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The boundary-value problem for a circular cylindrical bar in uniaxial tension is posed in two ways. In one the ends of the specimen are assumed to be cemented to rigid grips; while in the other they remain shear free. With the latter end-condition, necking initiates by a bifurcation from a state of uniform tensile stress. The eigenvalue problem governing bifurcation is solved by means of the finite element method, and a comparison is made between the results obtained here and the conventional maximum load criterion. The post-bifurcation behavior is then determined. The entire deformation history of the bar cemented to rigid grips is also calculated and the effect of end conditions on the deformations in the necked-down bar is assessed. 1972.
Journal of the Mechanics and Physics of Solids
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