Reduced modeling speeds simulations of mechanical metamaterials with complex patterns
Reduced order modeling for micromorphic computational homogenization of mechanical metamaterials with patterning fluctuation fields
Computational Engineering, Finance, and Science
Summary
Simulating materials with tiny repeating structures that fold or buckle is often too slow to do on big models directly. The paper presents a way to simplify these detailed simulations by capturing their key patterns in fewer calculations, making them faster. The authors combine techniques that reduce the complexity of the detailed parts while still keeping the important behaviors. This approach can help engineers study how these special materials deform on larger scales more efficiently.
What this means in practice
- •For mechanical design engineers: Perform large-scale simulations of metamaterials with detailed microstructure at practical computational cost.
- •For materials development teams: Evaluate the mechanical response of new metamaterial designs efficiently before prototyping.
Authors
Theron Guo, Ondřej Rokoš
Abstract
Mechanical metamaterials owe some of their exotic effective properties to microstructural instabilities such as buckling and pattern transformation. Their fine-scale geometry, combined with the interplay of local and nonlocal effects, renders direct numerical simulation (DNS) prohibitively expensive, if not intractable. Micromorphic computational homogenization~\citep{Rokos2019} has been proposed to make macroscopic simulations feasible: a representative volume element (RVE) carrying patterning fluctuation fields resolves the microscale, while an effective micromorphic continuum describes the macroscale. Such simulations nevertheless remain costly, since the RVE problem and its associated tangent problems must be solved at every macroscopic integration point, which becomes prohibitive, especially in three dimensions. We therefore propose a reduced order model for the microscopic problem, combining proper orthogonal decomposition with a hyperreduction method tailored to the micromorphic setting. Two numerical examples quantify the reduced basis and hyperreduction errors and discuss the offline costs and attainable online speed-ups. The results show that this approach can enable engineering-scale large deformation analysis of mechanical metamaterials.