L. On the significance of the limit load theorems for an elastic-plastic body

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Abstract
The limit load theorems of Drucker, Greenberg, and Prager (1951) for an elastic-plastic material flowing under constant surface tractions are contrasted with the theory of the yield of a plastic-rigid body (Hill 1951). Plastic-rigid theory is interpreted, as it must be for application to actual materials, as a model providing an approximation which can reasonably be expected to be satisfactory when plastic strains large in comparison with elastic strains have occurred. It is shown by the discussion of particular examples that the limit load for an elastic-plastic body is in general reached or closely approached while strains throughout are of the order of elastic strains, and at this stage the limit load theorems can be applied. Examples are cited to show that if plastic-rigid analysis is adopted, and strains large compared with elastic strains must be attained, the influence of boundary motion may invalidate application of the yield limit theory in circumstances when the limit load theorems for an elastic-plastic material provide significant results. It is shown that the uniqueness and variational theorems applicable to a plastic-rigid material at yield, apply to an elastic-plastic material at the limit load, thus permitting stress distributions in an elastic-plastic body to be determined on the basis of plastic-rigid theory. Examples are cited.

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