  We present the formulation for finding the distribution of eigenstrains, i.e.
the sources of residual stress, from a set of measurements of residual elastic
strain (e.g. by diffraction), or residual stress, or stress redistribution, or
distortion. The variational formulation employed seeks to achieve the best
agreement between the model prediction and some measured parameters in the
sense of a minimum of a functional given by a sum over the entire set of
measurements. The advantage of this approach lies in its flexibility: different
sets of measurements and information about different components of the
stress-strain state can be incorporated. We demonstrate the power of the
technique by analysing experimental data for welds in thin sheet of a nickel
superalloy aerospace material. Very good agreement can be achieved between the
prediction and the measurement results without the necessity of using iterative
solution. In practice complete characterisation of residual stress states is
often very difficult, due to limitations of facility access, measurement time
or specimen dimensions. Implications of the new technique for experimental
analysis are all the more significant, since it allows the reconstruction of
the entire stress state from incomplete sets of data.
