3D Elastic Scattering By Empty Cracks Using
The Traction Boundary Element Method
Author(s)
P. Amado Mendes & A. Tadeu
Abstract
The 3D wave propagation in solid media containing 2D cracks is modelled in the
frequency domain by developing a Traction Boundary Element Method
(TBEM). The proposed formulation makes it possible to model thin bodies for
which the classical Boundary Element Method (BEM) degenerates. The
algorithm developed simulates wave propagation in the presence of empty cracks
(even with no thickness) with arbitrary geometry and orientation. The resulting
hyper-singular integrals are evaluated analytically.
Once the TBEM has been implemented, the solutions are verified by solving
the case of an empty circular inclusion, for which analytical solutions exist.
Combining the BEM and the TBEM formulations allows the computation of
displacements in the opposite sides of the crack.
Time responses of the wave field scattered by an S-shaped empty crack in an
unbounded medium are computed using complex frequencies in order to avoid
aliasing phenomena. The main wave propagation features are illustrated by
snapshots of computer animations. The effect of these complex frequencies is
removed in the time domain by rescaling the responses using an exponential
factor.
Keywords: wave propagation, elastic scattering, empty cracks, Boundary
Element Method, Traction Boundary Element Method, two-and-a-halfdimensional
problem.
1 Introduction
Different scientific formulations have been developed to study the elastic and
acoustic wave scattering by inclusions and thin heterogeneities. Since the
analytical approaches (e.g. Pao & Mow [1]) are only known for simple and
Keywords
wave propagation, elastic scattering, empty cracks, Boundary
Element Method, Traction Boundary Element Method, two-and-a-halfdimensional
problem
Related Book
Other papers in this volume
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