USE OF DIGITAL IMAGE CORRELATION AND FINITE ELEMENT METHOD TO SOLVE INVERSE PROBLEM USING DISPLACEMENT FIELDS.

Resumo

One of the most common problems in solids mechanics is the determination of displacement,
strain and/or stress fields of a sample, given the geometry, constitutive parameters and boundary
conditions. This problem is known as Direct Problems, being solved numerically by techniques such as
the Finite Element Method (FEM). In this work, however, it is explored how to solve the inverse
problem. To calculate the constituent parameters of the sample, we use the displacement fields obtained
with a Digital Image Correlation (DIC) algorithm. Then, FEM simulations are performed using the same
geometry, loading, boundary conditions and an arbitrary set of elastic parameters (Young's Modulus and
Poisson's Coefficient). Displacement data measured via DIC serves as a reference in an optimization
algorithm that minimizes the difference between the FEM and DIC offset data set using the initial FEM
simulation as kickstart and updating the set of constituent material parameters for subsequent iterations.
Material parameters are obtained when the optimization is completed, and the two displacement fields
are close enough. At the end of the work, numerical examples are presented and compared with those
obtained by the Finite Element Method Updating (FEMU), which works with deformations states.