Multiscale analysis of brittle failure in heterogeneous materials

E Eid, R Seghir, J Réthoré - Journal of the Mechanics and Physics of Solids, 2021 - Elsevier
Journal of the Mechanics and Physics of Solids, 2021Elsevier
This paper presents a versatile model-free approach for linking the damage in highly
heterogeneous materials at multiple scales. The proposed scheme evolves from phase-field
modelling at the microscopic scale to simulate brittle failure, towards the estimation of the
effective elastic, toughness and strength properties of the material at the mesoscopic scale,
via a model-free coarse-graining technique. On one side, it's shown that, in comparison with
the classical homogenisation approaches, the considered upscaling method:(i) requires no …
Abstract
This paper presents a versatile model-free approach for linking the damage in highly heterogeneous materials at multiple scales. The proposed scheme evolves from phase-field modelling at the microscopic scale to simulate brittle failure, towards the estimation of the effective elastic, toughness and strength properties of the material at the mesoscopic scale, via a model-free coarse-graining technique. On one side, it’s shown that, in comparison with the classical homogenisation approaches, the considered upscaling method: (i) requires no RVE (representative volume element), (ii) can be applied when the statistical homogeneity of the material ceases to exist and (iii) when sharp localisations are present. On the other, (iv) the quasi-brittle behaviour of the material is justified without any assumption on the model at the mesoscopic scale. Most prominently this paper shows that (v) the consideration of an effective homogeneous continuum to substitute a microscopically heterogeneous one is dictated by the use of a much larger regularisation parameter than what has been classically established.
Elsevier
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