GEO 325C/398C Continuum Mechanics

Jackson School of Geosciences - University of Texas at Austin

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Course in Fall 2021

Class room

Office hours

Mon 1:30-2pm and Wed 3-3:30pm [poll]: Zoom ID 921 0937 9742 (password in email or on Canvas)

Additional course websites:

Relevant textbooks

Topic I: Introduction to tensors

Lecture 1 (Aug 26): Introduction (zoom)

Lecture 2 (Aug 31): Tensor algebra I

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

Lecture 3 (Sep 2): Tensor algebra II

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

Lecture 4 (Sep 7): Tensor calculus I

Topics: Differentiation of tensor fields (div, grad, curl)

Lecture 5 (Sep 9): Tensor calculus II

Topis: Integral theorems (Gauss, Stokes), Derivatives of tensor functions

Topic II: Stress

Lecture 6 (Sep 14): Cauchy stress tensor

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

Lecture 7 (Sep 16): Equilibrium equations

Topics: Cauchy stress tensor, Eqbm equations, symmetry of stress tensor

Lecture 8 (Sep 21): Normal and shear stress

Topics: Normal and shear stress, principal stresses, simple states of stress

Lecture 9 (Sep 23): Mohr circle and failure

Topics: Mohr circle in 2D, shear failure, frictional sliding, simple states of stress

Topic III: Kinematics

Lecture 10 (Sep 28): Deformation

Lecture 11 (Sep 30): Cauchy-Green strain tensor

Lecture 12 (Oct 5): Interpretation of strain tensor

Lecture 13 (Oct 7): Infinitesimal strain

Lecture 14 (Oct 12): Motions

Lecture 15 (Oct 19): Rates

Topic IV: Balance laws

Lecture 16 (Oct 21): Balance laws in integral form

Lecture 17 (Oct 26): Local Eulerian balance laws

Lecture 18 (Oct 28): Continuum thermodynamics

Lecture 19 (Nov 2): Local Lagrangian balance laws

Topic V: Constitutive theory

Lecture 20 (Nov 4): Frame-indifference and objectivity

Lecture 21 (Nov 9): Isotropic tensor functions

Topic VI: Fluid Mechanics

Lecture 22 (Nov 11): Ideal fluids

Lecture 23 (Nov 16): Newtonian fluids

Lecture 24 (Nov 18): Fluids special topic: Power-law creep

Topic VI: Solid Mechanics

Lecture 25 (Nov 23): Elastic stress response

Lecture 26 (Nov 30): Hyperelastic solids

Lecture 27 (Dec 2): Linear elastic solids

So Long, and Thanks for All the Fish!