A modification of the semi-analytic inversion method: determination of the yield stress and a comparison with the parametrization algorithm


INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, vol.22, no.4, pp.543-556, 2014 (SCI-Expanded) identifier identifier


In this study, an effective modification of the semi-analytic inversion method is presented. The semi-analytic inversion method is developed to solve an inverse coefficient problem arising in materials science instead of the parametrization method as a different and stronger method. The inverse coefficient problem is related to reconstruction of the unknown coefficient g = g(xi(2)), xi(2): = |del u|(2), from the nonlinear equation -del.(g(|del u|(2))del u) = 2 phi, x is an element of Omega subset of R-2. The semi-analytic inversion method has some advantages. The first distinguishable feature of this method is that it uses only a few measured output data to determine the whole unknown curve, whereas the parametrization algorithm uses many measured output data for the determination of only some part of the unknown curve. The second distinguishable feature of this method is its well-posedness. In the semi-analytic inversion method, the algorithm for determination of the yield stress, which is one of the main unknowns of the inverse problem, is very complicated. That is why we need to modify this algorithm. The demonstrated numerical results for different engineering materials also show that the modified semi-analytic inversion method allows us to determine the elastoplastic parameters of a kind of engineering materials with high accuracy, even various noise levels.