This course provides 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. The 2005 edition was attended by 27
participants who arrived from 11 European countries.
Introduction: classification of models
for inelastic material behavior, notation, fundamentals of tensor
algebra, principles of incremental-iterative nonlinear analysis.
physical motivation, basic equations in one dimension, extension to
multiaxial stress, postulate of maximum plastic dissipation, associated
and nonassociated plastic flow, hardening and softening, stress-return
algorithms, algorithmic stiffness, multi-surface plasticity.
mechanics: physical motivation, basic equations in one
dimension, isotropic damage models, smeared crack models, anisotropic
damage models based on principle of energy equivalence, damage
deactivation due to crack closure, combination of damage and plasticity.
localization: physical aspects, structural size effect,
conditions of stability and uniqueness, discontinuous bifurcation,
localization analysis based on acoustic tensor, loss of ellipticity and
its mathematical and numerical consequences.
continuum models: classification of enriched continuum
theories, nonlocal formulations of the integral type, explicit and
implicit gradient formulations, continua with
microstructure, localization analysis, implementation aspects,
discontinuity models: fundamentals of fracture mechanics,
cohesive crack and cohesive zone models, finite elements with
discontinuities (embedded crack models, extended finite elements),
implementation aspects and examples. The slides used in the
presentation of this topic can be downloaded in PDF format.
The course is designed for graduate students
on 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 Stuttgart
(1998), Rheinisch-Westfälische Technische Hochschule in Aachen
(1999), Universität der Bundeswehr in Munich (2000),
Universitat Politècnica de Catalunya in Barcelona (2002) and
Technical University in Prague (2004 and 2005).
Prerequisites: fundamentals of elasticity and finite element
Registration on Monday, September 19, from 8:15-9:00.
Morning sessions 9:00-10:15 and 10:30-11:45.
Afternoon sessions 14:00-15:15 and 15:30-16:45 (i.e., 2-3:15pm