## Modeling of Localized Inelastic Deformation

taught by Milan Jirásek

in Prague, Czech Republic, on 15-19 September 2014

### 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. In 2014 it attracted 21 participants from 9 European countries. The course is one of the RILEM educational courses.

### Main topics

• Introduction: notation, fundamentals of tensor algebra, basic types of inelastic material behavior, principles of incremental-iterative nonlinear analysis.
• Elastoplasticity: 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 stiffness.
• Fracture 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.
• Damage 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.
• Strain 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).
• Regularized 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, application examples.
• Strong discontinuity models: cohesive crack and cohesive zone models, finite elements with incorporated discontinuities (embedded crack models, extended finite elements), implementation aspects and examples. A pdf file with the presentation can be downloaded from here

### 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), and Universitat Politècnica de Catalunya in Barcelona (2002). In its current format, the course has been taught in Prague every year since 2004.
• 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 about 300 pages in a dense format.

### Schedule

• Registration on Monday, September 15, from 8:15-9:00.
• 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 reserved for general discussion.

### Registration

• The registration fee of 550 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 sent by airmail, 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 15 August 2014, 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) at 3-4 EUR, or in nearby restaurants.
• The course will be given on the campus of the Czech Technical University in Prague 6 - Dejvice, near the terminal station Dejvicka of underground (metro) line A. The participants are advised to book their accommodation in Prague 6, or in a hotel 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. It is recommended to book it as soon as possible, since September is still the top season in Prague.
• The course participants usually get together for lunch on Monday and for dinner on Thursday (not included in the registration fee, but the price is 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 metro terminal Dejvicka to the lecture room.

Last update: 27 February 2014