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

Course Description

Continuum Mechanics is a new upper division undergraduate/beginning graduate course focussed on developing the foundations of solid and fluid mechanics and thermodynamics of continua, and their application to geophysical and geological models such as mantle convection, ice sheet flow, and geophysical fluid dynamics. The emphasis is on a rigorous quantitative three-dimensional description, beginning with tensor analysis, forces, and stresses, and kinematics, motion, and strain; moving to the basic balance (i.e. conservation) laws of mass, momentum, and energy as well as constitutive relations for fluid and solid media; and ending with the particularization of these laws and relations to the governing equations of oceanography, seismology, glaciology, and geodynamics.

Previous versions of this course: Fall 2021

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

opics: 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!