Computational homogenization for multiscale forward modeling of resonant ultrasound spectroscopy of heterogeneous materials

Abstract

We present a computational framework for multiscale forward modeling of ultrasound resonance in heterogeneous materials that accounts for microstructure. The approach includes two steps. The first step is the accurate determination of the elastic properties of heterogeneous materials with finite element simulations on a representative volume element of the microstructure at the mesoscopic length scale. The second step is modeling resonance frequencies of a macroscopic component made of an effective homogeneous medium having the same elastic properties as the actual material with microstructure. The approach is validated in a case study on a Cu–W two-phase composite, for which resonance frequencies predicted with the proposed framework are compared against the experimental measurements. The present multiscale modeling approach, involving computational homogenization and leveraging 3D microstructure data, showed better accuracy compared to classical Voigt/Reuss bounds often used for forward modeling of resonant ultrasound spectroscopy.