Parameter identification using finite elements and full‐field data in the all‐at‐once context

Abstract

AbstractMaterial parameter identification within the field of mechanics of materials is driven by different issues: experiments affecting the parameters, constitutive models describing the physical behavior of a material, discretization schemes for solving the initial boundary‐value problem of the underlying tests, as well as schemes calibrating the parameters at experimental observations. Furthermore, the question of the quality of the parameters must be addressed. The result concerns the issue of which influence parameter uncertainties have on the uncertainty of simulation results and can be addressed during validation. In this contribution, we provide a short overview of concurrent approaches to identify the parameters, where most of the methods can be distinguished into the reduced formulation, which is based on the implicit function theorem, and a particular form of the all‐at‐once approach. The latter represents the weighted sum of two contributions, first, the distances between physical state equations and zero, and, second, the distance between model response (simulation result) and experimental data. Since the formulation of the all‐at‐once approach is not well‐known in computational solid mechanics, it is investigated for the simple example of linear elasticity employing artificially noised data. It turns out that the all‐at‐once approach is not as robust as the well‐established reduced approach, especially for problems considering full‐field data. Moreover, a strong sensitivity to the noise and the initialization of the optimized parameters are observed indicating a pronounced ill‐posedness of the all‐at‐once formulation for specific applications.