Corrigendum to “Identification of residual stresses by instrumented elliptical indentation and inverse analysis” [Mech. Res. Commun. 41 (2012) 21–29]

The residual stress tensor near the surface of a metal structural component or products of metallurgical processes (particularly welding) is considered in view of the estimation of its governing components. These are: the two principal stresses if the directions are "a priori" known as assumed here for the preliminary optimization of the indenter shape; otherwise two normal stresses and a shear stress according to a preselected reference system. In both situations the material is assumed to be endowed with known elastic-plastic properties. The novel parameter identification procedure investigated herein can be outlined as follows, when the unknown stresses are three: an instrumented indenter is adopted with elliptical section across the axis of an originally conical, or, as an alternative, of an originally spherical shape; three indentations are performed with the ellipse axis rotated by 45° in a sequence, in three locations near to each other at minimal distances apt to avoid interference; the three digitalized indentation curves (loading-unloading force versus penetration) are the source of the experimental data set used as input of inverse analysis; this is carried out by a fast method consisting of finite element simulations of the tests, "proper orthogonal decomposition", "radial basis function" interpolation, and a first-order algorithm for the minimization of the discrepancy function. When the unknowns are the two principal stresses (directions known) two orthogonal indentations turn out to be sufficient.