Concise syllabus

Mathematical preliminaries; stress and strain; constitutive responses; physics of plasticity; application of plasticity theory for different materials; Formulation of rate-independent plasticity; maximum dissipation postulate; yield criteria; flow rules and hardening rules; uniqueness theorems; extremum principles in plasticity; limit analysis; shakedown theorems; plane problems in plasticity; slip line theory and its applications; plastic stability; plastic buckling; global and local criteria of plastic stability; strain localization and shear bands; dynamic plasticity; waves; special topics from current research.

Detailed syllabus

I. (Introduction)

• Lecture 1: introduction to the concept of plastic deformation using simple ideas and familiar examples
• Lecture 2: On the role of microstructure and thermodynamics in plastic deformation
• Lectures 3-4: Revision of relevant concepts from continuum mechanics
• Lecture 5: Constitutive responses: elastic, viscoelastic, plastic, viscoplastic, anisotropy etc.
• Lecture 6: Physical overview of crystal plasticity, plasticity of granular media, plasticity in rubber-like materials, etc.

II. (Rate independent plastic deformation)

• Lecture 7: Rate dependent and rate independent plasticity
• Lecture 8: Plastic strain, incremental strain, objective rates, and hardening variables Lecture 8: Yield criteria
• Lecture 9: Ilyushin’s postulate of maximum plastic work (including Drucker’s postulate)
• Lecture 10: Maximum dissipation and normality rule (Associated flow rules)
• Lecture 11: Hardening rules (isotropic and kinematic)
• Lecture 12: Non-associated flow rules
• Lectures 13-14: Axisymmetric problems in plasticity

III. (Plane problems in Plasticity)

• Lecture 15: Basic equations of plane strain and plane stress
• Lectures 16-17: Slip lines and their properties
• Lectures 18-20: Solution to several problems (such as indentation, necking, drawing, etc)
• Lecture 21: Application of slip line theory (Geophysics, tectonics, metal forming, etc.)

IV. (Some theorems in plasticity)

• Lectures 22-24: Uniqueness theorems and variational principles in plasticity
• Lectures 25-27: Limit analysis and shakedown theorems

V. (Plastic stability and waves)

• Lecture 28: The concept of plastic stability
• Lectures 29-30: Global stability criteria according to Hill
• Lectures 31-32: Elastoplastic column buckling
• Lectures 33-34: Local stability criteria (localization, shear bands, ellipticity)
• Lecture 35: Introduction to dynamic plasticity Lecture
• Lectures 36-37: One-dimensional waves

VI. (Topics from current areas of research)

• Lectures 38-40: Phase transformation and plasticity, strain-gradient plasticity, dislocation plasticity, crystal plasticity, etc (instructor can pick topics according to his/her taste)

References:

1. Plasticty Theory, J. Lubliner
2. Fundamentals of the theory of plasticity, L. M. Kachanov
3. Nonlinear Solid Mechanics, D. Bigoni
4. Plasticity: Fundamentals and applications, P. M. Dixit and U. S. Dixit5. Theory of Plasticity, J. Chakrabarty