A Note on the 'Small Strain' Formulation for Elastic - Plastic Problems

摘要

Many ductile metals, particularly the higher strength structural alloys, exhibit a stress-strain curve having a slope in the plastic range which is of the same order of magnitude as the flow stress. This may occur even at strains which are quite small compared to unity. It is pointed out that this situation raises questions as to the validity of the conventional 'small strain' formulation of elastic-plastic problems. The small strain formulation is re-examined here and derived as a limiting case of a finite strain formulation. The difficulties encountered are similar to those in the superposition of small elastic deformations on large deformations: The conventional small strain formulation neglects terms of the same order of magnitude as those it retains when the hardening rate and stresses are of comparable order. Among the results, it is seen that for this case the conventional elastic-perfectly plastic small strain formulation emerges as an approximation of consistent order to the finite strain formulation. (Author)