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

Giannakopoulos, Antonios E. and Rosakis, Ares J. (2020) Dynamics of Flexoelectric Materials: Subsonic, Intersonic, and Supersonic Ruptures and Mach Cone Formation. Journal of Applied Mechanics, 87 (6). Art. No. 061004. ISSN 0021-8936. doi:10.1115/1.4046634.

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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.

Item Type:Article
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Rosakis, Ares J.0000-0003-0559-0794
Additional Information:© 2020 by ASME. Paper No: JAM-20-1100. Contributed by the Applied Mechanics Division of ASME for publication in the Journal of Applied Mechanics. Manuscript received February 28, 2020; final manuscript received March 2, 2020; published online March 11, 2020. A. J. R. acknowledges support from the US Geological Survey (USGS) (Grant No. G20AP00037) and from the 2019 Caltech/MCE Big Idea Fund (BIF).
Funding AgencyGrant Number
Caltech Big Ideas FundUNSPECIFIED
Subject Keywords:flexoelectricity, dynamic elasticity, crack/rupture propagation, Mach shock fronts, length scales, ellipticity/hyperbolicity, constitutive modeling of materials, micromechanics
Issue or Number:6
Record Number:CaltechAUTHORS:20210218-162638462
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Official Citation:Giannakopoulos, A. E., and Rosakis, A. J. (March 28, 2020). "Dynamics of Flexoelectric Materials: Subsonic, Intersonic, and Supersonic Ruptures and Mach Cone Formation." ASME. J. Appl. Mech. June 2020; 87(6): 061004.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108113
Deposited By: Tony Diaz
Deposited On:19 Feb 2021 17:22
Last Modified:16 Nov 2021 19:09

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