11th CISM-ECCOMAS Advanced course on "Parameter Identification Using Full-Field Measurements"

Full-field measurement techniques such as digital-image correlation or infrared thermography – and even digital volume correlation – provide spatially and temporally distributed displacement and temperature data. The course covers how camera systems and evaluation algorithms can be used to measure displacements, strains, and temperatures on or inside samples. These experimental data can be used for validation purposes of finite element simulations, or for the identification of material parameters of constitutive models. Therefore, the underlying structure of constitutive models will be addressed in (thermo-)elasticity, viscoelasticity, plasticity, and viscoplasticity, as well as their incorporation into finite element codes. One major focus of the course treats the question of how the material parameters can be determined from given experimental datasets. Different objective functions can be used to identify material parameters by forming minimization problems, for example, the classical least squares formulation, physical-informed neural networks, the virtual field method, and generalizations such as all-at-once approaches. Moreover, this course focuses particularly on the reliability of parameter determination and addresses Bayesian uncertainty quantification concepts to provide indicators of the quality of the parameters determined by some methods. Finally, the influence of the uncertain parameters is taken into account to validate the simulations, where the full-field measurements are chosen to compare – not only optically but defining metrics of deviations – the simulations with the data in the regions of interest. The course is structured in possible experiments, measurement techniques, design of specimens, full-field measurements, and filtering techniques. Then, the general structure of constitutive models of elasticity and inelasticity and their implementation into finite element programs is provided to solve discretized systems of equations associated with the underlying boundary-value problems to model experimental setups. These equations are treated within various parameter identification approaches (least-squares, neuronal networks, virtual fields method, equilibrium gap method, …). The reliability of parameter identification within both Bayesian and frequentist frameworks, together with the quantification of their associated uncertainties, is systematically examined. The course also addresses current limitations and problems of the approaches resulting from the experimental and theoretical points of view. The last part is devoted to illustrations and practical applications of various concepts introduced during the lectures.