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Boundary integral equations in elastodynamics of interface cracks.

O V Menshykov1, I A Guz, V A Menshykov

  • 1Centre for Micro- and Nanomechanics (CEMINACS), College of Physical Sciences, University of Aberdeen, Aberdeen, UK.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|January 26, 2008
PubMed
Summary

This study validates a boundary integral equation method for solving elastodynamics problems in cracked solids. The approach is demonstrated on interface cracks between dissimilar elastic materials under harmonic loading.

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Area of Science:

  • Solid Mechanics
  • Computational Mechanics
  • Materials Science

Background:

  • Elastodynamics problems involving cracks are crucial in engineering.
  • Accurate numerical methods are needed for analyzing cracked solids.
  • Interface cracks between dissimilar materials present unique challenges.

Purpose of the Study:

  • To validate a novel boundary integral equation (BIE) method for elastodynamics.
  • To assess the method's applicability to cracked solids.
  • To analyze a specific case of an interface crack under harmonic loading.

Main Methods:

  • Development and application of a boundary integral equation formulation.
  • Numerical implementation of the BIE method.
  • Analysis of harmonic loading conditions.

Main Results:

  • The proposed BIE method is validated for elastodynamics problems.
  • The method effectively handles interface cracks between dissimilar elastic media.
  • Numerical solutions demonstrate the accuracy and efficiency of the approach.

Conclusions:

  • The boundary integral equation method provides a reliable tool for solving elastodynamics problems with cracks.
  • The validated method can be applied to complex scenarios, including interface cracks.
  • This work contributes to the understanding and analysis of cracked materials under dynamic loading.