A direct D-bar reconstruction algorithm for recovering a complex conductivity in 2D

A direct reconstruction algorithm for complex conductivities in W-2,W-infinity(Omega), where Omega is a bounded, simply connected Lipschitz domain in R-2, is presented. The framework is based on the uniqueness proof by Francini (2000 Inverse Problems 6 107-19), but equations relating the Dirichlet-to-Neumann to the scattering transform and the exponentially growing solutions are not present in that work, and are derived here. The algorithm constitutes the first D-bar method for the reconstruction of conductivities and permittivities in two dimensions. Reconstructions of numerically simulated chest phantoms with discontinuities at the organ boundaries are included.

Limiting the influence of friction on the split Hopkinson pressure bar tests by using a ring specimen

The deformation of a ring under axial compression is analyzed in order to estimate a favorable ring specimen geometry capable of limiting the influence of friction on the stress-strain curve obtained from SHPB tests. The analysis shows that the use of a ring specimen with a large inner diameter and a small radial thickness offers some advantages comparing with the traditional disk sample. In particular, it can improve the reliability of the test results for ductile materials in the presence of friction. Based on the deformation analysis of a ductile ring under compression, a correction coefficient is proposed to relate the actual material stress strain curve with the reading from the SHPB. It is shown using finite element simulation that the proposed correction can be used for a wide range of conventional ductile materials. Experimental results with steel alloys indicate that the correction procedure is an effective technique for an accurate measurement of the dynamic material strength response. (C) 2012 Elsevier Ltd. All rights reserved.