Advanced course on Modeling of Localized Inelastic Deformation taught by Milan Jirásek in Prague, Czech Republic, 2-6 September 2024

Theme

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, numerical aspects, implementation, application examples.