Buckling pattern transition of periodic porous elastomers induced by proportional loading conditions

This paper focuses on the buckling instabilities of periodic porous elastomers under combined multiaxial loading. A numerical model based on the periodic boundary condition (PBC) for the 2D representative volume element (RVE) is proposed, in which two proportional loading parameters are employed to control the complex stressing state applied to the RVE model. A homogenization-based orthogonal transformation matrix is established by satisfying the equality of the total work rate to realize a proportional multiaxial loading on the RVE. First, the transition behavior of buckling patterns of periodic porous structures is revealed through instability analysis for the RVE consisting of 2 × 2 primitive cells with circular holes subjected to different proportional loading conditions. Simulation results show that the first-order buckling mode of RVE may change suddenly from a uniaxial shearing buckling pattern to a biaxial rotating buckling pattern at a critical loading proportion. Then the influences of the number of primitive cells in the enlarged RVE on the buckling behavior are discussed. When the number of primitive cells in any enlarging direction is odd, the points of buckling pattern transition of the enlarged RVEs vary significantly with the number of cells in RVE. When the number of primitive cells is even in both enlarging directions, there is no apparent difference for the critical buckling stresses of the enlarged RVEs.