Periodic repetition of the duoskelion motif along a single dimension results in
duoskelion beams. These beams have been proven to exhibit interesting mechanical
properties like axial-transverse coupling and bimodularity, namely the coexistence of
resistance to shortening and compliance to lengthening. The continuum description of
these structures is achieved through homogenization, defining a family of discrete
descriptions parametrized over the cell size. When the cell size tends to zero one
retrieves a non-linear generalization of the Timoshenko beam model with
an internal constraint involving the stretch and the shear angle. The limit
model is reduced to a second order boundary value problem involving only
the cross-section rotation angle, which is then recast into an initial value
problem describing the motion of a particle subjected to a potential. The initial
conditions of such an initial value problem have to be taken so as to fulfill the
kinematic conditions at the beam’s boundaries. Exploiting the properties of
this alternative representation of the boundary value problem governing the
equilibrium of a homogenized duoskelion beam, the present contribution
addresses the qualitative study and computation of large deformation equilibria
of duoskelion beams subjected to simultaneous axial and transverse end
load.