Foam mechanics: nonlinear response of an elastic 3D-periodic microstructure

The compressive response of a 3D open-cell foam with periodic tetrakaidecahedral cells is studied through combined theoretical and numerical efforts. Under compressive loading the response is characterized by an extended load plateau following the relatively sharp rise to a maximum load. Several processes of loading have been simulated numerically using appropriately nonlinear kinematics. The onset of failure under macroscopic loading conditions is shown to be the reason of the load plateau. A failure surface is defined in macroscopic stress space by the onset of the first buckling-type instability encountered along proportional load paths. The analysis is carried out through two methods. The first one consists in increasing specimen size with periodic boundary conditions leading to the termed microfailure surface. The second one consists in considering both periodic and nonperiodic displacements variations on a minimum unit cell. The resulting failure surfaces are shown to coincide. Moreover, the postbuckling analysis has been carried out for two particular loadings: the uniaxial compression and the uniaxial deformation