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# Advanced course on Modeling of Localized Inelastic Deformation

### Theme

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 RILEM educational courses. In 2021 it attracted 31 participants from 10 European countries.
Independently of the course on Modeling of Localized Inelastic Deformation (LID2022), it is also possible to attend a course on OOFEM, which takes place at the same location on 12-15 September 2022. OOFEM is an object-oriented open-source software package for solid mechanics, with extensions to fluid mechanics and transport problems..

### Main topics

• Introduction: notation, fundamentals of tensor algebra, strain localization and size effect, basic types of material models, techniques of incremental-iterative nonlinear analysis.
• Elastoplasticity: physical motivation, basic equations in one dimension, extension to multiaxial stress, associated and nonassociated plastic flow, hardening and softening, tangent stiffness.
• Damage 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.
• Strain 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).
• Regularized continuum 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, application examples..

### Level

• The course is designed for graduate students at the doctoral level, but it can be equally useful to motivated master 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 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 element methods.
• sample chapter of the lecture notes is available for free downloading. Note that this excerpt is taken from a rather old version of the lecture notes. The material distributed at the course has been updated and extended. The complete set of lecture notes has almost 400 pages in a dense format.

### Schedule

• Registration on Monday, September 5, 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 discussion.

### Registration

• The registration fee of 750 EUR covers admission to lectures, a set of lecture notes and handouts, and refreshments during coffee breaks. All participants will receive a certificate of attendance.
• For preliminary registration, please send an email to Milan.Jirasek@fsv.cvut.cz. Kindly indicate your name, 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 your payment of the registration fee by bank transfer is received.
• If the registration is canceled before 10 August 2022, 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 handled 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 in Prague 6 - Dejvice, near the Dejvicka station of underground (metro) line 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, booking.com, airbnb, or similar servers. It is recommended to book a room as soon as possible, since the tourists are back and September is still the high season in Prague.
• Course participants usually get together for a lunch on Monday, a bowling evening on Tuesday or Wednesday and a dinner on Thursday (not included in the registration fee, but the prices are affordable and Czech beer is excellent).

### Venue

• The lectures will take place in room B367 of the Faculty of Civil Engineering, street address Thákurova 7, Prague 6.
• Click here for photographs showing the way from the Dejvicka metro station to the lecture room.

Location

#### Faculty of Civil Engineering

7 Thákurova
160 00 Prague, Czech Republic