26 hours, optionally

1.Introduction to nonlinear mechanics Physical and geometrical nonlinearities Eulerian and Lagrangian meshes¨ 2.Strain measures (Green-Lagrange, Euler-Almansi, engineering, logarithmic), their behavior in large strain and large rotation Stress measures (Cauchy, 1. Piola-Kirchhoff, 2. Piola-Kirchhoff, Biot). Energeticaly conjugate stress and strain measures 3.Tangent stiffness matrix Material stiffness Geometrical stiffness Influence of nonlinear members of the strain tensor 4.Newton-Raphson method. Calculation of unbalanced forces 5.Modified Newton-Raphson method Postcritical analysis Deformation control Arc length method 6.Linear and nonlinear buckling Von Mises truss, snap through 7.Physical nonlinearity (supports, beams, concrete, subsoil) 8.Types of materials, introduction into constitutive material models Linear and nonlinear fracture mechanics. Fracture mechanical material parameters 9.Problem of strain localization, false sensitivity on the mesh Restriction of localization Crack band model Nonlocal continuum mechanics 10.Constitutive equations for concrete and other quasi-fragile materials Fracture-plastic model Mircroplane model 11.Influence of size to bearing capacity (size effect) Energetical and statistical causes Analysis of the influence of size on strength in tension in bending 12.Presentation of modeling by a software on nonlinear fracture mechanics 13.Presentation of modeling Examples of applications Mechanics of damage