GEO 325C/398C Continuum Mechanics

Jackson School of Geosciences - University of Texas at Austin

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Course in Fall 2023

Class room

Office hours (TBD)

Additional course websites:

Relevant textbooks

We will most closely follow:

Other useful books are:

Topic I: Tensors and Stress

Lecture 1 (Aug 22): Introduction and Review

Lecture 2 (Aug 24): Continuum Mass and Force Concepts

Topics: Body and surface forces, Hydrostatic equilibrium, Isostacy

Lecture 3 (Aug 29): Isostacy and index notation

Topics: Application of hydrostatic force balance

Lecture 4 (Aug 31): Introduction to Tensors

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

Lecture 5: Cauchy stress tensor

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

Lecture 6: Stress examples

Topics: Normal and shear stress, Projections, simpe stress states

Lecture 7: Rotations

Topics: Orthogonal tensors, Euler representation

Lecture 8: Change in basis and spectral decomposition

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

Lecture 9: Extremal stress values

Topics: Principal stresses, constrained optimization

Lecture 10: Mohr circle and failure

Topics: 2D and 3D Mohr circle

Lecture 11: Computing fault stresses

Topics: Coordinate systems, Fault normals, stress

Lecture 12: Gradient and Divergence

Topics: Divergence, Gradient

Lecture 13: Integral theorems

Topics: Curl, Laplacian Divergence and Stokes theorems, Poisson’s equation for gravity

Lecture 14: Equilibrium Equations

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

Topic II: Kinematics and Strain

Lecture 15: Deformation Map and Gradient

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

Lecture 16: Analysis of local deformation

Lecture 17: Cauchy-Green Strain Tensor

Lecture 18: Infinitesimal strain

Lecture 19: Motion and Material Derivative

Lecture 20: Rates of deformation & Reynolds Transport Theorem

Topic III: Balance Laws and Constitutive Theory

Lecture 21: Local Eulerian balance laws

Lecture 22: Energy balance

Lecture 23: Constitutive Theory: Objectivity

Lecture 24: Constitutive Theory: Representation Theorem

Topic IV: Applications

Lecture 25: Ideal fluids

Lecture 26: Newtonian fluids

Lecture 27: Stokes flow

Lecture 28: Power-law creep

So Long, and Thanks for All the Fish