A general theory of uniqueness and stability in elastic-plastic solids

A SUFFICIENT condition is established for uniqueness of the boundary-value problem set by given velocities on a part of the surface of a body and given nominal traction-rates on the remainder. No restriction is placed on changes in geometry either in the boundary-value problem itself or in the postulated material properties, which are a generalization of those conventionally assumed for workhardening elastic-plastic solids. The solution, when it is unique, is characterized by an extremum principle. Stability under dead loading is also examined, and a criterion is proposed. This has a formal resemblance to the uniqueness criterion, but differs from it in a significant respect when the body is partly plastic, so that stability and uniqueness need not be parallel properties. Finally, the present, theorems are compared with those previously proved for rigid-plastic solids ( HILL 1957a, b. d).