Identification of the thermal conductivity tensor for transversely isotropic materials

Abstract

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.

Parameter identification and uncertainty quantification of the thermal conductivity tensor for transversely isotropic composite materials

“…5. It is noteworthy that the computed uncertainties in this work slightly differ from the ones in [2], since the uncertainties were there computed under the assumption that the quality measures can be computed based on the full Hessian matrix. As pointed out by [4, App.…”

“…In this contribution, experimental full-field temperature data, which is measured by drawing on infrared thermography, is employed in a nonlinear least-squares scheme to identify the two coefficients of the thermal conductivity tensor for transversely isotropic composite materials. The respective approach was originally presented by the authors as NLS-TG/FEM approach, see [2], where also the specific experimental setup and the preparation of the measured full-field temperature data are described. To optimize the experimental setup for ensuring identifiability as well as minimizing the correlation between the material parameters, a numerical sensitivity analysis is performed first.…”

“…The temperature of the surrounding fluid Θ ∞f and the temperature of surrounding surfaces Θ ∞s are set equal to the ambient temperature during the experiments, Θ ∞f = Θ ∞s = Θ ∞ = 22.5 • C. After the spatial discretization, because of the consideration of radiation and convection, a system of nonlinear equations has to be solved. For further details regarding the finite element model, we refer to[2].To evaluate the correlation between both thermal conductivities, the correlation matrix C is chosen. Here, the linear correlation coefficient C 12 is a proper estimation for the correlation between both parameters.…”

Full-field validation of finite cell method computations on wire arc additive manufactured components

“…( 15) may result in unphysical parameters, which is often caused by experimental observations that do not properly address all the parameters. This is related to the concept of local identifiability, see [18] for general remarks and [10,43] for certain applications of local identifiability during material parameter identification.…”

Special Issue on Experimental Solid Mechanics

“…In the first issue of this special volume, four contributions are compiled proposing (1) a shear evaluation tool using digital image correlation (DIC) for plane problems [5], the coupling of infrared thermography (IRT) and 3D DIC for both (2) identifying material parameters in metal plasticity [6] as well as (3) applicability studies of foams and auxetic materials [3], and, finally, (4) identifying the heat conductivity parameters in transversal isotropy using IRT [8].…”