The Note presents the formulation of a class of two-scale damage models involving a micro-structural length. A homogenization method based on asymptotic developments is employed to deduce the macroscopic damage equations. The damage model completely results from energy-based micro-crack propagation laws, without supplementary phenomenological assumptions.
We show that the resulting two-scale model has the property of capturing micro-structural lengths. When damage evolves, the micro-structural length is given by the ratio of the surface density of energy dissipated during the micro-crack growth and the macroscopic damage energy release rate per unit volume of the material.
The use of fracture criteria based on resistance curves or power laws for sub-critical growth of micro-cracks leads to quasi-brittle and, respectively, time-dependent damage models.
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Cristian Dascalu 1
@article{CRMECA_2009__337_9-10_645_0, author = {Cristian Dascalu}, title = {A two-scale damage model with material length}, journal = {Comptes Rendus. M\'ecanique}, pages = {645--652}, publisher = {Elsevier}, volume = {337}, number = {9-10}, year = {2009}, doi = {10.1016/j.crme.2009.09.008}, language = {en}, }
Cristian Dascalu. A two-scale damage model with material length. Comptes Rendus. Mécanique, Volume 337 (2009) no. 9-10, pp. 645-652. doi : 10.1016/j.crme.2009.09.008. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2009.09.008/
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