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 2017 it attracted 16 participants from 8 European countries and India. 

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, 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: physical aspects, structural size effect, 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 damage and plasticity formulations, variational damage models and phase-field approaches, micromorphic damage models, localization analysis, implementation aspects, application examples.
• Strong discontinuity models: brief introduction to finite elements with embedded discontinuities and to extended finite elements.