A COMPARATIVE-STUDY OF SIMPLE SHEAR AT FINITE STRAINS OF ELASTOPLASTIC SOLIDS

Exact analytical solutions are given for the simple-shear deformation pattern at finite strain. Three different J2 constitutive relations with isotropic hardening are employed; the usual flow and deformation theories and the hypoelastic deformation-type theory. A detailed comparison is made between the solutions, predicted by the three different theories, for some particular hardening characteristics. It appears, on the basis of these examples, that flow theory predicts the stiffest shear response, while the weakest response is obtained with the hypoelastic model. Deformation-theory results for the shear stress are between those given by the flow and hypoelastic theories. The deformation theory and the hypoelastic theory predict the existence of an instability point where the required shear stress attains a maximum value. The normal stresses obtained from these two theories, in contrast to the flow-theory solution, cannot be regarded as a second-order effect. The hypoelastic theory breaks down at very high strains at a point where the required shear stress vanishes. © 1990 Oxford University Press.