FINITE-ELEMENT ANALYSES OF SHEAR LOCALIZATION IN RATE AND TEMPERATURE-DEPENDENT SOLIDS
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The effects of strain hardening, strain rate sensitivity, thermal softening, heat conduction and the imposed strain rate on the shear localization process in plane strain compression are examined. The deformation, stress and temperature fields are computed in an infinite solid which contains a periodic rectangular array of inhomogeneities. The inhomogeneities give rise to non-uniform deformation fields which, under certain conditions, may localize in the form of a shear band. Boundary conditions are prescribed such that the resulting fields possess periodicity with respect to the inhomogeneity distribution. In this manner, attention may be confined to a rectangular region of the solid which surrounds a single inhomogeneity. Full two-dimensional analyses are performed within the context of a viscoplasticity theory which, in the rate independent limit, corresponds to flow theory with combined isotropic and kinematic hardening. Full account is taken of finite strain and rotation effects, but attention is confined to quasi-static loading. The initiation and propagation of shear bands is examined for the bounding theories of isotropic and kinematic hardening. The predicted response depends significantly on the multi-axial hardening characterization of the solid. 1987.