How to induce dynamic fracture by focusing flexural waves

Abstract

Flexural waves in beams are dispersive, causing a propagating broadband wavelet to spread in space and time. This property has been used in non-destructive testing to locate defects in tubes requiring only circumferential measurements, as well as in beams and plates requiring only a one point measurement. This was achieved by using the time reversal principle to retrace the propagation path of the measured waves. Here, we utilize the dispersion of flexural waves and the superposition of multiple reflections to spatiotemporally focus strain energy in a beam, thereby inducing precisely controlled dynamic fracture. An electromechanical transducer excites flexural waves at one end of a glass beam over a long duration of time. The waves focus at a narrow spot in space and time to produce a high amplitude bending moment pulse, which causes the fracturing of the glass beam. The excitation signal for the transducer is the optimal composition of 31 distinct wavelets, for which up to 30 reflections are taken into account. Each of these wavelets is determined in a time reversed spectral element simulation. In experiments, the bending moment at the focal point was found to be 20 times larger than the maximum moment produced by the transducer.