NUMERICAL STUDY OF NECKING IN THE PLANE TENSION TEST

The boundary value problem for the plane-strain uniaxial tension of a rectangular bar is posed in two ways. In one case the ends of a specimen of compressible elastic-plastic material are assumed to remain shear free. Uniform deformation is terminated by an abrupt bifurcation. The eigenvalue problem governing bifurcation which is based on Hill's variational statement of uniqueness is solved by means of the finite element method. An updating Lagrangian formulation for large elastic-plastic strain is employed. The influence of the rate of work hardening and the specimen slenderness ratio on the bifurcation point is studied and a comparison is made with the conventional engineering criterion for stability. The post bifurcation behavior is then determined. Here the computations along with those for the second case, which considers the entire deformation history of a bar cemented to rigid grips, are based on a variational form of the rate equilibrium equations. The effect of end conditions on the deformations in the necked down bar is assessed. © 1979.