Dynamics of Flexoelectric Materials: Subsonic, Intersonic, and Supersonic Ruptures and Mach Cone Formation

Motivated by recent, unexpected, experimental observations of “intersonic” rupture growth in which both shear and dilatational Mach fronts were observed at the tips of dynamic frictional ruptures propagating at rupture speeds below the dilatational wave speed of the surrounding solid, and we formulate the general dynamic flexoelectric problem and we investigate its plane strain/plane polarization specialization. The coupling of the mechanical problem is analogous to a problem of Toupin–Mindlin gradient elasticity, where two micromechanical characteristic lengths and two microinertial lengths emerge as a combination of the mechanical, dielectric, and flexoelectric constants. The solution of the rupture growth problem allows us to provide an explanation of the experimental results. This becomes possible since flexoelectricity predicts a new aspect that was not observed in the classical analysis: subsonic super shear and supersonic crack tip (or rupture) motions are not related exclusively with the problem being elliptic or hyperbolic, respectively. This is due to the influence of the microinertial lengths, which, in addition to the ratios of the rupture to the wave speeds, also affect the slopes of the Mach cones. Moreover, we are able to explain the experimental paradox of the observation of double Mach cone pairs at the tips of supershear, but subsonic, frictional, ruptures in poly-methyl-methacrtylate (PMMA) by demonstrating that both dilatational and shear Mach cones could appear in flexoelectric solids at rupture speeds below the material dilatation wave speed, something that is impossible from the classical elasticity analysis and is due to the dispersive nature of the present problem. Our analysis is of relevance to the dynamic deformation and fracture of both synthetic and naturally occurring flexoelectric materials and systems, with implications to both engineering and earthquake source mechanics.

Multiple Nonlinear Regression Analysis for the Prediction of Macroscopic Elastic Properties on Composite Containing Interphase

A convenient method to predict the macroscopic elastic performance of composite containing interphase was proposed in this paper. Firstly, a 3-D three-phase micromechanical model with randomly distributed fibers was established with the Moving Window Method (MWM), and the macroscopic elastic properties of T300/914C were predicted using energy method. Secondly, the multiple nonlinear regression correlation between the macroscopic elastic properties and micromechanical characteristic parameters of the interphase was established based on numerical data. Finally, the macroscopic elastic properties of T300/914C containing interphase were predicted using the regression model. Results indicate that the relative error for the longitudinal modulus is within ±1% while it is within ±3.5% for the transverse modulus, and shear modulus.