Mechanical behavior of cellular structures: A finite element study

Cellular solids, such as foams are widely used in engineering applications. In these applications, it is important to know their mechanical properties and the variation of these properties with the presence of defects. Several models have been proposed to obtain the mechanical properties of cellular materials. However, some of these models are based on idealized unit cell structures, and are not suitable for finding the mechanical properties of cellular materials with defects. Also, a gradual increase in the cell size distribution, can impart many properties such as mechanical shock resistance and thermal insulation. Furthermore, functional gradation is one of the characteristic features of living tissue. Bio-inspired functionally graded materials open new approaches for manufacturing implants for bone replacement.;The objective of this work is to understand the effect of missing walls and filled cells on mechanical and creep behavior of both the regular hexagonal and non-periodic Voronoi structures using finite element analysis. Furthermore, mechanical properties of functionally graded cellular structures as a function of density gradient have not been previously addressed. In this study, the finite element method is used to investigate the compressive uniaxial and biaxial behavior of functionally graded Voronoi structures. The effect of missing cell walls on its overall mechanical (elastic, plastic, and creep) properties is also investigated.;The results showed that the missing walls have a significant effect on overall elastic properties of the cellular structure. For both regular hexagonal and Voronoi materials, the yield strength of the structure decreases by more than 60% by introducing 10% missing walls. In contrast, the results indicated that filled cells have much less effect on the mechanical properties of both regular hexagonal and Voronoi materials.;The finite element analysis also showed that the overall effective elastic modulus and yield strength of structures increased by increasing the density gradient. However, the overall elastic modulus of functionally graded structures was more sensitive to density gradient than the overall yield strength. The study also showed that the functionally graded structures with different density gradient had similar sensitivity to random missing cell walls. Creep analysis suggested that the structures with higher density gradient had lower steady-state creep rate compared to that of structures with lower density gradient.