## Modeling of Localized Inelastic Deformation

taught by Milan Jirásek

in Prague, Czech Republic, on 24-28 September 2007

### 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 2007 it was attended by 18 participants from 11 different countries.

### 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, stress-return algorithms, algorithmic stiffness, multi-surface plasticity.
• 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, localization analysis based on acoustic tensor, 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 formulations, continua with microstructure, localization analysis, implementation aspects, application examples.
• 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.
• Strong discontinuity models: cohesive crack and cohesive zone models, finite elements with incorporated discontinuities (embedded crack models, extended finite elements), implementation aspects and examples.

Last update: 30 November 2007