Abstract
We discuss the propagation of a running crack in a bounded linear
elastic body under shear waves for a simplified 2D-model. This model
is described by two coupled equations in the actual configuration:
a two-dimensional scalar wave equation in a cracked, bounded domain
and an ordinary differential equation derived from an energy balance
law. The unknowns are the displacement fields u = u ( y , t ) and
the one-dimensional crack tip trajectory h = h ( t ). We assume that
the crack grows straight. Based on a paper of Nicaise-Sändig,
we derive an improved formula for the ordinary differential equation
of motion for the crack tip, where the dynamical stress intensity
factor occurs. The numerical simulation is an iterative procedure
starting from the wave field at time t = t i . The dynamic stress
intensity factor will be extracted at t = t i . Its knowledge allows
us to compute the crack-tip motion h ( t i +1 ) with corresponding
nonuniform crack speed assuming ( t i +1 - t i ) is small. Now, we
start from the cracked configuration at time t = t i +1 and repeat
the steps. The wave displacements are computed with the FEM-package
PDE2D. Some numerical examples demonstrate the proposed method. The
influence of finite length of the crack and finite size of the sample
on the dynamic stress intensity factor will be discussed in detail.
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