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1. Geometrical deformation instability arises when the additional strain hardening ex- perienced by an infinitesimal cross-section in a tensile deformation specimen is not large enough to compensate for the geometrically increased stress due to the re- duction in cross-section compared to another section that deforms less. In other words, this means that, locally, the relative increase in flow stress becomes less than the relative decrease in cross-sectional area during a strain increment, such that additional straining is easier (requires less force) there than in the surrounding material. (a) Consider a plastically deforming volume (of constant cross-section A). Under the condition that plastic deformation does not alter the volume V, derive that the relative change of the cross-sectional area is equal but opposite to the rel- ative change in length 1 of the deforming volume.
(b) Derive the so-called “Considère criterion" do/de so for the onset of unstable necking in tensile deformation!