Elastoplastic response and recoil of lattice structures under hyperbolic hardening

Elastoplastic response and recoil analyses for hexagonal honeycomb lattice structures are presented when hardening is described by a hyperbolic law. By exploiting the translational symmetry of the problem, the analysis is reduced to that of a thin beam under combined bending and axial loading coupled with the kinematics of lattice deformation and its relationship with cell wall deformation. A closed-form solution for the load-curvature relationship of a beam with rectangular cross-section is obtained. A systematic study of beam response, as the stress-strain curve of the constituent material approaches an ideal elastic-perfectly plastic law, is presented. The analysis is then applied to an infinite honeycomb sheet under remote tensile load to obtain the apparent non-linear structural response. Apparent recoil of such a lattice material upon unloading is also calculated in closed form, when unloading is assumed to take place along a linear stress-strain curve. The analytical results are in excellent agreement with the numerical calculations.