Inverse identification of elastic constants using Airy stress function: theory and application

Development of a novel and efficient inverse method for anisotropic material identification based on a complex-variable formulation of Airy stress function is presented. The overall equilibrium and compatibility, as well as the free traction along the boundary of the internal geometric cutouts, are analytically satisfied by means of conformal mapping and analytic continuation. The inverse problem is posed as an optimization problem where the objective functional is the difference between the measured data and its counterpart evaluated using the complex-variable method. Validity of the proposed inverse method is demonstrated by identifying the elastic constants of a loaded perforated orthotropic member from measured data originated in a region adjacent to a traction-free boundary. Both simulated in-plane displacement components that are superimposed with white noise scatter and experimental strain values were used to illustrate the effectiveness of the proposed method. Numerical experiments indicate that the proposed inverse procedure is capable of accurately characterizing material with large variation of initial estimates of the elastic constants. This alleviates the problem of not knowing a priori the values of the elastic constants. The need to use only few measured data close to the hole boundary and without full-knowledge of the distant geometry and boundary conditions are some advantages of the proposed inverse procedure.