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anisotropy applied axes axis buckling co-ordinates coefﬁcients compressive condition conﬁrms constant cylinder deﬁned deﬁnition deformation deviatoric direction displacement displacement vector elastic elastic-plastic Equation equivalent plastic strain equivalent stress extrusion ﬁeld Figure ﬁnd ﬁnite ﬁrst ﬂow curve ﬂow rule follows force friction given gives gradient grain hardening Hencky hodograph identiﬁed inﬂuence initial yield instability isotropic loading material matrix Mech metal Mises modiﬁed normal orthogonal orthotropic plane strain plane stress plastic strain increment Prandtl-Reuss predictions pressure principal stress radial radius ratio reﬂected residual stress roll rotation shear strain shear stress sheet shown in Fig shows slip line solution strain paths strain tensor stress and strain stress components stress plane stress-strain stress-strain curve Substituting tensile tensile stress tension testpiece theory thickness torque torsion Tresca uniaxial vector velocity discontinuities wave yield criterion yield function yield locus yield point yield stress yield surface zone
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