An exploratory study on the physical nonlinear response of two micro-structured materials is provided. The design examples of two materials with very low Young’s modulus E include an auxetic with a Poisson’s ratio \(\nu =-0.99\) and a standard with a Poisson’s ratio \(\nu =0.20\) . The design framework relies on a heuristic molecular (HM) model, whose representative unit-cell is derived from a Rigid-Body-Spring-Model (RBSM) composed of shaped atoms with centered and non-centered spring-based bonds. The elastic stiffness of the bonds is found through energy equivalence between the HM and a macroscopic elastic and isotropic Cosserat continuum. Within an exploratory scope, and considering the use of a standard printing material, the effect of the mechanical nonlinearity of the bonds is studied. Under the hypothesis of an elastic-perfectly plastic constitutive response for the printing material, the anisotropic strength is evaluated for each HM under different combinations of bi-axial stress. The results extend the discussion from the elastic quasi-isotropic response exhibited by these ultra-soft materials to their behaviour in the plastic range.