A classification of higher-order strain gradient models - linear analysis

The use of higher-order strain-gradient models in mechanics is studied. First, existing second-gradient models from the literature are investigated analytically. In general, two classes of second-order strain-gradient models can be distinguished: one class of models has a direct link with the underlying microstructure, but reveals instability for deformation patterns of a relatively short wave length, while the other class of models does not have a direct link with the microstructure, but stability is unconditionally guaranteed. To combine the advantageous properties of the two classes of second-gradient models, a new, fourth-order strain-gradient model, which is unconditionally stable, is derived from a discrete microstructure. The fourth-gradient model and the second-gradient models are compared under static and dynamic loading conditions. A numerical approach is followed, whereby the element-free Galerkin method is used. For the second-gradient model that has been derived from the microstructure, it is found that the model becomes unstable for a limited number of wave lengths, while in dynamics, instabilities are encountered for all shorter wave lengths. Contrarily, the second-gradient model without a direct link to the microstructure behaves in a stable manner, although physically unrealistic results are obtained in dynamics. The fourth-gradient model, with a microstructural basis, gives stable and realistic results in statics as well as in dynamics

New horizons in computer analysis of damage and fracture in quasi-brittle materials

Continuum approaches are reviewed which can properly model localised deformations that act as a precursor to final fracture in quasi-brittle materials. Next, one such higher-order damaging continuum model is combined with a stochastic approach to describe the heterogeneity in quasi-brittle materials

New horizons in computer analysis of damage and fracture in quasi-brittle materials

Continuum approaches are reviewed which can properly model localised deformations that act as a precursor to final fracture in quasi-brittle materials. Next, one such higher-order damaging continuum model is combined with a stochastic approach to describe the heterogeneity in quasi-brittle materials

A discrete model for cyclic mode I loading

AbstractThe cyclic behaviour of a double-edge notched specimen loaded in tension is studied. Cracks in the material are modelled by displacement discontinuities that can propagate during computation. Within these discontinuities, a cohesive zone model is used. The model assumes an additive split of the inelastic jump into a recoverable and an unrecoverable part. The influence of model parameters and discretisation is studied and the results have been compared with experimental data

Some future directions in computational failure mechanics

Continuum approaches are reviewed which can properly model localised deformations that act as a precursor to final fracture in quasi-brittle materials. Next, one such higher-order damaging continuum model is combined with a stochastic approach to describe the heterogeneity in quasi-brittle materials

An allgorithm for mesh rezoning with application to strain localization problems

This paper describes an algorithm for automatic rezoning of the finite element mesh, which can be used in adaptivity techniques where the initial topology is conserved. Difficulties like the definition of an adequate mesh density, its continued interpolation and the description of curved boundaries have been overcome successfully. The algorithm has been used in some strain localization problems. The output of a first analysis with a coarse, constant density mesh is used as an indicator to control the mesh spacing in a subsequent calculation, leading to an improved solution. The improvement of the solution upon remeshing is shown