Profesor Joaquín Mura impartió dos Conferencias en Europa

La primera actividad se enmarcó en el 11th World Congress on Computational Mechanics realizado en el la ciudad de Barcelona el 23 de julio. En la oportunidad el académico dictó la charla "Identification of low-contrast inclusions in poroelastic materials”.

Abstract: This contribution is devoted to the determination of subsurface images for the identification of solid inclusions in poroelastic media, which is important in applications as diverse as hydrology, mining processes, biological tissues, among many others. To this end, the Biot’s model is considered for a fully saturated poroelastic medium in time harmonic regime, where the location and shape of several inclusions can be detected by applying recent developments for shape optimization problems, more precisely, the small amplitude homogenization method [1, 2, 3].Using partial boundary and/or interior data, regions having different elastic parameters than that of the skeleton (or matrix) can be recovered by minimizing the misfit between the measured data from an array of receivers and that given by numerical guesses. By assuming that the contrast between the two possible values for the parameters is not very large, the construction of the minimizing sequence is performed by an asymptotic approximation, made up to second order with respect to the contrast parameter. Hence, a cascade of equations is obtained and the limit equations are established through a relaxation process, allowing then mixtures zones. Once this procedure is archived, the evaluation of a steepest descent method becomes a simple matter. Once remarkable difficulty for obtaining the limit equation, is the appereance of products of weakly convergent sequences, whose limit and respective correction terms are obtained via H-measures. Finally, numerical results will be shown to demonstrate the performance and reliability of this method.

Luego se dirigió a Londres, donde el lunes 28 de mayo expuso en el King's College el tema "Porosity estimation in weakly compressible materials"

Abstract: In this talk we focus our attention on materials composed by an incompressible elastic matrix and small compressible gas inclusions under time harmonic excitations. In a biomedical context, this model describes the dynamics of some biological tissues when wave analysis methods (such as MRE) are used to estimate some tissue properties. Due to the multiscale nature of the problem, direct numerical simulations are prohibitive. By extending a recent two-scale homogenization model describing the solid-gas mixture to time harmonic regime, we derive and numerically validate analytical approximations for the effective elasticity tensor in terms of macroscopic parameters only. This description allow us to set up an efficient variational approach for the estimation of the porosity field along the tissue by using the mechanical response to external excitations.

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