GEO 325C/398C Continuum Mechanics

Jackson School of Geosciences - University of Texas at Austin

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Course in Fall 2024

Class room

Office hours (TBD)

Additional course websites:

Relevant textbooks

We will most closely follow:

Other useful books are:

Topic I: Review

Lecture 1 (Aug 27): Vector review and index notation

Lecture 2 (Aug 29): Linear momentum and force

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

Lecture 3 (Sep 3): Angular momentum and torque

Topics: Angular momentum, torque, moment, tipping

Topic II: Tensors and Stress

Lecture 4 (Sep 5): Tensor algebra

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

Lecture 5 (Sep 10): Cauchy stress tensor

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

Lecture 6 (Sep 12): Rotations

Topics: Orthogonal tensors, Euler representation, Fault normals

Lecture 7 (Sep 17): Change in basis and spectral decomposition

Topics: Change in basis tensor, eigen problem, spectral decomposition, invariants

Lecture 8 (Sep 19): Prinipal stresses

Topics: Normal and shear stress, principal stresses

Lecture 9 (Sep 24): Mohr circle

Topics: Mohr circle, maximum shear stress, failure

Lecture 10 (Sep 26): Divergence and gradient

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

Lecture 11 (Oct 1): Integral theorems

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

Lecture 12 (Oct 3): Equilibrium Equations

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

Midterm Exam (Oct 8):

Topic III: Kinematics and Strain

Lecture 13: Deformation Map and Gradient

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

Lecture 14: Cauchy-Green Strain Tensor

Lecture 15: Interpretation of the Strain Tensor

Lecture 16: Infinitesimal Strain Tensor

Lecture 17: Motion and Material Derivative

Lecture 18: Rates of deformation & Reynolds Transport Theorem

Topic IV: Balance Laws and Constitutive Theory

Lecture 19: Eulerian balance laws

Lecture 20: Continuum Thermodynamics

Lecture 21: Lagrangian balance laws

Lecture 22: Constitutive laws I - Objectivity and Galilean transformations

Lecture 23: Constitutive laws II - Representation theorem and constraints

Topic V: Applications

Lecture 24: Fluids I - Navier Stokes

Lecture 25: Fluids II - Creeping Flows

Lecture 26: Power-law creep