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Introduction to Computational Geomechanics

The Finite Element Method in Geotechnical engineering
Principle of Virtual Works.
A simple introduction to the Finite Element method.
Principle of Virtual Works for continuum: displacement approach.

Shape functions.
Linear and quadratic shape functions.
Discretization of Principle of Virtual Works.
Derivatives of the shape functions with respect to the cartesial coordinate system.
Compatibility matrix as a function of the derivatives of the shape functions.
Geometry discretization and jacobian matrix.
Numerical integrations

FE solver implementation for a truss structure.
Stiffness matrix implementation for a linear finite element in plane strain.
Stiffness matrix implementation for a quadratic finite element in plane strain.

The finite element method for nonlinear materials: the "structural" Newton loop.
An example of non-linear material: integration of the Drucker-Prager model.

Introduction to Finite Element modelling
Introduction to Abaqus FE code
Example: linaer elastic cantilever: geometry, material, boundart conditions and mesh.

The influence of the element type: volumetric locking.
Examples.