MAIN TOPICS

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

SUGGESTED READING

• M. Jirásek: Plasticity, damage and fracture, fragments of lecture notes, November 2002.
• M. Jirásek: Objective modeling of strain localization, Revue française de génie civil, 6 (2002), 1119-1132.
• M. Jirásek: Embedded crack models for concrete fracture, in Computational Modelling of Concrete Structures (EURO-C), ed. by R. de Borst, N. Bicanic, H. Mang, and G. Meschke, Balkema, Rotterdam, 291-300.
• M. Jirásek: Numerical modeling of strong discontinuities, Revue française de génie civil, 6 (2002), 1133-1146.
• S. Rolshoven and M. Jirásek: Nonlocal formulations of softening plasticity, in Proceedings of the Fifth World Congress on Computational Mechanics (WCCM V), July 7-12, 2002, Vienna, Austria, http://wccm.tuwien.ac.at.
• M. Jirásek and B. Patzák: Nonlocal formulations for softening materials, Chapter 5 in Computational Structures Technology, ed. by B. H. V. Topping and Z. Bittnar, Saxe-Coburg Publications, Stirling, Scotland, 123-152.

• M. Jirásek and Z.P. Bazant: Inelastic Analysis of Structures, John Wiley and Sons, Chichester, 2002.