GEO 325C/398C Continuum Mechanics

Jackson School of Geosciences - University of Texas at Austin

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Course in Fall 2025

Class room

Class Time: TTH 9:30 am-11:00 am
Class Room: EPS 1.126
Class unique: 28965/29340

Office hours

[Office hours poll]
Time: MW 9-10am
Location: JGB 4.216B (Geophysics Dojo)

Additional course websites:

Piazza - Discussion board

Relevant textbooks

We will most closely follow:

A first course in continuum mechanics, by Gonzalez and Stewart
Continuum Mechanics in the Earth Sciences, by Newman

Other useful books are:

Rheology of the Earth, by Ranalli
Physics of continous matter, by Lautrup
Introduction to continuum mechanics, by Gurtin
Nonlinear solid mechanics, by Holzapfel

Topic I: Review

Lecture 1 (Aug 26): Vector review and index notation

Topics: Introduction to the class, review of vectors, index notation
Slides: Introduction to course
Notes: Vectors and Index Notation

Lecture 2 (Aug 28): Linear momentum and force

Topics: Newton’s laws, Body and surface forces, Hydrostatic equilibrium, Isostacy

Notes: Force Notes, Isostacy

Lecture 3 (Sep 2): Angular momentum and torque

Topics: Angular momentum, torque, moment, tipping

Lecture: Part 1 [pdf] [rec], Part 2 [pdf] [rec]
Notes: Triple vector product, Torque, Toppling Icebergs, Stability
Movie: Ice bergs toppling over

Topic II: Tensors and Stress

Lecture 4 (Sep 4): Tensor algebra

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

Lecture: [pdf], [rec]
Notes: Tensor Intro

Lecture 5 (Sep 9): Cauchy stress tensor

Topics: Traction, Action & Reaction, Cauchy’s principle

Notes: Cauchy stress tensor

Lecture 6 (Sep 11): Rotations

Topics: Orthogonal tensors, Euler representation, Fault normals

Notes: Rotations, Fault normals

Lecture 7 (Sep 16): Prinipal stresses

Topics: Normal and shear stress, principal stresses

Notes: Principal stresses, Anderson’s Theory of Faulting

Lecture 8 (Sep 18): Change in basis and spectral decomposition

Topics: Change in basis tensor, eigen problem

Lecture: pdf rec
Notes: Change of basis, Nankai Fault Stress Example [script] [pdf]

Lecture 9 (Sep 23): Mohr circle

Topics: Mohr circle, maximum shear stress, failure

Notes: Mohr circle,

Lecture 10 (Sep 25): Divergence and gradient

Topics: Gradient, divergence, Laplacian, Poisson’s equation for gravity

Notes: Div and Grad

Lecture 11 (Sep 30): Integral theorems

Topics: Curl, Divergence and Stokes theorems, Derivatives of tensor functions

Notes: Curl, Gauss, Stokes

Lecture 12 (Oct 2): Equilibrium Equations

Topics: Equilibrum equations, symmetry of stress tensor, hydrostatic shapes, Figure of the Earth

Notes: Mechanical Equilibrium, Figure of the Earth

Midterm Exam (Oct 7):

Topic III: Kinematics and Strain

Lecture 13 (Oct 9): Deformation Map and Gradient

Topics: Deformation map and gradient; change of material lines, volumes and areas

Notes: Deformation Map and Gradient

Topic IV: Balance Laws and Constitutive Theory

Lecture 19 (Oct 30): Eulerian balance laws

Notes: Balance laws

Lecture 20 (Nov 4): Energy balance - heating

Notes: Energy balance with net heating

Lecture 21 (Nov 6): Energy balance - working

Notes: Energy balance with net working

Lecture 22 (Nov 11): Constitutive laws

Notes: Objectivity, Galilean transformations,Representation Theorem

Topic V: Applications

Lecture 23 (Nov 13): Navier Stokes

Notes: Navier-Stokes

Lecture 24 (Nov 18): Boundary layers

Notes: Viscous boundary layer and energy dissipation

Lecture 25 (Nov 20): Creeping flow

Notes: Kinetic energy, Stokes equation, Power-law creep