Analytical bounds of in-plane Young’s modulus and full-field simulations of two-dimensional monocrystalline stochastic honeycomb structures

• Numerical simulations and analytical bounds of Young’s moduli of monocrystalline honeycombs.
• Structural characteristics and elastic anisotropy enter the analytical bounds.
• Ratio of honeycomb to bulk Young’s modulus depends on crystallographic orientation.

In this study, we focus on the interplay between the honeycomb structure and the crystallographic orientation. Specifically, the in-plane Young’s moduli of monocrystalline stochastic honeycombs are calculated by a numerical and an analytical approach. The in-plane Young’s moduli of the honeycombs were calculated numerically using a solution scheme for the full-field mechanical equilibrium based on spectral methods and anisotropic crystal elasticity. The analytical approach formulates two alternative assumptions, i.e. uniform force and uniform strain per strut, considers the elastic anisotropy of the base material, and depends on the two-variable distribution of the strut length and inclination angle as the structural parameters characterizing the stochastic honeycombs. The uniform strain assumption agrees closely with the numerical simulation results and constitutes an improvement compared to analytical solutions proposed in previous studies.

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