THE INSTABILITY OF A NONLINEARLY ELASTIC BEAM UNDER TENSION

The stability of the equilibrium position of a non-linearly elastic re ctangular beam under tension when it is subject to small plane perturb ations is investigated. The material is assumed to be homogeneous, iso tropic and incompressible. Sufficient criteria of stability and instab ility of the uniform deformation of a beam under tension are obtained. It is established that flexural instability always takes the form of surface bulging. For a thin beam, it is shown that there are no lower- order flexural modes. It is also shown that for medium values of the r elative thickness of the beam a loss of stability with the formation o f a ''neck'' occurs for smaller extensions than flexural bulging. The asymptotic form of the critical deformation is constructed with a wide range of applicability. Specific models of highly elastic materials a re described for which instability of the equilibrium of the beam unde r a tensile load is possible. (C) 1997 Elsevier Science Ltd.