2021/11/04 by Matteo Negri, Negri, Matteo
Engineering · Materials Science · #Analysis of PDEs (math.AP) #Composite Material Mechanics #Corrosion Behavior and Inhibition #FOS: Mathematics #Mechanical Behavior of Composites
paper · pdf · doi:10.48550/arxiv.2111.02761
openalex publication_date 2021/11/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a periodic, linear elastic laminate with a brittle crack, evolving along a prescribed path according to Griffith's criterion. We study the homogenized limit of this evolution, as the size of the layers vanishes. The limit evolution is governed again by Griffith's criterion, in terms of the energy release (of the homogenized elastic energy) and an effective toughness, which in general differs from the weak* limit of the periodic toughness. We provide a variational characterization of the effective toughness and, by the energy identity, we link the toughening effect (in the limit) to the micro-instabilities of the evolution (in the periodic laminate). Finally, we provide a couple of explicit calculations of the effective toughness in the anti-plane setting, showing in particular an example of toughening by elastic contrast.