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.

这项研究的目的是提出一种逆热机械方法，以从实验变形测量中识别热边界条件和热膨胀系数。通过分析的方法，我们在加热表面的温度与给定的横坐标远离表面的固体的机械变形之间建立了热弹性机械传递函数。随后，我们使用应变仪在不连续的时间间隔内测量该变形，并对这些测量应用去卷积积，以识别受热表面的温度。通过这种方式，不再需要知道温度场来解决我们实验装置的热机械问题。我们证明，通过使用Tikhonov或截​​断的奇异值分解作为正则化方法，即使在被测信号受噪声影响的情况下，该反演程序也可以成功应用。最后，将从变形测量结果确定的表面温度与温度测量结果进行比较。变形和温度测量值用于估算热膨胀系数。