This course provided an overview of modeling approaches used in the
mechanics of inelastic materials and structures, with special attention
to the objective description of highly localized deformation modes such
as cracks or shear bands. It was organized as one of the RILEM
educational courses. In 2019 it attracted 17
participants from 10 European countries.
Introduction: notation, fundamentals of
algebra, basic types of inelastic material behavior, principles of
incremental-iterative nonlinear analysis.
physical motivation, basic equations in one dimension, extension to
multiaxial stress, associated
and nonassociated plastic flow, hardening and softening, tangent
mechanics: physical motivation, basic equations in one
dimension, isotropic damage models, smeared crack models, brief comments on anisotropic
damage models, damage
deactivation due to crack closure, combination of damage and plasticity.
localization: physical aspects, structural size effect,
conditions of stability and uniqueness, discontinuous bifurcation,
incipient weak discontinuity,
localization analysis based on acoustic tensor, loss of ellipticity and
its mathematical and numerical consequences, classification of models
for localized inelastic behavior, mesh-adjusted softening modulus
(crack band approach).
models: classification of enriched continuum
theories, nonlocal formulations of the integral type (nonlocal damage and
nonlocal plasticity), explicit and
implicit gradient damage formulations, phase-field approaches,
localization analysis, implementation aspects,
The course is designed for graduate students at the doctoral
level, but it can be equally useful to motivated
students, post-doctoral researchers, or senior researchers who are not
specialists in this field. Similar courses were given by the lecturer
at the Swiss Federal Institute of Technology in Lausanne (1998), Czech
Technical University in Prague (1998), Universität
(1998), Rheinisch-Westfälische Technische Hochschule in Aachen
(1999), Universität der Bundeswehr in Munich (2000), and
Universitat Politècnica de Catalunya in Barcelona (2002). In its
current format, the course has been taught in Prague every year since
2004. It will be organized again in September 2020.