a b s t r a c tGradient-elasticity and more generally gradient-enhanced continuum models have been extensively developed since the beginning of the twentieth century. These models have shown the ability to account for the effect of the underlying material heterogeneity at the macroscopic scale of the continuum. Despite of a great theoretical interest, gradient-enhanced models are usually difficult to interpret physically and even more to identify experimentally. This paper proposes an attempt to validate and identify from experimental data, a gradient-elasticity model for a material with a periodic micro-structure. A set of dedicated experimental and numerical tools are developed for this purpose: first, the design of an experiment, then two-scale displacement field measurements by digital image correlation with dedicated post-processing techniques and finally a model updating technique. This paper ends up with the full set of first and second-order elastic constants of a gradient-elastic model which macroscopic kinematic has been validated by investigating the deformation of the unit cells at the microscopic scale.
We use matching asymptotic expansions to treat the antiplane elastic problem associated with a small defect located at the tip of a notch. In a first part, we develop the asymptotic method for any type of defect and present the sequential procedure which allows us to calculate the different terms of the inner and outer expansions at any order. This requires in particular separating in each term its singular part from its regular part. In a second part, the asymptotic method is applied to the case of a crack of variable length located at the tip of a given notch. We show that the first two nontrivial terms of the expansion of the energy release rate are sufficient to well approximate the dependence of the energy release rate on the crack length in the range of values of the length which are sufficient to treat the problem of nucleation. This problem is considered in the last part where we compare the nucleation and the propagation of a crack predicted by two different models: the classical Griffith law and the Francfort-Marigo law based on an energy minimization principle. Several numerical results illustrate the interest of the method.
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