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Advanced course on Modeling of Localized Inelastic Deformation


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 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.

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.


  • 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 more than 300 pages in a dense format.


From Monday 6 September 2021
to Friday 10 September 2021


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