What is it about?

In this study, a rigorous strong formulation for elastodynamic scattering utilizing boundary integral representations are developed to obtain the displacement fields on both the surfaces of spherical cavity scatters along with far field displacements. Solutions to these boundary integral representations utilize both free and half-space Green's displacement tensors (the half-space Green's displacement tensor is obtained using the method of images with the superposition of a second free-space Green's displacement tensor. Therefore, integration is only required over a single cavity to obtain the results for two symmetric spherical cavities including their interaction effects) are employed with the corresponding boundary integral representations using the boundary element method (BEM) with the off-boundary technique to obtain the desired displacement fields in the frequency domain.

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Why is it important?

Solutions to elastodynamic scattering problems form the basis for quantitative non-destructive evaluation (QNDE). These solutions are employed to assess the deterioration of structures and materials by detecting and characterizing inherent and developing discrete flaws. These results are then employed to evaluate the requirements for the reliability of structures, their components, along with their constituent materials.


This article provides an in depth development of a rigorous strong formulation for the surface and far field displacement fields for multiple scattering cavities using boundary integral representations. Solutions from the boundary integral equations are then used with quantitative non-destructive evaluation (QNDE) results for the characterization of inherent and developing internal defects in a structure.

Thomas Warren

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This page is a summary of: Interaction effects from the elastodynamic scattering by two symmetric spherical cavities, AIP Advances, February 2023, American Institute of Physics,
DOI: 10.1063/5.0116877.
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