GEO 325C/398C Continuum Mechanics

Jackson School of Geosciences - University of Texas at Austin

Project maintained by mhesse Hosted on GitHub Pages — Theme by mattgraham

Back to main course page

Course in Fall 2022

Class room

Office hours

Mon + Wed 2-3pm in room JGB 2.104B (new!) in the Student Service Center, close to Luck Lab Coffee [Zoom ID 921 0937 9742]

Additional zoom office hours with Afzal Tue 11-noon [Zoom ID 378 6912 461]

Additional course websites:

Relevant textbooks

We will most closely follow:

Other useful books are:

Topic I: Tensors and Stress

Lecture 1 (Aug 23): Introduction (zoom)

Lecture 2 (Aug 25): Introduction to Tensors

Topics: Tensor representation and basis, dyadic product, trace, transpose, determinant, scalar product.

Lecture 3 (Aug 30): Tensor algebra and properties

Topics: Orthogonal tensors, change of basis, spectral decomposition, polar decomposition.

Lecture 4 (Sep 1): Cauchy stress tensor

Topics: Mass and force, Traction, Action & Reaction, Cauchy’s principle

Lecture 5 (Sep 6): Stress examples

Lecture 6 (Sep 8): Change of basis and eigen problem

Lecture 7 (Sep 13): Normal and shear stress

Lecture 8 (Sep 15): Mohr circle and failure

Lecture 9 (Sep 22): Tensor Calculus (div, grad curl)

Lecture 10 (Sep 27): Equilibrium Equations

Topic II: Kinematics and Strain

Lecture 11 (Sep 29): Deformation Map and Gradient

Lecture 12 (Oct 4): Analysis of local deformation

Lecture 13 (Oct 6): Cauchy-Green Strain Tensor

Lecture 14 (Oct 11): Infinitesimal strain

Lecture 15 (Oct 13): Motion and Material Derivative

Lecture 16 (Oct 18): Rates of deformation & Reynolds Transport Theorem

Topic IV: Balance laws

Lecture 17 (Oct 25): Balance laws in integral form

Lecture 18 (Oct 27): Local Eulerian balance laws

Lecture 19 (Nov 1): Continuum thermodynamics

Lecture 20 (Nov 3): Local Lagrangian balance laws

Topic V: Constitutive theory

Lecture 21 (Nov 8): Fourth-order tensors

Lecture 22 (Nov 10): Objectivity and Representation Theorem

Topic VI: Fluid Mechanics

Lecture 23 (Nov 15): Ideal fluids

Lecture 24 (Nov 17): Newtonian fluids

Lecture 25 (Nov 29): Stokes flow

Lecture 26 (Dec 1): Power-law creep

So Long, and Thanks for All the Fish!