We derive effective, parsimonious models from a heterogeneous second-gradient nonlinear elastic material taking into account chiral scale-size effects. Our classification of the effective equations depends on the hierarchy of four characteristic lengths: The size of the heterogeneities $\ell$, the intrinsic lengths of the constituents $\ell_{ \rm SG}$ and $\ell_{ \rm chiral}$, and the overall characteristic length of the domain ${ \rm L}$. Depending on the different scale interactions between $\ell_{ \rm SG}$, $\ell_{ \rm chiral}$, $\ell$, and ${ \rm L}$ we obtain either an effective Cauchy continuum or an effective second-gradient continuum. The working technique combines scaling arguments with the periodic homogenization asymptotic procedure. Both the passage to the homogenization limit and the unveiling of the correctors' structure rely on a suitable use of the periodic unfolding and related operators.
Categories: math.AP