Identification of the thermal conductivity tensor for transversely isotropic materials

The knowledge of the thermal conductivities is of particular interest for the thermo-mechanical modeling of transversely isotropic composite materials. Hence, the identification of these material parameters by solving an inverse problem is significant, as they cannot be directly measured. In this study, a suitable experimental setup is presented, where infrared thermography is used to measure the surface temperatures of thin specimens. Further, a local identifiability concept is employed to study whether locally unique parameters can be obtained. This leads to a particular step-wise identification concept. The parameter identification is performed applying a nonlinear least-square approach and finite elements. In the step-wise identification process the convection coefficient is required first, and, subsequently, the coefficients of the thermal conductivity tensor are determined. Due to the step-wise identification, the uncertainties of previously identified parameters have to be considered in the subsequent identification steps. The resulting uncertainties are estimated using the Gaussian error propagation concept. It turns out that the thermal conductivities of transversely isotropic materials are generally identifiable from surface temperature data. Furthermore, since all uncertainties have an essential influence on the results of real numerical simulations, their error propagation should be considered in resulting boundary-value problems. Thus, the uncertainty quantification is demonstrated by a validation experiment.