An Adaptive Offset-Tracking Method Based on Deformation Gradients and Image Noises for Mining Deformation Monitoring

The offset-tracking method (OTM) utilizing SAR image intensity can detect large deformations, which makes up for the inability of interferometric synthetic aperture radar (InSAR) technology in large mining deformation monitoring, and has been widely used. Through lots of simulation experiments, it was found that the accuracy of OTM is associated with deformation gradients and image noises in the cross-correlation window (CCW), so CCW sizes should be selected reasonably according to deformation gradients and noise levels. Based on the above conclusions, this paper proposes an adaptive CCW selection method based on deformation gradients and image noises for mining deformation monitoring, and this method considers influences of deformation gradients and image noises on deformations to select adaptive CCWs. In consideration of noise influences on offset-tracking results, smaller CCWs are selected for large deformation gradient areas, and larger CCWs are selected for small deformation gradient areas. For some special areas, special CCWs are selected for offset-tracking. The proposed method is implemented to simulation and real experiments, and the experiment results demonstrate that the proposed method with high reliability and effectiveness can significantly improve the accuracy of OTM in mining deformation monitoring.

Review of models of gradient plasticity theory

Gradient plasticity theories have potential applications for evaluating the load-bearing capacity of structures, since they more accurately describe stress fields in the crack vertex region by including the influence of dislocation distribution density. Gradient plasticity theories take into account scale effects, assuming that stresses depend not only on deformations, but also on the gradient of deformations. The main idea is that the material is strengthened by changing the total density of dislocations, some of which are derived from the stress gradient. These dislocations begin to play a dominant role in the process of metal deformation at the micro level. This paper provides a literature review of gradient plasticity theories that not only rationalize large-scale effects, but also help to understand the processes occurring in the crack vertex region in the presence of the largest plastic deformation gradients.

Convex integration solutions for the geometrically nonlinear two-well problem with higher Sobolev regularity

In this paper, we discuss higher Sobolev regularity of convex integration solutions for the geometrically nonlinear two-well problem. More precisely, we construct solutions to the differential inclusion [Formula: see text] subject to suitable affine boundary conditions for [Formula: see text] with [Formula: see text] such that the associated deformation gradients [Formula: see text] enjoy higher Sobolev regularity. This provides the first result in the modelling of phase transformations in shape-memory alloys where [Formula: see text], and where the energy minimisers constructed by convex integration satisfy higher Sobolev regularity. We show that in spite of additional difficulties arising from the treatment of the nonlinear matrix space geometry, it is possible to deal with the geometrically nonlinear two-well problem within the framework outlined in [A. Rüland, C. Zillinger and B. Zwicknagl, Higher Sobolev regularity of convex integration solutions in elasticity: The Dirichlet problem with affine data in int[Formula: see text], SIAM J. Math. Anal. 50 (2018) 3791–3841]. Physically, our investigation of convex integration solutions at higher Sobolev regularity is motivated by viewing regularity as a possible selection mechanism of microstructures.

Possibilities of the practical use of a stationary strain gradient in the interelectrode volume of unpolarized ferroceramic plates

It has been established that in plates made of hot-pressed ferroelectric ceramics PZT-19 ([Formula: see text]C), after metal electrodes from Ag are burned into opposite surfaces with different depths of mechanical damage, counter-directional stationary deformation gradients and, accordingly, internal electric displacement fields create a stationary flexoelectric effect. As a result, unpolarized ceramics below the Curie temperature become a pyroelectric, and above it become a pyroelectric bolometer. After polishing the less damaged surface and replacing the Ag (valency [Formula: see text]) electrode with Cr ([Formula: see text]) by thermal evaporation in vacuum from the intact surface, a new thermally stable polarization is created, directed from the damaged surface in the interelectrode volume. Such plates have an asymmetric dielectric hysteresis loop, retain the values of the pyroelectric effect and piezoelectric effect in the ferroelectric phase, as well as the bolometric effect in the paraelectric phase after repeated heating cycles to [Formula: see text]C and cooling to [Formula: see text].