Section: Resultsmentioning

confidence: 99%

Size and disorder effects in elasticity of cellular structures: From discrete models to continuum representations

Liebenstein

Sandfeld

Zaiser

2018

International Journal of Solids and Structures

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Cellular solids usually possess random microstructures that may contain a characteristic length scale, such as the cell size. This gives rise to size dependent mechanical properties where large systems behave differently from small systems. Furthermore, these structures are often irregular, which not only affects the size dependent behavior but also leads to significant property variations among different microstructure realizations. The computational model for cellular microstructures is based on networks of Timoshenko beams. It is a computationally efficient approach allowing to obtain statistically representative averages from computing large numbers of realizations. For detailed analysis of the underlying deformation mechanisms an energetically consistent continuization method was developed which links the forces and displacements of discrete beam networks to equivalent spatially continuous stress and strain fields. This method is not only useful for evaluation and visualization purposes but also allows to perform ensemble averages of, e.g., continuous stress patterns -an analysis approach which is highly beneficial for comparisons and statistical analysis of microstructures with respect to different degrees of structural disorder. (Stefan Liebenstein ) 1 In the following, we denote by 'microstructure' internal sub-structures of a material which are characterized by length scales well below the size of a specimen or device, the geometry of which defines the 'macrostructure'.

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