in Prague, Czech Republic, on 22-26
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 2008, the course was attended by 26
participants from 12 European countries.
Introduction: notation, fundamentals of
algebra, basic types of inelastic material behavior, principles of
incremental-iterative nonlinear analysis.
physical motivation, basic equations in one dimension, extension to
multiaxial stress, postulate of maximum plastic dissipation, associated
and nonassociated plastic flow, hardening and softening.
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
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.
localization: physical aspects, structural size effect,
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.
continuum models: classification of enriched continuum
theories, nonlocal formulations of the integral type, explicit and
implicit gradient formulations, localization analysis, implementation
discontinuity models: cohesive crack and cohesive zone
models, finite elements with
discontinuities (embedded crack models, extended finite elements),
implementation aspects and examples.