List of topics

Introduction

Workflow : geometry with Gmsh, dolfin-convert, export Paraview

Linear problems

Elastostatics :

standard continuous galerkin

• 2D plane stress/strain
• orthotropic
• axisymmetric

Mixed methods

Approach of https://doi.org/10.1016/j.cma.2020.113381

discontinous galerkin : volumetric locking

mixed formulation using Hu-Washizu : volumetric locking

Problems with initial stresses : thermoelasticity

Elastodynamics

• modal analysis
• time integration Newmark scheme, theta (lumped mass matrix, efficient solving)

Poroelasticity

Mixing continuum and interfaces

• elastic interfaces/supports (beam on elastic foundation)

Linear Fracture Mechanics

• G-theta method to compute J-integral and stress intensity factors

Homogenization in elasticity

(treatment of rigid particles with Lagrange multipliers)

Linear Buckling

Cosserat

Strain gradient

Nonlinear problems

Hyperelasticity :

• compressible neo-hookean
• incompressible neo-hookean

Viscoelasticity

• Maxwell model
• Kelvin-Voigt model

Elasto-plasticity

• radial return for von Mises 2D
• 3D with locking
• limit analysis

Viscoplasticity

• yield stress fluids

Nonlinear problems with MFront

• elastoplastic plates with plane stress behaviour and/or additional dof
• implementation of Marc François concrete plasticity criterion

Contact

• resolution of normal contact with TAO
• contact with AL and penalization: membrane with rigid indenter
• impact dynamics of rigid indenter
• contact with multimesh between deformable bodies (Nitsche's method)

Damage

• phase field approach
• damage with viscous regularization

Von-Karman plates

Beams and Plates

Membrane

Shells

Robust flat-facet triangular shell finite element https://doi.org/10.1002/nme.6944

Love-Kirchhoff plates with DG

Reissner-Mindlin plates

• quads
• DG

Higher-order plate models (warping, Bending-Gradient)

Misc

Topology Optimization (undocumented example)

Linear Matching Method

Tips and Tricks