Continuum Mechanics in Rock
- Stress definition and relationships in isotropic and non-isotropic three dimensional elastic media, convention and definitions
- State of stress, Stress tensor and deviatoric stress tensor, Projection of stress components on a surface
- Stress balance equations, principal stresses, Invariant stress tensor, and Mohre circle
- Maximum shear stresses and octahedral stresses
- Deformation in Lagrangian and Eulerian coordinates
- Strain and displacement definition, conventions, Linear and nonlinear relationships and tensors, Strain-Displacement compatibility equations
- Mi-term Exam
- Stress-strain relationships in non-isotropic and isotropic elastic environments, elastic strain energy
- Linear elasticity and generalized hook law
- Linear elastic relationships in Anisotropic and Isotropic materials
- Problems solution of Rock Mechanics based on the linear elasticity
Solving 1-D and 2-D problems, plane strain, plate stress
- Elasticity equations based on displacement components, Navier equations, and stress, Beltrami-Michel equations
- Stress functions, Airy stress functions, Problem solving in geomechanics using Airy stress functions
- Perfect elastic-plastic behavior of solids, typical stress-strain curve of a homogeneous isotropic material under tension in isotherm conditions
- Tresca, Von Mises, Mohr-Coulomb and Draker-Prager Criteria, Yield surface function and Floe rule
- Solution of some applied problems in rock mechanics based on the non linear plastic criteria