Size and Disorder Effects in Elasticity of Cellular Structures: From Discrete Models to Continuum Representations

TL;DR

This paper investigates how size and disorder influence the elasticity of cellular structures, developing a computational model and a continuum method to analyze and compare microstructural effects on mechanical properties.

Contribution

It introduces a Timoshenko beam network model and an energetically consistent continuization technique for detailed, statistical analysis of cellular microstructures.

Findings

Size-dependent elastic behavior observed in cellular structures.

Disorder leads to significant property variations among microstructure realizations.

The continuum approach enables effective visualization and statistical analysis.

Abstract

Open 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 behaviour 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.