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Dynamic behavior of a finite-sized elastic solid with multiple cavities and inclusions using BIEM

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Abstract

The 2D elastodynamic problem is solved for a finite-size solid containing multiple cavities and/or elastic inclusions of any shape that are arranged in an arbitrary geometrical configuration. The dynamic load is a tensile traction field imposed along the sides of the finite-size solid matrix and under time-harmonic conditions. Furthermore, the cavity surfaces are either traction-free or internally pressurized, while the inclusions have elastic properties ranging from very weak to nearly rigid. The presence of all these heterogeneities within the elastic matrix gives rise to both wave scattering and stress concentration phenomena. Computation of the underlying kinematic and stress fields is carried out using the boundary integral equation method built on the frequency-dependent fundamental solutions of elastodynamics for a point load in an unbounded continuum. As a first step, a detailed validation study is performed by comparing the present results with existing analytical solutions and with numerical results reported in the literature. Following this, extensive numerical simulations reveal the dependence of the scattered wave fields and of the resulting dynamic stress concentration factors (SCF) on the shape, size, number and geometrical configuration of multiple cavities and/or inclusions in the finite elastic solid. The pronounced SCF values invariably (but not always) observed are attributed to multiple dynamic interactions between these heterogeneities that may either weaken or strengthen the background elastic matrix.

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Abbreviations

BIEM:

Boundary integral equation method

FEM:

Finite element method

SCF:

Stress concentration factor

BVP:

Boundary value problem

BIE:

Boundary integral equation

BE:

Boundary element

DOF:

Degrees-of-freedom

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Authors and Affiliations

  1. Department of Civil Engineering, University of Architecture, Civil Engineering and Geodesy (UACEG), 1046, Sofia, Bulgaria

    S. L. Parvanova

  2. Institute of Mechanics, Bulgarian Academy of Mechanics (BAS), 1113, Sofia, Bulgaria

    P. S. Dineva

  3. Department of Civil Engineering, Aristotle University of Thessaloniki (AUTH), 54124, Thessaloniki, Greece

    G. D. Manolis

Authors
  1. S. L. Parvanova
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  2. P. S. Dineva
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  3. G. D. Manolis
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Correspondence to G. D. Manolis.

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Parvanova, S.L., Dineva, P.S. & Manolis, G.D. Dynamic behavior of a finite-sized elastic solid with multiple cavities and inclusions using BIEM. Acta Mech 224, 597–618 (2013). https://doi.org/10.1007/s00707-012-0759-0

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  • DOI: https://doi.org/10.1007/s00707-012-0759-0

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