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Explore homogenization methods for weakly compressible elastic materials in this 33-minute lecture from the Hausdorff Trimester Program Multiscale Problems: Workshop on Numerical Inverse and Stochastic Homogenization. Delve into the modeling of weakly elastic materials composed of incompressible elastic matrices and small compressible gaseous inclusions. Learn about the extension of a recently proposed homogenized model to a time harmonic regime, describing the solid-gas mixture from a macroscopic perspective using an effective elasticity tensor. Discover the derivation and numerical validation of analytical approximations for effective elastic coefficients in terms of macroscopic parameters. Examine how this simplified description enables an efficient variational approach for estimating tissue porosity using mechanical responses to external harmonic excitations. Gain insights into addressing multiscale problems where direct numerical simulations are prohibitively complex.
