  In the present work, the overall nonlinear elastic behavior of a 1D
multi-modular structure incorporating possible imperfections at the discrete
(micro-scale) level, is derived with respect to both tensile and compressive
applied loads. The model is built up through the repetition of n units, each
one comprising two rigid rods having equal lengths, linked by means of
pointwise constraints capable to elastically limit motions in terms of relative
translations (sliders) and rotations (hinges). The mechanical response of the
structure is analyzed by varying the number n of the elemental moduli, as well
as in the limit case of infinite number of infinitesimal constituents, in light
of the theory of (first order) Structured Deformations (SDs), that interprets
the deformation of any continuum body as the projection, at the macroscopic
scale, of geometrical changes occurring at the level of its sub-macroscopic
elements. In this way, a wide family of nonlinear elastic behaviors is
generated by tuning internal microstructural parameters, the tensile buckling
and the classical Euler Elastica under compressive loads resulting as special
cases in the so-called continuum limit, say when n tends to 1. Finally, by
plotting the results in terms of first Piola-Kirchhoff stress versus
macroscopic stretch, it is for the first time demonstrated that such SDs-based
1D models can be helpfully used to generalize some standard hyperelastic
behaviors by additionally taking into account instability phenomena and
concealed defects.
