Dynamic response of a solid with multiple inclusions under anti-plane strain conditions by the BEM

• We developed and accurate and efficient method for stress concentration studies.
• Any configuration of inclusions in an elastic matrix can be considered.
• Discretization of only the surfaces and interfaces of the problem is required.
• Interacting inclusions in a solid matrix has important applications in composite materials.

In this work, a 2D problem in elastodynamics that involves the finite elastic solid containing multiple cylindrical and elliptical inclusions and/or cavities of arbitrary size, number, material properties and geometrical configuration is solved. More specifically, anti-plane strain conditions are assumed to hold and all external loads have a time harmonic variation. The numerical method used for this purpose is the direct, displacement-based boundary element method (BEM) with sub-structuring capabilities. The BEM employs frequency-dependent fundamental solutions for a point load in the unbounded continuum, and requires discretization of all external and internal surfaces and interfaces only. The method is well suited for the computation of stress concentration factors, while solution at points inside the domain of interest can be expressed directly in terms of boundary data without recourse to domain discretization. Thus, an effective numerical scheme is developed, verified and subsequently used for extensive parametric studies. The numerical results obtained here show a marked dependence of the stress and displacement wave fields on the shape of the inclusions, their material properties, number and position, as well as their mutual interaction with the incoming horizontally polarized shear (SH) waves. The potential of the BEM to efficiently produce accurate results for the dynamic response of both finite and semi-infinite solids that are strengthened and/or weakened by multiple inclusions, as compared to other domain-type methods, makes it a valuable computational tool for solving certain categories of engineering problems. These range from fields as diverse as material science and non-destructive testing evaluation, to seismology and exploratory geophysics.