Continuum Mechanics
Continuum Mechanics - MEPE30
Dr.-Ing. Ashok Kumar Nallathambi - Mechanical Engineering - NIT Tiruchirappalli
This course is designed for B.Tech students. After attaining the knowledge of Engineering Mechanics, Solid Mechanics, and Fluid Mechanics, this course will enrich and unify the theory of continuum such as rigid, deformable solid and fluid materials.
2021 - 57, 2022 - 53, 2023 - 61 in total 171 students studied this elective course.
2024 - registered student strength - 67
Last update: May 2024
Syllabus
Tensor algebra: Scalar, Vector, second and higher order Tensors, Eigen values & vectors, Transformation of Tensors, Tensor valued functions, gradient operators and Integral theorems.
Kinematics: References and deformations configurations, Mapping and deformation gradients, material and spatial representations, Nanson’s formula, Strain measures, Rotation & stretch tensors, rate of deformation.
Kinetics: Concept of stress, Cauchy’s stress theorem, first and second Piola- Kirchoff’s & Cauchy’s stress tensors, Normal and shear stress, Extremal stress values, stress states.
Balance Principles: Mass conservation, Reynold’s transport theorem, Momentum and energy balances in references and current configuration, Weak and strong forms of balance equation, Continuum thermodynamics, Clausius-Duhem inequality, Frame dependent and independent quantities, Objective rates.
Constitutive Modeling: Fluid and solid constitutive equations, generalized Hooke’s law, material symmetry, visco elasticity, metal plasticity: Yield criteria, Flow rule, Hardening rule, loading & unloading conditions, multiplicative strain decomposition, rheological models.
Tutorials
Study Materials
Balance Principles - Mass and Linear Momentum - Conventional
Balance Principles - Mass and Linear Momentum - Continuum Approach
Assignments
Assignment - 1 - Tensor Algebra
Question Papers
Cycle Test 2 - 2023 Question Paper Cycle Test 2 - 2023- Answers
Reference Books
1. Nonlinear Solid Mechanics: A Continuum Approach for Engineering, Gerhard A. Holzapfel, Wiley Publications, ISBN: 978-0-471-82319-3, 2000.
2. Introduction to Continuum Mechanics, by W Michael Lai, David H. Rubin, Erhard Krempl, David Rubin, Butterworth-Heinemann; 4th edition, ISBN: 978-9380501581
3. An Introduction to Continuum Mechanics, J.N. Reddy, Cambridge University Press; 2nd edition, ISBN: 978-1316614204
4. Schaum's Outline of Continuum Mechanics, George E. Mase, McGraw Hill; First edition, ISBN: 978-9389691283
5. Mysore N. L. Narasimhan, Principles of Continuum Mechanics, Wiley-Inter science, ISBN: 978-0471540007, 1992.
6. Fundamentals of Continuum Mechanics, John W Rudnicki, Wiley, ISBN: 978-1-118-92767-0
7. Computational Continuum Mechanics, Ahmed A. Shabana, Wiley; 3rd edition, ISBN: 978-1119293217, 2005.
8. Continuum Mechanics, A.J.M.Spencer, Dover Publications Inc. ISBN: 978-0486435947
9. Elasticity and plasticity of large deformations. Bertram, A., Springer-Verlag Berlin Heidelberg, 3rd Edition, 2012, ISBN: 978-3642246142.
10. Computational inelasticity. Vol. 7., Simo, Juan C., and Thomas JR Hughes, Springer Science & Business Media, 2013,
ISBN: 978-1475771695.
11. Fridtjov Irgens, Continuum mechanics, Springer, ISBN: 978-3-540-74297-5, 2008.
12. C.S. Jog, Continuum Mechanics: Volume 1: Foundations and Applications of Mechanics, Cambridge University Press, 978-1107091351, 2015