We present a new technique for simulating the time-dependent behavior of an elastic material in general and the nonlinear dynamics of a linearly elastic cable in particular. Results will be presented for both the small displacement of a highly nonlinearly elastic material and the large displacement of a linearly elastic cable. The first simulation, a small displacement of a nonlinearly elastic material, will be used to validate our numerical scheme against a known analytical solution while the second simulation, the large displacement of a linearly elastic cable, will be used to investigate the looping that can occur when wave interactions produce regions of strong local compression.
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