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Material instabilities for architected materials

2 November 2022
4:00 pm
San Francesco Complex - classroom 1

Shear bands are local instabilities, ubiquitously observed in ductile materials to strongly affect their failure. Therefore, modelling of shear band formation and growth provides a fundamental understanding of the intimate behaviour of failure and can be used in the design of materials displaying superior mechanical properties.
The perturbative approach to shear bands will be introduced and applied in particular to the case in which a dispersion of thin rigid inclusions (lamellae) is present inside a metallic matrix material.
Results on shear bands are shown to be related to instabilities of architected materials made up of linear elastic rods, prestressed with axial force.
A rigorous application of homogenization theory shows that the inclusion of sliders in a grid of rods leads to loss of ellipticity in tension, so that the locus for material instability becomes bounded. This result explains: (i.) how to design elastic materials passible of localization of deformation and shear banding for all radial stress paths; (ii.) how for all these paths a material may fail by developing strain localization and without involving cracking.
Finally, inclusion of follower microforces is shown to lead to materials elastic, but not hyperelastic.


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Davide Bigoni, University of Trento