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 organized as one of the
educational courses. In 2019 it attracted 17 participants from 10 European countries.
Due to the covid pandemic, the course was not held in 2020. However, the situation in Czechia
has greatly improved and the 2021 edition of the course can take place in safe conditions.
Independently of the course on Modeling of Localized Inelastic Deformation (LID2021), it is also possible to attend a course on OOFEM,
which takes place at the same location on 13-15 September 2021.
OOFEM is an object-oriented open-source software package for solid mechanics,
with extensions to
fluid mechanics and transport problems.
Introduction: notation, fundamentals of
algebra, strain localization and size effect, basic types of material models, techniques 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: examples of localized failure,
onset of localization - 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 damage and plasticity formulations, variational damage models
and phase-field approaches,
micromorphic damage models, 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),
Universitat Politècnica de Catalunya in Barcelona (2002), and Università degli Studi di Palermo (2019). In its
current format, the course has been taught in Prague every year since
2004 (with the exception of the pandemic year 2020).
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 more than 300
pages in a dense format.
Registration on Monday, September 6, from 8:40-9:00.
Morning sessions 9:00-10:15 and 10:45-12:00.
Afternoon sessions 14:00-15:15 and 15:45-17:00.
The last session on Friday afternoon will be devoted to general
The registration fee of 660 EUR covers admission to lectures, a
notes and handouts, and refreshments during coffee breaks. All
receive a certificate of attendance.
For preliminary registration, please send an email to Milan.Jirasek@fsv.cvut.cz.
affiliation (university or company), VAT number of the institution to
which the invoice should be addressed, postal address and
email address. Please specify whether you need a printed invoice
signed by hand, or whether an electronic invoice in a PDF file
sent by e-mail is sufficient. The registration becomes confirmed when
of the registration fee by bank transfer is received.
If the registration is canceled before 10 August 2021, the
registration fee will be refunded after deduction of bank processing
fees. After this date, no refunds are possible, but you can transfer
your registration to a colleague from the same institute or company, or
use it next year.
The course capacity is limited to 30 participants. The
applications will be treated on the first-come-first-served basis.
Meals and accommodation
Lunches are available in the university restaurant (mensa) or in nearby restaurants.
The course will be given on the campus of the Czech Technical University
6 - Dejvice, near the Dejvicka station of underground (metro)
A. The participants are advised to book their
accommodation in Prague 6, or in another district close to any metro station.
Prague offers a wide range of
facilities from student hostels to luxury hotels. You will certainly
find suitable accommodation using the TripAdvisor,
or similar servers. It is recommended
to book a room as soon as possible, since the demand may grow.
Course participants usually get together for lunch on Monday,
bowling on Tuesday or Wednesday
and dinner on Thursday (not included in the registration fee, but
the prices are affordable and Czech
The lectures will take place in room B367 of the Faculty of
Civil Engineering, street address Thákurova
Click here for photographs showing
way from the metro terminal Dejvicka to the lecture room.