### Tuesday, 12 October 2004 - 2:40 PM

### This presentation is part of : Damage and Composites I

### Dynamic Steady-State Crack Propagation in an Anisotropic Linear Viscoelastic Body

**Jay R. Walton**, Texas A&M University, Texas A&M University, Department of Mathematics, Texas A&M University, College Station, TX 77845-3368
Presented here is a framework utilizing Fourier transform and complex variable methods for carrying out a rigorous analysis of a semi-infinite generalized plane strain crack propagating in a general anisotropic linear viscoelastic body. It is evident from the analysis that no general result is possible; rather separate cases must be considered depending upon the material's symmetry group structure and the orientation of the fracture plane relative to the material's symmetry planes and axes. In general, the method requires the solution of a matrix Riemann-Hilbert (or Wiener-Hopf) problem. However, for an instropic body or a transversely isotropic body with a fracture plane parallel to the material ``fibers'', the matrix Riemann-Hilbert problem uncouples resulting in three scalar Riemann-Hilbert problems which can be solved analytically even when Poisson's ratio is not assumed constant. These solution are These solutions are exhibited analytically and examined numerically.

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