## Plasticity Theory |

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angle associated flow rule assumed axes axial force beam behavior bending body boundary conditions collapse load components compression constant cross-section curve defined deflection denoted derived determined dislocation displacement field Drucker elastic equilibrium equations function given hardening incremental indicial notation inelastic strain inequality infinitesimal integration internal variables isotropic kinematically kinematically admissible linear lower bound material matrix mechanism Mises modulus notation obtained perfectly plastic plane strain plane stress plastic deformation plastic dissipation plastic hinge plastic strain plastic zone plate pressure principal stresses problem rate equations represents result rotation Section shear stress shell shown in Figure simple shear slip solution statically determinate strain rate strain tensor stress field stress-strain curve stress-strain relation symmetric temperature tensor theorem theory tion torsion traction uniaxial upper bound vanish vector velocity field virtual virtual displacement viscoplasticity work-hardening yield criterion yield locus yield stress yield surface zero