Micromorphic two-scale modelling of periodic grid structures

Enthalten in
International journal for multiscale computational engineering 
Volume
11
Issue
2
Start Page
161
End Page
176
Citation
International Journal for Multiscale Computational Engineering 2 (11): 161-176 (2013)
Publisher DOI
10.1615/IntJMultCompEng.2012003279
Scopus ID
2-s2.0-84875754623
Publisher
Begell
The present contribution focuses on the numerical homogenization of periodic grid structures. In order to investigate the micro-to-macroscale transition, a consistent numerical homogenization scheme will be presented, replacing a heterogeneous Cauchy microcontinuum by a homogeneous micromorphic substitute continuum on the macroscale. The extended degrees of freedom, namely, the microdeformation and its gradient, are to be interpreted in terms of geometrical deformation modes and the related loading conditions of the underlying unit cells. Assuming strain energy equivalence of the macro- and the microscale, the effective constitutive properties of a square and a honeycomb grid structure are identified and quantitatively validated in comparison to reference calculations with microscopic resolution. © 2013 by Begell House, Inc.
Schlagworte
Cellular materials
FE method 2
Homogenization
Micromorphic media
Size effects
DDC Class
620: Ingenieurwissenschaften