Last modified: 2018-10-20
Abstract
The work presents an application of peridynamics for investigation of vibro-acoustic wave interaction in a cracked orthotropic plate. The experimental work – known from the literature review – confirms high applicability of the mentioned technique to nondestructive evaluation for mechanical structures. As reported, very narrow and short notches can be effectively detected. The numerical analyses are carried out by the authors of the present work to study the phenomenon of wave modulation and sidebands generation for a 2-D nonlocal model of a composite-like structure with introduced geometric discontinuity. The effectiveness of the process of damage detection, considering the results of simulations carried out with peridynamics to investigate the above mentioned phenomenon, is discussed.
Peridynamics is a relatively new approach for modeling mechanical continuum. Although it was originally formulated as an analytical tool, it may be also transformed into easily applied numerical framework. The approach introduces a nonlocal formulation for physical reactions within the solid, which – in turn – allows for more flexible modeling, especially regarding geometric discontinuities, e.g. resulting from notches, as well as sharp spatial changes of the material properties. The applied form of a governing equation constitutes an integral-based problem formulation. Hence, indeed, different types of nonlinearities and discontinuities may be introduced into the model in a convenient way. No spatial partial derivative is required to be solved. All local and nonlocal pairwise forces considered for each portion of matter act within the area defined by a horizon radius. Finally, peridynamics allows for spontaneous crack growth as well.
The created numerical model assumes homogenized properties of an orthotropic material (e.g. a composite). This is valid under the assumption that – in case of a composite material – the waves generated in the model characterize the wavelengths much greater than the distances between fibers and their diameters. Inhomogeneity, which is unquestionably present at micro scale, can be therefore ignored. The peridynamic model undergoes simultaneous presence of two interacting in-plane elastic waves, of both high and low frequency. The high frequency wave gets modulated since a breathing crack is introduced in the model. The deformations of the crack faces are, in turn, activated by the low frequency force. The frequency response functions confirm the existence of the damage. Wave modulation is observed since a bilinear (i.e. nonlinear) stiffness is considered and the contact phenomenon is taken into account.
The work was supported by the Foundation for Polish Science (FNP-WELCOME/2010-3/2).