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Elastic-Plastic Deformation. Simple Constitutive Relations. And Their Graphs. Flow Rule. Anisotropy. Yield Surfaces. Drucker postulate. Kinematic hardening. Kinematic hardening is a monotonically growing & saturating function of strain and is a complex function of temperature. - PowerPoint PPT Presentation

### Transcript of Elastic-Plastic Deformation

• Elastic-Plastic Deformation

• Simple Constitutive Relations

• And Their Graphs

• Flow Rule

• Anisotropy

• Yield Surfaces

• Drucker postulate

• Kinematic hardeningKinematic hardening is a monotonically growing & saturating function of strain and is a complex function of temperature

• Isotropic HardeningLatent hardening is a monotonically growing and saturating function of strain and is a complex function of temperature

• Example on the simple BeamsLet us consider the simple problem or two, which should give us general feeling what is the plasticity is aboutWe look at 1D problemWe look at non-hardening problemWe look at isothermal problemNothing is more illustrative as beam examples

• Simple BeamGiven: E, l1, l2, PPN1N2

• Yield of Each Part Limiting or critical Force is: Compare

• RESIDUAL STRESS

• Elements of Shake Down MethodPEc=E; Es=2E;

• Shake DownElastic solution:Limiting Load:Let us apply the Force P1 to the system:Let us now unload the system:Let us apply the Force -P2 to the system:

• Limiting CycleP1P2ABCDEFGHOOHGF Elastic Regime

ABGH and FGDE system adjusts after first cycle; P1+P2

• Slip Theory

• Plasticity is Defined by Shear

• Principal stress

• Governing Equations

• Slip Lines Equations

• Henckys Equations

• Henckys equations

• Examples

• Examples

• More Examples

• More Examples

• Punch and Its Force