Abstract
This paper is concerned with the use of polynomial metamodels for the design of acoustical materials, considered as equivalent fluids. Polynomial series in microstructural parameters are considered, and allow us to approximate the multiscale solution map in some well-defined sense. The relevance of the framework is illustrated by considering the prediction of the sound absorption coefficient. In accordance with theoretical results provided elsewhere in the literature, it is shown that the surrogate model can accurately approximate the solution map at a reasonable computational cost, depending on the dimension of the input parameter space. Microstructural and process optimization by design are two envisioned applications.
Highlights
The inverse design of materials has recently gained popularity in both academia and industry
The effective properties can be estimated by using the semi-phenomenological JCAPL model [7, 8, 9, 10], which involves transport properties that are obtained by solving a set of independent boundary value problems (BVPs) (Stokes, potential flow and thermal conduction equations; see e.g., Chapter 5 in [11] and Appendix B in [12] for a condensed presentation of this model)
These BVPs are solved by using the finite element method and the commercial software COMSOL Multiphysics
Summary
The inverse design of materials has recently gained popularity in both academia and industry. Materials by design approaches typically require (i) the construction of a mapping between the microstructural features at some relevant scale and the properties of interest (with a desired level of accuracy), and (ii) the design of an optimization algorithm that can efficiently explore innovative solutions. We investigate the use of a multiscale-informed polynomial surrogate to define an approximation of the macroscopic acoustical properties in terms of microstructural variables. A classical remedy to this computational burden relies on the construction of a surrogate mapping qthat properly approximates q (that is, the map m → q(m) approaches the solution map m → q(m) in some sense) and remains much cheaper to evaluate than full-field upscaling simulations.
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