ADVANCED SOLID MECHANICS

General formulation of the finite element method and application to solid mechanics in statics field (weighted residual method, variational method, Bubnov-Galerkin method, principle of virtual work, discretization in space, isoparametric finite elements).

Finite element method for non-linear problems (linearization, Newton's method, quasi-Newton and modified Newton).

Linear and Non-linear trusses and beams: deformation - equilibrium - tangent stiffness matrix - use of shape functions - assembling - total or lagrangian formulation.
Euler-Bernoulli beam.

Elasto-plastic solids: elastic solids - general theory of plasticity - return mapping algorithm - models for granular materials (finite elasto-plasticity).

Deformation and equilibrium of solids: deformation - non-linear deformation - strain decomposition - virtual work and stresses (Piola-Kirchhoff, Cauchy, stress rates) - total and updated lagrangian formulation.

Computational Contact Mechanics: - General formulation - Penalty method - Lagrange multiplier method.

Techniques of three dimensional modeling.