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. It is one of the RILEM
educational courses. In 2015 it attracted 22
participants from 6 European countries. The course will be organized again in September 2016.
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, postulate of maximum plastic dissipation, associated
and nonassociated plastic flow, hardening and softening, tangent
mechanics: stress concentration around defects,
asymptotic fields in the vicinity of a crack tip, local and global
criteria for crack propagation, fracture toughness and fracture energy,
nonlinear process zone, cohesive crack models.
mechanics: physical motivation, basic equations in one
dimension, isotropic damage models, smeared crack models, anisotropic
damage models based on principles of strain equivalence and 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,
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, explicit and
implicit gradient formulations, continua with
microstructure, localization analysis, implementation aspects,
discontinuity models: cohesive crack and cohesive zone
models, finite elements with
discontinuities (embedded crack models, extended finite elements),
implementation aspects and examples.
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
Prerequisites: fundamentals of elasticity, plasticity and finite
A sample chapter of the lecture
notes is available for
free downloading. Note that this excerpt is taken from a rather old
of the lecture notes. The material distributed at the course has been
updated and extended. The complete set of lecture notes has about 300
pages in a dense format.