Numerical reconstruction of residual stress fields from limited measurements

By finding stress states which are consistent both with any existing experimental measurements and with elasticity theory, residual stress fields can often be reconstructed from incomplete measurement data. We discuss such methods of residual stress reconstruction, their implementation using finite element analysis, and the measurement strategies which enable them. In general, reconstruction of residual stress fields must be formulated as an inverse problem, which can usually be solved using stress basis functions. However, prior knowledge of the form of the residual stress field and/or underlying eigenstrain distribution often allows the problem to be reduced such that inverse methods become unnecessary, greatly simplifying the analysis. Two examples of when residual stress field reconstruction can be simplified in this way are given.