Physics / advanced
Matter as a deformable continuum
Derive continuum balances and constitutive laws, then examine elastic waves, bending, defects, and the assumptions behind material models.
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Module 01 advanced
Matter as a deformable continuum
Derive continuum balances and constitutive laws, then examine elastic waves, bending, defects, and the assumptions behind material models.
- 01
Follow matter through a continuum description
Connect coarse graining, material labels, deformation gradients, and mass conservation without pretending that matter has no microscopic structure.
30 min - 02
Separate small strain from small rotation
Derive the infinitesimal strain tensor and distinguish engineering shear, rigid rotation, and finite-strain corrections.
32 min - 03
Recover the force on a cut from Cauchy stress
Use an explicit stress-index convention to calculate traction, normal stress, and shear on arbitrary oriented surfaces.
31 min - 04
Build local momentum balance for a solid
Connect surface tractions, stress divergence, body forces, inertia, and boundary data in a continuum equation of motion.
32 min - 05
Connect stress and strain in an isotropic solid
Use Lamé parameters, bulk and shear moduli, and loading constraints to distinguish uniaxial stress from uniaxial strain.
34 min - 06
Elastic Energy and Material Stability
Separate volumetric and distortional energy to determine whether an isotropic elastic law resists every small strain.
26 min - 07
Longitudinal and Transverse Elastic Waves
Derive the two bulk wave speeds in an isotropic solid and separate polarization, propagation, and interference.
28 min - 08
Beam Bending and Euler Buckling
Connect cross-section geometry to bending stiffness and derive the first instability load of a pin-ended elastic column.
29 min - 09
Dislocations and Plastic Deformation
Connect crystal slip to line defects, resolved shear, and the dimensional meaning of the Orowan strain-rate relation.
28 min - 10
Viscoelastic Response and Relaxation
Derive Maxwell stress relaxation, distinguish it from creep, and interpret a relaxation time without confusing it with oscillator damping.
28 min