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Foundations of Continuum Mechanics
Online
12 Weeks
Free Quick Facts
| Medium Of Instructions | Mode Of Learning | Mode Of Delivery |
|---|---|---|
| English | Self Study | Video and Text Based |
Courses and Certificate Fees
| Fees Informations | Certificate Availability | Certificate Providing Authority |
|---|---|---|
| INR 1000 | yes | IIT Mandi |
The Syllabus
Introduction and mathematical foundations (Module 1)
- Cartesian tensors, indicial notation, summation rule, Kronecker delta.
Mathematical foundations
- permutation symbol, epsilon-delta identity, vector and tensor products.
Mathematical foundations
- matrices and determinants, tensor transformations, isotropy and invariance.
Mathematical foundations
- principal values and directions, tensor calculus, integral theorems.
Stress principles (Module 2)
- body and surface forces, definition of the Cauchy stress tensor, equilibrium equations.
Stress principles
- stress transformation laws, principal stresses and directions, Stress maxima and minima, Mohr’s circle, plane stress, spherical and deviatoric stress components.
Kinematics (Module 3)
- configurations, deformation and motion, material and spatial coordinates, Lagrangian and Eulerian descriptions, material derivative.
Kinematics
- deformation gradient tensor, Lagrangian and Eulerian finite strain tensors, infinitesimal deformation theory and the infinitesimal strain tensor, normal and shear strain tensors, dilatation, and plane strain.
Kinematics
- differential displacement vector, infinitesimal rotation tensor, velocity gradient tensor, rate of deformation tensor, vorticity tensor, material derivatives of elements.
Conservation laws (Module 4)
- (Reynolds) transport theorem, equation of the conservation of mass in Eulerian and Lagrangian forms, linear momentum principle, Piola-Kirchoff stress tensors, angular momentum principle.
Constitutive modelling (Module 5)
- introduction and closure problem, 4th-order constitutive tensor, linear isotropic and anisotropic models for solids and fluids; non-linear constitutive models including hyperelasticity, plasticity, non-Newtonian fluid behaviour and viscoplasticity; time-dependent models such as viscoelasticity, creep, stress relaxation, thixotropy and rheopexy.
- Application of continuum mechanics: derivation of Navier-Stokes equation for linear and non-linear fluids; special cases; modelling and solving specific fluid dynamics problems using continuum mechanics principles.
Articles
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24 Jan'25, 12:14 PM
19 Sep'25, 11:37 AM
24 Jan'25, 12:14 PM