This paper presents a theoretical investigation into the continued quasi-static compression of a thin metal strip between two rigid, parallel rough dies. Three different constitutive postulates for the strip material are considered: (a) rigid isotropic hardening, (b) rigid-perfectly plastic with an anisotropic yield criterion, and (c) rigid-kinematic (anisotropic) hardening. An initially homogeneous such strip develops inhomogeneities through its thickness as it is compressed. This is due to the dependence of the yield locus on the rigid-body spin for an anisotropic material and on the strain-history for a hardening material. The length of the dies is supposed to be much greater than the current strip thickness. The solution is hence effectively independent of position along the length of the strip and can be found by integrating an ordinary differential equation.

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