Jackson School of Geosciences - University of Texas at Austin

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

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 Time: TTH 2:00 p.m.-3:30 p.m.
- Class Room: EPS 1.126
- Class Zoom: Zoom ID 921 0937 9742 - Class (password in email or on Canvas)

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]

- Piazza - Discussion board

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

- Topics: Introduction to the class, review of vectors, index notation
- Lecture: [pdf] [rec]
- Introduction to course
- Review of vectors
- Index notation

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

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

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

- Lecture: [pdf] [rec]
- Notes: Tensor Algebra Intro

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

- Lecture: [pdf] [rec]
- Notes: [Cauchy stress]

- Lecture: [pdf] [rec]
- Notes: Stress examples

- Lecture: [pdf] [rec]
- Notes: [Tensor Algebra II]

- Lecture: [pdf] [rec]
- Notes: Mohr circle
- Demos: [LiveScript], [pdf]

- Lecture: [pdf] [rec]
- Notes: [Rates] [Derivatives of tensor functions] [Reynaolds Transport Theorem]

- Topics: Integral balance laws in discrete and continuum systems, Introduction to continuum thermodynamics
- Lecture: [pdf] [rec]
- Notes: [pdf]

- Topics: Net working, Energy balance and entropy inequality
- Lecture: [pdf] [rec 1] [rec 2]
- Notes: [pdf]

- Topics: Mass and momentum balancs, first and second laws in Lagrangian form
- Lecture: [pdf] [rec]
- Notes: [pdf]

- Lecture: sorry no write up! [rec]
- Notes: [Constraints] [Ideal Fluids]