# Solid Mechanics

## Lecture notes

Introduction to Tensor algebra [Video lecture] [Lecture notes]

Traction vector [Video lecture] [Lecture notes]

Stress at a point [Video lecture] [Lecture notes]

Transformation of stress [Video lecture] [Lecture notes]

Stress equilibrium equation [Video lecture] [Lecture notes]

Principal stress [Video lecture] [Lecture notes]

Principal planes [Video lecture] [Lecture notes]

Maximum shear stress [Video lecture] [Lecture notes]

Mohr's circle [Video lecture] [Lecture notes]

Mohr's circle continued [Video lecture] [Lecture notes]

Introduction to strain [Video lecture] [Lecture notes]

Shear strain [Video lecture] [Lecture notes]

Volumetric strain [Video lecture] [Lecture notes]

Local Rotation (contd.) [Video lecture] [Lecture notes]

Strain compatibility condition [Video lecture] [Lecture notes]

Stress Strain relation [Video lecture] [Lecture notes]

Stress Strain relation for isotropic material [Video lecture] [Lecture notes]

Plane stress condition [Video lecture] [Lecture notes]

Plane strain condition [Video lecture] [Lecture notes]

Aries stress function [Video lecture] [Lecture notes]

Aries stress function contd. [Video lecture] [Lecture notes]

Linear momentum balance in cylindrical coordinate system [Video lecture] [Lecture notes]

Linear momentum balance in cylindrical coordinate system contd [Video lecture] [Lecture notes]

Strain matrix in cylindrical coordinate system [Video lecture] [Lecture notes]

Torsion-extension-inflation in hollow cylinder [Video lecture] [Lecture notes]

Torsion-extension-inflation in hollow cylinder [Video lecture] [Lecture notes]

Special case (not covered in live lecture) [Video lecture] [Lecture notes]

Finite strain tensors [video lecture][lecture notes]

Failure theories [video lecture][lecture notes]

Nonlinear elasticity and plasticity [video lecture][lecture notes]

## Syllabus

Introduction to general concept of elasticity

General introduction to stress, stress at a point (2D and 3D), transformation of stress, Mohr’s circle.

Principal stress and Principal plane, Maximum shear plain, Pure shear

Equilibrium and compatibility equations, plane stress, plane strain

Stress invariants, octahedral stress, deviatoric and hydrostatic state of stress

Strain at a point, transformation of strain, Principal strain, shear strain

Constitutive relation, Strain-displacement relation, Generalized Hooke’s law, Material anisotropy, Strain compatibility equation, Airy’s stress function, Energy Methods

Large strain, large deformation, Green strain, Euler strain, strain-displacement relation revisited.

Yield criteria and concept of plasticity, Rule of plastic flow, Particular stress strain relation, the total strain theory, Theorems of limit-analysis, Uniqueness theorem, Extremum principal

## References

Solid Mechanics (NPTEL) by Dr Ajeet Kumar [video link]

S P Timoshenko and J N Goodier,

*Theory of Elasticity*, Mc Graw Hill.L S Srinath,

*Advanced Mechanics of Solids*, Tata McGraw HillM H Sadd,

*Elasticity: Theory, Applications and Numerics*, Elsevier, 2005J Chakrabarty,

*Theory of Plasticity*, Butterworth-HeinemannS M A Kazimi,

*Solid Mechanics*, Tata McGraw HillJ.N. Reddy,

*Mechanics of Laminated Composite Plates and Shells*, CRC Press, 2e, 2004

## Homework

October 08, Transformation of stress [homework][solution]

October 08, Transformation of stress and stress equilibrium [homework][solution]

October 09, Principal Stress [homework][solution]

October 10, Principal Stress [homework][solution]

October 13, Principal Planes [homework][solution]

October 16, Principal Planes [homework][solution]

October 27, Longitudinal Strain [homework][solution]

October 31, Shear Strain [homework][solution]

October 31, Volumetric Strain [homework][solution]

November 17, Strain compatibility and relation among elastic constants [homework][solution]

## Assignments

November 01, Assignment 1 (Stress) [assignment][solution][codes]

## Course info

**Credit: **3 Units (3-0-0)

**Lectures: **Tuesdays, Wednesdays & Fridays 8:00 -- 9:00 am, Microsoft Teams (Online).

**Instructor****:**** **Dr. Souvik Chakraborty, Block IV, Room 342-C, souvik@am.iitd.ac.in

**Teaching Assistants:**** **Navaneeth N. (navaneeth.n@am.iitd.ac.in), Neha Pandey (neha.pandey@am.iitd.ac.in).

**Course Objective:** This is a fundamental course on mechanics of materials and covers essential concepts related to stress and strain in a body. Material behavior in both elastic and plastic regime will be covered. It is expected that by the end of this course, students will be equipped with essential tools and concepts of Solid Mechanics.

**Intended audience:** DIIT Students (Indian Navy Students), MS and PhD students in Mechanical Enginneering, Civil Engineering, Applied Mechanics and Materials Science.