Mechanics of filled cellular materials

The in-plane elastic properties of hierarchical composite cellular materials: Synergy of hierarchy, material heterogeneity and cell topologies at different levels

“…, it emerges that in the resulting energy the coefficients scale with different order in , as in [7], [1]. Specifically, the microrotation gradients scale with first order in , while the others coefficients are independent of .…”

“…Note that representing the material within the cells by a Winkler foundation is a simplification to obtain a more mathematically tractable problem. However, notwithstanding the limitations introduced, the analysis in [1] reveals the validity of the modeling approach based on the Winkler model. A suitable relation between the Young's modulus of the filling material, E w , is also provided [1]: i) and (i) the length of the cell walls.…”

“…However, notwithstanding the limitations introduced, the analysis in [1] reveals the validity of the modeling approach based on the Winkler model. A suitable relation between the Young's modulus of the filling material, E w , is also provided [1]: i) and (i) the length of the cell walls. Assuming that the material inside the cells is a honeycomb made of an aluminum alloy as the whole hierarchical composite cellular structure analyzed in the present paper, leads to [2] ρ…”

“…Also, an elastic foundation represents the elastic material filling the cells. In particular, the Winkler foundation model simulates each beam, as in [1]. The unit cell of the periodic array (Fig.…”

“…See Appendix D for further details. The terms k e b and k e wf in (B.2) are, respectively, the stiffness matrix of the classical elastic beam and of the Winkler foundation [3], denoted by lowercase letters since they are expressed in the local reference (see [1] for a detailed description). Their components are and As it can be seen, the elastic energy is the sum of three terms.…”