Digital Repository, Giornata IGF Forni di Sopra (UD) 2011

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Gradient elasticity theories and finite element implementations for static fracture
H. Askes

Last modified: 2011-02-25


Gradient elasticity theories are a powerful tool to describe the state of stress and strain around
sharp crack tips. With the appropriate format of field equations and boundary conditions, gradient elasticity can
be used to predict non-singular stresses and strains, which can aid in simplifying engineering interpretation and
the formulation of propagation criteria. The additional terms in the continuum equations are accompanied by
internal length scales that represent the microstructure, and these internal length scales may be used to interpret
fracture process zones or critical distances in fatigue theory. One of the difficulties of gradient elasticity
theories, and the main reason why they have not been disseminated widely in the engineering communities, is
that their finite element implementation is not straightforward. However, much progress has been made in
recent years, and in this paper a few relatively simple implementations will be shown.

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