In the framework of solid mechanics, the task of deriving material parameters from experimental data has recently reemerged with the progress in full-field measurement capabilities and the renewed advances of machine learning. In this context, new methods such as the virtual fields method and physics-informed neural networks have been developed as alternatives to the already established least-squares and finite element-based approaches. Moreover, model discovery problems are emerging and can be addressed in a parameter estimation framework. These developments call for a new unified perspective, which is able to cover both traditional parameter estimation methods and novel approaches in which the state variables or the model structure itself are inferred as well. Adopting concepts discussed in the inverse problems community, we distinguish between all-at-once and reduced approaches. With this general framework, we are able to structure a large portion of the literature on parameter estimation in computational mechanics—and we can identify combinations that have not yet been addressed, two of which are proposed in this paper. We also discuss statistical approaches to quantify the uncertainty related to the estimated parameters, and we propose a novel two-step procedure for identification of complex material models based on both frequentist and Bayesian principles. Finally, we illustrate and compare several of the aforementioned methods with mechanical benchmarks based on synthetic and experimental data.

In this study, the monotonic and cyclic material properties of steel material of medium static strength produced additively in the wire arc additive manufacturing (WAAM) process were investigated. This investigated material is expected to be particularly applicable to the field of mechanical engineering, for which practical applications of the WAAM process are still pending and for which hardly any characteristic values can be found in the literature so far. The focus of the investigation was, on the one hand, to determine how the material characteristics are influenced by the load direction in relation to the layered structure and, on the other hand, how they are affected by different interlayer temperatures. For this purpose, monotonic tensile tests were carried out at room temperature as well as at elevated temperatures, and the cyclic material properties were determined. In addition, the hardness of the material and the residual stresses induced during production were measured and compared. In addition to the provision of characteristic properties for the investigated material, it was aimed to determine the extent to which the interlayer temperature influences the strength characteristics, since this can have a considerable influence on the production times and, thus, the economic efficiency of the process.