Non-affinity in multi-material mechanical metamaterials

Abstract

AbstractNon-affine deformations enable mechanical metamaterials to achieve their unusual properties while imposing implications for their structural integrity. The presence of multiple phases with different mechanical properties results in additional non-affinity of the deformations, a phenomenon that has never been studied before in the area of extremal mechanical metamaterials. Here, we studied the degree of non-affinity, $$\Gamma $$Γ, resulting from the random substitution of a fraction of the struts,$${\rho }_{h}$$ρh, that make up a lattice structure and are printed using a soft material (elastic modulus = $${E}_{s}$$Es) by those printed using a hard material ($${E}_{h}$$Eh). Depending on the unit cell angle (i.e., $$\theta $$θ = 60°, 90°, or 120°), the lattice structures exhibited negative, near-zero, or positive values of the Poisson’s ratio, respectively. We found that the auxetic structures exhibit the highest levels of non-affinity, followed by the structures with positive and near-zero values of the Poisson’s ratio. We also observed an increase in $$\Gamma $$Γ with $$\frac{{E}_{h}}{{E}_{s}}$$EhEs and $${\rho }_{h}$$ρh until $$\frac{{E}_{h}}{{E}_{s}}$$EhEs =104 and $${\rho }_{h}$$ρh= 75%-90% after which $$\Gamma $$Γ saturated. The dependency of $$\Gamma $$Γ upon $${\rho }_{h}$$ρh was therefore found to be highly asymmetric. The positive and negative values of the Poisson’s ratio were strongly correlated with $$\Gamma $$Γ. Interestingly, achieving extremely high or extremely low values of the Poisson’s ratio required highly affine deformations. In conclusion, our results clearly show the importance of considering non-affinity when trying to achieve a specific set of mechanical properties and underscore the structural integrity implications in multi-material mechanical metamaterials.