One-week course on


taught by

Milan Jirásek
Laboratory of Structural and Continuum Mechanics
Department of Civil Engineering
School of Architecture, Civil and Environmental Engineering
Swiss Federal Institute of Technology at Lausanne

and organized by

Graduate Studies and Research in Civil Engineering
School of Civil Engineering in Barcelona (ETSECCPB)
Technical University of Catalonia (UPC)

Barcelona, 18-22 November 2002


  1. Introduction: general overview of material models and constitutive frameworks, phenomenon of localization (examples)
  2. Classical softening continuum and its deficiencies (ill-posedness of the boundary value problem, pathological mesh sensitivity)
  3. Localization analysis, acoustic tensor
  4. Models with strong discontinuities (discrete cracks or shear lines), interface elements, elements with embedded discontinuities, extended finite elements
  5. Models with weak discontinuities (crack bands or shear bands), mesh-dependent adjustment of the softening parameters, elements with embedded localization bands
  6. Localization limiters: basic ideas, classification
  7. Integral-type nonlocal damage and plasticity
  8. Models with gradients of internal variables, strain-gradient theories, micropolar theories


The participants are also advised to have a look at the following book (in particular Chapters 15, 20-23 and 26):

Last update: 28 November 2002