Identifying heterogeneous elastic parameters from full-field measurements with reduced bases

Full-field measurements provide a large quantity of data to extract mechanical properties from experiments. Multiple methods have been developed to identify the properties of homogeneous materials. A strategy based on a covariance-weighted Equilibrium Gap Method and Karhunen-Loève modes is proposed to calibrate heterogeneous elastic parameters. The Equilibrium Gap Method has a low computational cost due to its quadratic cost function. An auto-correlation kernel and a correlation length are assumed to generate modes for identifying heterogeneous material properties. The generated modes are used to determine contrast fields with respect to a macroscopic anisotropic stiffness tensor. The uncertainties on the identified parameters are quantified. The method is tested on a biaxial test on a composite material. The optimal choice for the size of the reduced basis depends on measurement uncertainties. Heuristics based on measurement uncertainties, residual discrepancy and parameter uncertainties are proposed to guide this choice.