Elastic wave propagation in 2D & 3D for locally-resonant metamaterials in geophysics.

Leader: Imperial College London

In WP3, the study and development of seismic metamaterials in full elastic media is tackled using numerical simulations based on the spectral element method (SEM). Thanks to a diagonal mass matrix, and the use of high order polynomials for the approximation of the displacement field, SEM are accurate, efficient and massively parallelizable even for very complex models. These features are fundamental for integrating the elastic wave equation in metamaterials that have a very subwavelength structure (Fig. 1).

The SPECFEM3D software package, originally developed for global seismology applications and based on SEM, allows the reproduction of any 3D model meshed through the CUBIT software (https://cubit.sandia.gov). It integrates the elastic wave equation for anisotropic, (an)elastic, acoustic, and poro-elastic media that contain sharp multi-scale property contrasts and complex boundaries. The combination of all of these features with high parallel performance, accurate asymptotic stability, and the availability of perfectly matched layer (PML) boundary conditions make this the ideal tool for our applications. The choice of a good meshing strategy is traditionally the most challenging problem when using hexahedral meshes. This becomes particularly important when metamaterials, like in our case, are made of many subwavelength resonators or inclusions. The software CUBIT comes with a powerful Python-scripting interface that automates complex geometry decomposition and eases the creation of doubling layers and pillowing regions. These techniques can be used to confine mesh refinements only to the regions where strictly necessary and at the same time reduce element distortions that might affect the simulation’s quality (Fig. 1).

The analysis of the results is completely parallelized through Python and Paraview scripting. The most important feature of the post-processing is the very dense spatial and temporal sampling that is afforded by parallel computing, thus allowing for a deep understanding of the metamaterial’s physics. All the three phases: meshing, parallel simulation and post-processing are fully automated on both the intra-departmental cluster CIMENT in Grenoble or CURIE at TGCC allowing large parametric studies on metamaterial models as those carried out in previous works on plates (Colombi et al, 2014, 2015, 2016). In the META-FORET project, the automated approach is used to develop and improve the performance of two new types of metamaterials capable of detouring or stopping surface seismic waves incident on an object.