Size and disorder effects in elasticity of cellular structures: From discrete models to continuum representations. (1st August 2018)

• Record Type: Journal Article
• Authors: Liebenstein, Stefan; Sandfeld, Stefan; Zaiser, Michael
• Is Part Of: International journal of solids and structures. Volume 146(2018)
• Page Start: 97
• Page End: 116
• Publication Date: 2018-08-01
• Subjects: Cellular solids -- Size effects -- Homogenization -- Microstructure -- Timoshenko beam -- Cosserat -- Disorder; Mechanics, Applied -- Periodicals; Structural analysis (Engineering) -- Periodicals; Elastic solids -- Periodicals; Mécanique appliquée -- Périodiques; Constructions, Théorie des -- Périodiques; Solides élastiques -- Périodiques; Elastic solids; Mechanics, Applied; Structural analysis (Engineering); Periodicals; 624.18
• DOI: 10.1016/j.ijsolstr.2018.03.023
• Languages: English
• ISSNs: 0020-7683

Abstract

Abstract: 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.