Identification of thermal boundary conditions and the thermal expansion coefficient of a solid from deformation measurements

The aim of this study is to present an inverse thermomechanical methodology to identify thermal boundary conditions and the thermal expansion coefficient from experimental deformation measurements. By means of an analytical approach, we establish a thermoelastic mechanical transfer function between the temperature of a heated surface and the mechanical deformation of a solid at a given abscissa far from the surface. Subsequently, we measure this deformation at discrete time intervals using strain gauge and we apply a deconvolution product for those measurements to identify the temperature of the heated surface. By this way, it is no longer necessary to know the temperature field to solve the thermomechanical problem of our experimental device. We demonstrate that the inversion procedure can be applied successfully even in situations where the measured signal is affected by noise, through using the Tikhonov or a truncated singular value decomposition as regularization method. Lastly, the surface temperature identified from the deformation measurements is compared to a temperature measurement. The deformation and temperature measurements are used to estimate the thermal expansion coefficient. •An inverse problem to identify temperature from deformation measurements.•Identification using analytical transfer function and convolution product.•Regularization is implemented by using two technics: truncated singular value decomposition and the Tikhonov penalization.