The partition of elastic strain energy in solid foams and lattice structures

Rapid advances in additive manufacturing techniques promise that, in the near future, the fabrication of functional cellular structures will be achieved with the desired cellular microstructures tailored to specific applications. It is therefore essential to develop a detailed understanding of the relationship between macroscopic mechanical response and cellular microstructure. The present study reports on the results of a series of computational experiments that explore the effect of topology and microstructural irregularity (or non-periodicity) on deformation modes of cellular structures under both uniaxial and biaxial stress states. A simple quantitative technique based on the partition of elastic strain energy into bending and stretch components is used to identify the distribution of deformation modes at a microstructural level. The relationship between nodal connectivity, morphological regularity and deformation modes is then explored through their influence on biaxial yield surfaces as obtained from finite element analyses.