A two-dimensional generalization of the Considère criterion


Peter P. Gillis, Wonjib Choi, S. E. Jones




The Consider criterion for reaching the maximum load under uniaxial tension has been extended to the case of biaxial deformation of a flat surface. Shortly before the maximum load is reached, it is assumed that the deformation stress of the flat surface is distributed homogeneously over the entire surface. The criterion for reaching the maximum load under biaxial deformation is obtained for the main direction of tension. It is shown that unless operating with an equi-biaxial force, the maximum loads in the principal and secondary directions cannot occur simultaneously. The surface material is assumed to be in tension. It is further assumed that it is a function of the rate of tension and that it is anisotropic. The results can be summarized as the main way can be accurately predicted based on the hardening parameter of the material, the stress rate and the strain rates in the main stress direction.