Governing Equations#
This chapter presents the solution schemes we use for solving variations of the elasticity equation using the finite-element method. In all of our derivations, we use the notation described in Mathematical notation.
Symbol |
Description |
|---|---|
\(\vec{a}\) |
Vector field a |
\(\mathbf{a}\) |
Second order tensor field a |
\(\vec{u}\) |
Displacement vector field |
\(\vec{v}\) |
Velocity vector field |
\(\vec{{d}}\) |
Fault slip vector field |
\(\vec{f}\) |
Body force vector field |
\(\vec{\tau}\) |
Traction vector field |
\(\mathbf{\sigma}\) |
Stress tensor field |
\(\vec{n}\) |
Normal vector field |
\(\rho\) |
Mass density scalar field |
- Derivation of Elasticity Equation
- Finite-Element Formulation with PETSc
- Elasticity with Infinitesimal Strain and No Faults
- Elasticity with Infinitesimal Strain and Prescribed Slip on Faults
- Incompressible Isotropic Elasticity with Infinitesimal Strain (Bathe)
- Poroelasticity with Infinitesimal Strain and No Faults