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in this contribution, a single crack of length is fixed at the midplane of a thin plate of thickness and and the quasi-static evolution of a pair of moving cracks is considered. the aim is to examine the role of the crack speed , the plate thickness and of the ratio (the ratio of the total load to the plate thickness ) on the evolution of the crack shapes. the underlying physical problem is akin to that appearing in the study of fracture of thin skins under concentrated loads[ 22 ].
the mathematical problem is related to that appearing in the study of crack propagation in couple-stress materials[ 20, 21 ], although different boundary conditions (bcs) apply. the crack and boundary conditions are outlined in figure8 and figure9, respectively. the bcs are inspired by those used in the study of fracture of thin skins under concentrated loads[ 22 ]. the bc is assumed to be traction-free at the lower crack edge, traction-free at the upper crack edge and traction-free at the lower surface of the plate. the bc on the upper surface is a transversally loaded plate by a concentrated distributed load ( figure10 ). as shown in figure11, the crack is initially open and is then closed by a moving loading at constant speed . the initial crack length is considered to be much smaller than the plate thickness . the movement of the loading is along the left side of the plate (as in figure10 ).
in many engineering applications, it is required to dissipate a portion of the energy released in a system by suitably selecting the appropriate wave-generation mechanism and estimating the power it can be expected to provide. this is the fundamental rationale behind the class of methods known as thermal waveguides [ 2 4 ]. while the majority of the proposed solutions are based on the use of thermo-acoustic phenomena, other approaches such as wave-reactive heat sources are also conceivable [ 6 ]. the aim of the present paper is to explore the possibility of exploiting the crack propagation phenomenon, when a rectilinear crack is excited by an external load, to enhance the energy release rate in a way that it is comparable with that achievable by the use of acoustic resonators. in particular, the energy release rate is shown to scale as c-1. this result is justified through energy considerations and it is reminiscent of a similar scaling law observed in the study of edge wave propagation in a plate of finite thickness [ 5 ].
our consideration is of a semi-infinite rectilinear crack propagating along its length in an infinite kirch-love (k-l) thin elastic plate ( figure1 ). the plate, of thickness e, is elastically supported by a winkler foundation with stiffness i1=i12i2 such that i. waves license center crack in a semi-infinite rectilinear crack of infinite length in an infinite kirch-love (k-l) thin elastic plate, the dispersion of the fourier components of the wavefield at a speed close to the critical speed, c
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