Extending the elastic and plastic design space of metamaterials through load-specific, multiscale inner material architectures

In the current work we investigate the extension of the elastic and plastic design space of metamaterials by means of multiscale, load-specific inner material architectures. In particular, we analyse the use of a second scale of material architecturing at the level of the elements of the primal lattice structure. To that scope, we consider a wide range of inner element designs, from mere hollow shapes to double-curved architectures that allow for reduced relative density values. Thereupon, we evaluate both analytically and numerically the effective elastic and plastic behaviour of square, two-scale metamaterial lattice structures, as a function of their second level of inner material architecturing. We observe that hollow inner element designs allow for a substantially enhanced shear response performance both in the elastic and plastic analysis range, retaining invariant their specific axial loading behaviour. The performance improvement depends on the inner element design parameters and can be up to eighty per cent with respect to the reference, single-scale lattice design within the elastic analysis range. Accordingly, the results suggest that double-curved inner element architectures allow for a shear response improvement that can outperform the one of hollow element designs at the cost of a reduced axial loading performance.