Tensile material instabilities in elastic beam lattices lead to a bounded stability domain.
Saved in:
| Title: | Tensile material instabilities in elastic beam lattices lead to a bounded stability domain. |
|---|---|
| Authors: | Bordiga, Giovanni, Bigoni, Davide, Piccolroaz, Andrea |
| Source: | Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences; 9/5/2022, Vol. 380 Issue 2231, p1-25, 25p |
| Subject Terms: | RADIAL stresses, SHEAR (Mechanics), PRESTRESSED concrete, PLASMA instabilities, METAMATERIALS |
| Abstract: | Homogenization of the incremental response of grids made up of preloaded elastic rods leads to homogeneous effective continua which may suffer macroscopic instability, occurring at the same time in both the grid and the effective continuum. This instability corresponds to the loss of ellipticity in the effective material and the formation of localized responses as, for instance, shear bands. Using lattice models of elastic rods, loss of ellipticity has always been found to occur for stress states involving compression of the rods, as usually these structural elements buckle only under compression. In this way, the locus of material stability for the effective solid is unbounded in tension, i.e. the material is always stable for a tensile prestress. A rigorous application of homogenization theory is proposed to show that the inclusion of sliders (constraints imposing axial and rotational continuity, but allowing shear jumps) in the 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 subject to localization of deformation and shear banding for all radial stress paths; and (ii) how for all these paths a material may fail by developing strain localization and without involving cracking. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'. [ABSTRACT FROM AUTHOR] |
| Copyright of Philosophical Transactions of the Royal Society A: Mathematical, Physical & Engineering Sciences is the property of Royal Society and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Complementary Index |
Nájsť tento článok vo Web of Science Be the first to leave a comment!