Numerical tours of continuum mechanics using FEniCS
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Nonlinear problems in solid mechanics
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Contents:
Linear viscoelasticity
Constitutive evolution equations
Problem position
Time discretization and formulation of the variational problem
Solutions of elementary tests
Relaxation and creep tests for a Maxwell model
Relaxation and creep tests for a Kelvin-Voigt model
Hertzian contact with a rigid indenter using a penalty approach
Contact problem formulation and penalty approach
Implementation
References
Elasto-plastic analysis of a 2D von Mises material
Introduction
Problem position
Constitutive relation update
Global problem and Newton-Raphson procedure
Post-processing
References
Elasto-plastic analysis implemented using the
MFront
code generator
Introduction
Prerequisites
Problem position
Material constitutive law definition using
MFront
Global problem and Newton-Raphson procedure
Results and future works
References
Cohesive zone modelling of debonding and bulk fracture
Traction-separation law
Nonlinear resolution
FEniCS implementation
References
Table Of Contents
Introduction
What is it about ?
Citing and license
How do I get started ?
About the author
Linear problems in solid mechanics
2D linear elasticity
Orthotropic linear elasticity
Axisymmetric formulation for elastic structures of revolution
Linear thermoelasticity (weak coupling)
Thermo-elastic evolution problem (full coupling)
Modal analysis of an elastic structure
Time-integration of elastodynamics equation
Axial, bending and shear stiffnesses of generic beam cross-sections
Homogenization of heterogeneous materials
Periodic homogenization of linear elastic materials
Eigenvalue problems in solid mechanics
Modal analysis of an elastic structure
Linear Buckling Analysis of a 3D solid
Nonlinear problems in solid mechanics
Linear viscoelasticity
Hertzian contact with a rigid indenter using a penalty approach
Elasto-plastic analysis of a 2D von Mises material
Elasto-plastic analysis implemented using the
MFront
code generator
Cohesive zone modelling of debonding and bulk fracture
Documented demos coupling FEniCS with MFront
Stationnary non-linear heat transfer
Stationnary non-linear heat transfer: 3D problem and performance comparisons
Transient heat equation with phase change
Monolithic transient thermo-elasticity
Small-strain von Mises elastoplasticity
Finite-strain elastoplasticity within the logarithmic strain framework
Multiphase model for fiber-reinforced materials
Phase-field approach to brittle fracture
Beams
Eulerian buckling of a beam
Elastic 3D beam structures
Nonlinear beam model in finite rotations
Plates
Reissner-Mindlin plate with Quadrilaterals
Reissner-Mindlin plate with a Discontinuous-Galerkin approach
Locking-free Reissner-Mindlin plate with Crouzeix-Raviart interpolation
Shells
Linear shell model
Generating a shell model for a shallow arch I-beam with the
Gmsh
Python API
Topology optimization of structures
Topology optimization using the SIMP method
Tips and Tricks
Lumping a mass matrix
Computing consistent reaction forces
Efficient projection on DG or Quadrature spaces
Useful packages
FEniCS add-ons
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