Abstract:
Classical theories of elastoplasticity lack an inherent length scale and are unable adequately to
capture size effects, and more generally effects at the micron level. In addition, computational
approaches in the presence of softening behaviour lead to solutions that are mesh-dependent.
These shortcomings have led to the development of models such as strain gradient theories which
are able to model phenomena at the meso-scale, and for which computational approximations
exhibit the desirable properties of accuracy and convergence.
The purpose of this presentation is to present an overview of the key mathematical and computational
issues arising in the treatment of problems involving gradient plasticity. The problems
are formulated as variational inequalities, and the relationship between the well-posedness of
these models and the anticipated physical behaviour is explored. Finite element approximations
based on a Discontinuous Galerkin formulation are developed and analysed, and properties of
the associated predictor-corrector solution algorithms are presented. Finally, the theoretical
results obtained are illustrated through a selection of numerical examples.
This seminar is easily accessible to persons with disabilities. For more information or for assistance, please contact the Mathematics Department at 743-3500.