The numerical analysis of elastic wave propagation in unbounded media may be difficult due to spurious waves reflected at the model artificial boundaries. This point is critical for the analysis of wave propagation in heterogeneous or layered solids. Various techniques such as Absorbing Boundary Conditions, infinite elements or Absorbing Boundary Layers (e.g. Perfectly Matched Layers) lead to an important reduction of such spurious reflections. In this paper, a simple absorbing layer method is proposed: it is based on a Rayleigh/Caughey damping formulation which is often already available in existing Finite Element softwares. The principle of the Caughey Absorbing Layer Method is first presented (including a rheological interpretation). The efficiency of the method is then shown through 1D Finite Element simulations considering homogeneous and heterogeneous damping in the absorbing layer. 2D models are considered afterwards to assess the efficiency of the absorbing layer method for various wave types and incidences. A comparison with the PML method is first performed for pure P‐waves and the method is shown to be reliable in a more complex 2D case involving various wave types and incidences. It may thus be used for various types of problems involving elastic waves (e.g. machine vibrations, seismic waves, etc.). Copyright © 2010 John Wiley & Sons, Ltd.

Abstract:The numerical analysis of elastic wave propagation in unbounded media may be difficult to handle due to spurious waves reflected at the model artificial boundaries. Several sophisticated techniques such as nonreflecting boundary conditions, infinite elements or absorbing layers (e.g. Perfectly Matched Layers) lead to an important reduction of such spurious reflections. In this Note, a simple and efficient absorbing layer method is proposed in the framework of the Finite Element Method. This method considers Rayleigh/Caughey damping in the absorbing layer and its principle is presented first. The efficiency of the method is then shown through 1D Finite Element simulations considering homogeneous and heterogeneous damping in the absorbing layer. 2D models are considered afterwards to assess the efficiency of the absorbing layer method for various wave types (surface waves, body waves) and incidences (normal to grazing). The method is shown to be efficient for different types of elastic waves and may thus be used for various elastodynamic problems in unbounded domains.Abstract: La simulation numérique de la propagation d'ondes élastiques en milieux infinis peut s'avérer délicate du fait des réflexions d'ondes parasites sur les frontières du modèle discrétisé. Plusieurs méthodes sophistiquées, telles que les frontières absorbantes, les éléments infinis ou les couches absorbantes (e.g. « Perfectly Matched Layers ») permettent une réduction importante des réflexions parasites. Dans cette note, une méthode de couche absorbante simple et efficace est proposée dans le cadre de la méthode des éléments finis. Cette méthode s'appuie sur une formulation de l'amortissement dans la couche de type Rayleigh/Caughey et ses principes sont d'abord détaillés. L'efficacité de la méthode est alors démontrée grâce à des simulations unidimensionnelles en considérant un amortissement homogène ou variable dans la couche absorbante. Des modèles bidimensionnels permettent ensuite d'apprécier l'efficacité de la méthode de couche absorbante proposée pour différents types d'ondes (ondes de surface, ondes de volume) et des incidences variées (normale à rasante). La méthode s'avère ainsi efficace pour différents types d'ondes élastiques et pourrait être utilisée pour traiter divers problèmes élastodynamiques en milieux non bornés. 1.Numerical methods for elastic waves in unbounded domains Various numerical methods are available to simulate elastic wave propagation in solids: finite differences [1,2], finite elements [3,4], boundary elements [5,6,7], spectral elements [8,9], etc. Such methods as finite or spectral elements have strong advantages (for complex geometries [9], nonlinear media [10], etc) but may have such drawbacks as numerical dispersion [4,11,12] for low order finite elements, or spurious reflections at the mesh boundaries [4,13]. The problem of spurious reflections may be dealt with using the Boundary Element Method [5,6,7] or coupling it with other numerical methods [14]. Domain Reduction Methods are also available in th...

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