Mechanics of Materials Elasticity and Plasticity

Course Details
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Subject Nature : Theory

Coordinator : Srinivas Behera

Syllabus
Module 1 :
Module 1: Fundamentals of Stress, Strain, and Elasticity (8Hrs)
Stress and Strain Analysis Equilibrium Equations Compatibility Equations Constitutive Equations Plane Problems in Elasticity Stress Functions and Applications
Module 2: Advanced Elasticity and Variational Methods (8Hrs)
Complex Potentials in 2D and Axisymmetric Problems Variational Methods in Elasticity Anisotropic Elasticity Finite Deformation Elasticity
Module 3: Plasticity Theory and Yield Criteria (09Hrs)
Yield Surfaces Deformation and Flow Theories Plastic Constitutive Equations Axisymmetric and Spherically Symmetric Problems
Module 4: Applications in Plasticity (11hrs)
Slab Theory, Slip-line Theory, and Upper Bound Theory Applications to Forging, Extrusion, Drawing, and Indentation.

Course Objective
1 .
Understand different methods that used to analyse stress and strain in solid body.

2 .
Apply various principles to solve problems in a practical situation and compare its solution with that obtained by solid mechanics approach.

3 .
Examine different yield criteria in diverse failure situations.

4 .
Relate theory of plasticity to manufacturing.

Course Outcome
1 .
1. Understand and apply the fundamental concepts of stress and strain, including equilibrium, compatibility, and constitutive equations, to solve solid mechanics problems.
2. Utilize stress functions, plane stress and plane strain concepts, and complex potentials to analyze two-dimensional and axisymmetric elasticity problems.
3. Explain and apply plasticity theories, including yield surfaces, deformation and flow rules, and constitutive equations, to material flow behavior beyond the elastic limit.
4. Investigate finite deformation elasticity and anisotropic elasticity principles to understand advanced material behavior in engineering applications.
5.Implement slab theory, slip-line theory, and upper bound methods to analyze metal forming processes such as forging, extrusion, drawing, and indentation.

Essential Reading
1 .
Valentin Molotnikov · Antonina Molotnikova, Theory of Elasticity and Plasticity: A Textbook of Solid Body Mechanics, Springer Nature , 1st Translated edition by Subachev . V 2021

2 .
P.M. Dixit and U.S. Dixit, Plasticity: Fundamentals and Application, CRC Press , 2nd Edition 2025

Supplementary Reading
1 .
L S Srinath, Advanced Mechanics of Solids, Tata McGraw-Hill , 3rd Edition

2 .
Johnson and Mellor, Engineering Plasticity, Van-Nostrand., 1st edition, 1983 , -

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