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 2018 it attracted 26 participants from 9 European countries, India and Australia. 

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.

• Prerequisites: fundamentals of elasticity, plasticity and finite element methods.