On internal stability problems in structured materials

Summary Internal instability of structured materials and elements is occasionally observed and has been verified by experiments. The specific problems in this contribution treated analytically and numerically consist of internal instability phenomena of prestressed elastic materials and the so-called membrane buckling of thin elastic plates and shells. A stability theory taking into consideration independent local rotations is outlined; this theory is then used to treat the membrane buckling of cylindrical shells and the in-plane buckling of rectangular plates. It is shown that under certain circumstances, the in-plane buckling mode may precede the out-of-plane buckling deformation. To simulate the internal stability phenomena numerically, a number of discrete models of structured materials are considered; based on these models numerical Finite Element (FE) buckling analyses are carried out, including linear analyses for the membrane buckling of a circular cylindrical shell model and the in-plane buckling analysis of a flat plate. The FE simulations effectively afford buckling loads and buckling modes.