Objective of the course is to introduce the student to the basic concepts of mechanical behavior of metals in the plastic range.  After completing the course, the student should be able to carry out basic calculations of plasticity of mechanical engineering components.

Introduction: Micromechanisms of plastic deformation in metals, polymers and geomaterials.
Yield criteria: The general form of the yield criterion in isotropic materials. Yield criteria independent of hydrostatic stress. Geometric interpretation of the yield criterion in principal stress space, the π‐plane.
The plastic flow rule: Description of hardening. The postulates of Drucker and Il’iushin, plastic work.  Convexity of the yield surface. The normality rule (“associated” flow rule). The Prandtl‐Reuss equations.
Solution of elastoplastic problems: Beam bending, torsion, unloading and calculation of residual stresses.  Hollow cylinder under internal pressure. Combination of tension and torsion, dependence of solution on the loading path.
Limit analysis: Statically admissible stress fields and kinematically admissible velocity fields. Stress and  velocity discontinuities. The theorems of limit analysis. Examples. Application to plane‐strain problems, the “trapezoidal” stress field.
Slip line fields: The general method of solution of a system of first order quasi‐linear equations of two
variables. Plane deformation of a rigid perfectly plastic continuum. The hyperbolicity of the governing equations and the calculation of the “characteristics” (slip lines). Discontinuous stresses and velocities. Properties of the slip lines. Examples of simple slip line fields. Numerical methods for the determination of slip line fields.
Applications to metal forming: Analysis of extrusion, drawing and rolling.

Suggested bibliography:
• N. Aravas, «Theory of Plasticity», Class Notes, University of Thessaly Press.
• J. Lubliner, «Plasticity Theory», Macmillan Publishing Company, 1990.
• R. Hill, «The Mathematical Theory of Plasticity», Oxford University Press, 1998.
• L. M. Kachanov, «Foundations of the Theory of Plasticity», Dover Publications, 2004.
• W. Johnson and P. B. Mellor, «Engineering Plasticity», Ellis Horwood, 1983

Greek

Lectures