Small‐scale magnetic holes (SSMHs) in the magnetosphere plasma sheet are investigated in this paper. A developed electron magnetohydrodynamics (EMHD) soliton model is proposed as a new approach to SSMHs formation. The Biermann battery effect is taken into account in resolving the magnetic evolution equation with a slow‐mode solution in the weak nonlinear regime. Statistical investigation of SSMH observation data in the plasma sheet by Cluster is carried out in comparison with the theory. We apply multispacecraft data for distinguishing sheet‐like or cylindrical SSMHs observed and clarified by the solitary wave in the EMHD model. Furthermore, the major parameters, such as amplitude, width, maximum magnetic field perturbation, and perpendicular temperature variation of the SSMHs, are found consistent with the theoretical analysis.

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Please cite this article as: Gao, G., Yao, W., Xia, K., Li, Z., Investigation of the rate dependence of fracture propagation in rocks using digital image correlation (DIC) method, Engineering Fracture Mechanics (2015), doi: http://dx. ABSTRACTLoading rate is the main controlling factor in dynamic failure of rocks. In this paper, digital image correlation (DIC) combined with ultra-high speed photography is utilized to study the loading rate effect of a granitic rock -Laurentian granite using notched semi-circular bend (NSCB) method. The dynamic stress intensity factors and crack tip positions are determined from the displacement fields obtained using DIC. Fracture time, fracture toughness and crack growth velocity all exhibit loading rate dependence. The dependence of fracture propagation toughness on crack growth velocity is also obtained, which is in good agreement with that reported in the literature. HighlightsThe full displacement and strain fields are measured using DIC.The history of dynamic stress intensity factor of rocks is determined.The effect of loading rate on dynamic fracture properties are characterized.Dependence of fracture propagation toughness on fracture velocity is obtained.

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