EQUILIBRIA OF AXIAL-TRANSVERSELY LOADED HOMOGENIZEDDUOSKELION BEAMS

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 ahomogenized 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.