Jackson School of Geosciences - University of Texas at Austin
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, Fall 2022
We will most closely follow:
Other useful books are:
Topics: Body and surface forces, Hydrostatic equilibrium, Isostacy
Topics: Application of hydrostatic force balance
Topics: Tensor representation and basis, dyadic product, trace, transpose.
Topics: Traction, Action & Reaction, Cauchy’s principle
Topics: Normal and shear stress, Projections, simpe stress states
Topics: Orthogonal tensors, Euler representation
Topics: Change in basis tensor, eigen problem, spectral decomposition, invariants
Topics: Principal stresses, constrained optimization
Topics: 2D and 3D Mohr circle
Topics: Coordinate systems, Fault normals, stress
Topics: Divergence, Gradient
Topics: Curl, Laplacian Divergence and Stokes theorems, Poisson’s equation for gravity
Topics: Equilibrum equations, symmetry of stress tensor, hydrostatic shapes, Figure of the Earth
Topics: Deformation map and gradient; change of material lines, volumes and areas