Course Overview
Starting from 2025, this traditional course will be taught in a new format, namely in two parts that can be attended independently:
- Part I: Modeling of Inelastic Deformation (Thu-Sat, 4–6 September)
- Part II: Objective Modeling of Localized Failure (Mon-Wed, 8–10 September)
The first part provides an overview of modeling approaches used in the mechanics of inelastic materials and structures, in particular in plasticity and damage mechanics, with brief comments on fracture mechanics. The second part focuses on the objective description of highly localized deformation modes such as cracks or shear bands, using regularized models (e.g., nonlocal, gradient-enriched, phase-field, micromorphic). The whole event is organized as one of the RILEM educational courses.
Course History
Similar courses were given by Milan Jirásek 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 full format, the course has been taught in Prague every year since 2004 (with the exception of the pandemic year 2020).
Main Topics
- Part I
- Introduction: notation, fundamentals of tensor algebra, strain localization and size effect, basic types of material models, techniques of incremental-iterative nonlinear finite element analysis.
- Elastoplasticity: physical motivation, basic equations in one dimension, extension to multiaxial stress, associated and nonassociated plastic flow, hardening and softening, tangent stiffness, computational aspects.
- Fracture mechanics: brief introduction, crack propagation criteria, linear fracture mechanics, nonlinear process zone and cohesive crack models.
- Damage mechanics: physical motivation, basic equations in one dimension, isotropic damage models, brief comments on anisotropic damage models, damage deactivation due to crack closure, combination of damage and plasticity, smeared crack models.
- Strain localization I: localization in uniaxial setting, spurious mesh sensitivity, crack band approach (mesh-adjusted softening modulus).
- Part II
- Strain localization II: examples of localized failure, onset of localization - incipient weak discontinuity, localization analysis based on acoustic tensor, localization properties of damage and plasticity models, loss of ellipticity and its mathematical and numerical consequences, classification of models for localized inelastic behavior.
- 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, calibration and parameter identification, numerical aspects, implementation, application examples.
Target Audience
The course is designed for graduate students at the doctoral level, but it can be equally useful to motivated master students, post-doctoral researchers, professionals, or senior researchers who are not specialists in this field.
- Prerequisites for Part I: fundamentals of elasticity, plasticity and finite element methods.
- Prerequisites for Part II: basic understanding of plasticity, fracture and damage mechanics.
Schedule
- Morning sessions: 09:00–10:15 and 10:45–12:00
- Afternoon sessions: 14:00–15:15 and 15:45–17:00
Registration
- Course fee: EUR 500 for one part · EUR 900 for both, includes lecture notes (400 pages) and coffee breaks.
- Email Milan.Jirasek@cvut.cz for preliminary registration.
- 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. The registration becomes confirmed when your payment of the registration fee by bank transfer is received.
- If a registration is canceled before 10 August 2025, 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.
Venue
- The lectures will take place in a classroom at the Faculty of Civil Engineering, street address Thákurova 7, Prague 6.
- The participants are advised to book their accommodation in Prague 6, or in another district close to a metro station (preferably on line A).
- Course participants usually get together for lunch on the first day of each part (Thursday and Monday). A bowling event will be proposed on Friday and a dinner on Tuesday (not included in the registration fee, but the prices are affordable and Czech beer is excellent).
Gallery
City of Prague with its bridges, seen from Letná Park
Participants of LID 2024 on the last day of the course