Basic of non-linear finite element analysis - Heat transfer problem - Incremental-iterative approach - Incremental procedure - Simple non-linear problem - Stress update algorithm - Hardening material - Delta epsilon - Rate dependent - Selective reduced integration - Constitutive equation - Stress update algorithms - Continuum mechanics - Mapping function - Transformation of a surface - Projection tensor - Kirchhoff stress measure - Material derivative - Yield surface - Gateaux derivative - Internal energy - Stress measures and Strain measures - Frame indifferent quantities - Constitutive equations - Hyperelastic case - Anisotropic and Isotropic materials - Strain energy function - Equilibrium equation - Lagrangian formulation - Geometric stiffness term