New math model predicts how materials fail when riddled with tiny holes
Engineers have developed a faster way to predict how perforated materials—from aerospace composites to industrial filters—will perform under stress, without relying on periodic patterns. The breakthrough could accelerate product design cycles and reduce costly physical testing in manufacturing.
Originaltitel: MESOSCALE MODELS AND APPROXIMATE SOLUTIONS FOR SOLIDS CONTAINING CLOUDS OF VOIDS
<p>For highly perforated domains the paper addresses a novel approach to study mixed boundary value problems for the equations of linear elasticity in the framework of mesoscale approximations. There are no assumptions of periodicity involved in the description of the geometry of the domain. The size of the perforations is small compared to the minimal separation between neigh-boring defects and here we discuss a class of problems in perforated domains, which are not covered by the homogenization approximations. The mesoscale approximations presented here are uniform. Explicit asymptotic formulas are supplied with the remainder estimates. Numerical illustrations, demonstrating the efficiency of the asymptotic approach developed here, are also given.</p>