Jackson School of Geosciences - University of Texas at Austin

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

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

- Piazza - Discussion board

- Introduction to continuum mechanics, by Gurtin
- A first course in continuum mechanics, by Gonzalez and Stewart
- Nonlinear solid mechanics, by Holzapfel
- Physics of continous matter, by Lautrup
- Rheology of the Earth, by Ranalli

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

- Lecture: [pdf] [rec 1] [rec 2 (extra)]
- Tensor algebra I

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

- Lecture: [pdf] [rec]
- Tensor algebra II

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

- Lecture: [pdf] [rec]
- Tensor calculus I

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

- Lecture: [pdf] [rec]
- Tensor calculus II

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

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

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

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

- Lecture: [pdf] [rec]
- Notes: Mohr circle, Simple stress states

- Topics: Local analysis of deformation, right Cauchy-Green strain tensor
- Lecture: [pdf] [rec]
- Notes: [pdf]

- Topics: Other strain tensors, Cauchy-Green strain relations, Volume changes
- Lecture: [pdf] [rec]
- Notes: [pdf]

- Topics: Changes in area, linearization of kinematic quantities, infintesimal strain tensor
- Lecture: [pdf] [rec]
- Notes: [pdf]

- Topics: Motions, Material spatial fields, Material and spatial time derivatives
- Lecture: [pdf] [rec]
- Notes: [pdf]

- Topics: Rate of strain & spin tensors, Reynolds transport theorem
- Lecture: [pdf] [rec]
- Notes: [Rates of deformation] [Reynolds transport Thm]

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

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

- Topics: Isotropic functions, 4-th order tensors, material constraints
- Lecture: [pdf] [rec]
- Notes: [Isotropic functions] [4th order tensors] [Material constraints]

- Topic: Frame indifference of ideal fluid model, Bernoulli, Vorticity equation
- Lecture: [pdf] [rec]
- Notes: [pfd]

- Topics: Newtonian stress, Navier-Stokes Equation, Stokes Equation, Kinetic energy
- Lecture: [pdf], sorry forgot to reccord!
- Notes: [pdf]

- Topics: Elastic Solid, stress response function, isotropic material
- Lecture: [pdf] [rec]
- Notes: [pdf]

- Topis: Strain enegy density, Mechanic energy inequality, common models
- Lecture: [pdf] [rec]
- Notes: [pdf]