An investigation of radial basis function method for strain reconstruction by energy-resolved neutron imaging

The main objective of the current work is to determine meshless methods using the radial basis function (rbf) approach to estimate the elastic strain field from energy-resolved neutron imaging. To this end, we first discretize the longitudinal ray transformation with rbf methods to give us an unconstrained optimization problem. This discretization is then transformed into a constrained optimization problem by adding equilibrium conditions to ensure uniqueness. The efficiency and accuracy of this approach are investigated for the situation of 2d plane stress. In addition, comparisons are made between the results obtained with rbf collocation, finite-element (fem) and analytical solution methods for test problems. The method is then applied to experimentally measured continuous and discontinuous strain fields using steel samples for an offset ring-and-plug and crushed ring, respectively.