This work is subjected to the development of a method to identify the elasticity tensor of homogeneous and heterogeneous materials. The materials are created in the form of checkerboards. We solved the direct problem to obtain the strain field using the finite element method, after obtaining this strain field, we created synthetic experimental displacement data by simulation. A re-calibration of the created experimental and simulated data is done based on the principle of the finite element model updating (FEMU), used in almost all domains, in the inverse problem. The minimization of the cost function obtained by FEMU is done by Levenberg-Marquardt algorithm which is very fast and elegant algorithm. A complete study has been done by studying the sensitivity of the identified values with respect to the refinement of the mesh and with respect to the level of disturbance.

The aim of this study is to identify simultaneously the thermal conductivity tensor and the heat capacity per unit volume of a bimaterial, whose heat conduction obeys Fourier’s law. This approach is validated by numerical simulation. The simulated temperature fields are obtained by the direct resolution of the heat conduction equation solved numerically with the help of finite element method formulation. To identify the parameters, an inverse method is developed by using the finite element model updating (FEMU) based on the Levenberg-Marquardt algorithm. This inverse finite element method approach allowed us to estimate the thermophysical parameters sought. We validated the numerical procedure by using noiseless temperature fields at different time and space steps and two types of material: an homogeneous and a bimaterial one. To be close to real conditions, the influence of the noise on the temperature fields is also studied and shows the efficiency of the inverse method. The results of this procedure show that the identified parameters are very less sensitive to the number of infra-red images varying from 40 to 80 and the number of elements ranging from 20 to 50 for a specimen size equals to 36.6 × 36.6 mm2.

The aim of this study is to identify simultaneously the thermal conductivity tensor and the volume heat coefficient of a bimaterial (checkerboard) whose heat conduction obeys Fourier's law. This approach is validated by numerical simulation. The simulated temperature fields are obtained by the direct resolution heat conduction solved numerically by the finite element method formulation. To identify parameters, an inverse method is developed by using the finite element temperature approach (FEU-T) model fitting method based on the Levemberg-Marquardt algorithm. We validated the numerical procedure by using noiseless temperature fields at different time and space steps. The influence of the noise on the temperature fields is also studied and shows the efficiency of the inverse method. The results show that this procedure is not very sensitive to the number of elements (or space steps) and the number of time steps.

This work is subjected to an identification of elasticity properties which are the Young’s modulus E and the Poisson’s ratio v of a heterogeneous material. We have created the experimental displacements by solving the direct problem. A re-calibration of the experimental and the simulated displacements is done based on the principle of the finite element model updating (FEMU). The minimization of the cost function obtained by the FEMU method in the inverse problem is done by Newton type algorithms. A complete study has been done by studying the sensitivity of the identified values with respect to the refinement of the mesh and with respect to the level of disturbance.