Theories of Plastic Buckling

The theory for the plastic buckling of columns, which appears finally to have achieved a satisfactory form, rests upon the wellestablished uniaxial stress-strain relation. The development of a correspondingly satisfactory theory for the plastic buckling of plates has been hampered by the nonexistence of an established poly axial stress-strain relation in the plastic range. Present theories for the polyaxial stress-strain relation beyond the elastic range can be divided into two types, often called flow and deformation theories. Theories of plastic buckling based on deformation theories are in better agreement with experiment than those based on flow theories. On the other hand, tests in which a material is compressed into the plastic range and then subjected to shear at constant compressive stress are in better agreement with flow than with deformation theories. Legitimate doubt therefore has existed as to the validity of any theory for the plastic buckling of plates. As a result of studying these apparent contradictions, a new theory of plasticity has been developed which is of neither the flow nor the deformation type. I t is based upon the concept of slip, and its formulation was guided more by physical, and less by mathematical, considerations than previous theories. Experimental evidence of limited scope but of crucial character is in better agreement with the new theory than with either flow or deformation theories. The new theory accounts for the apparent contradictions previously alluded to and justifies the use of deformation theory in the analysis of the plastic buckling of plates.