# Investigating Bayesian Parameter Identification Using Non-Standard Laboratory Specimens
## 1 Introduction  
Numerical models are essential tools in engineering for analyzing complex physical processes, including both linear and nonlinear material behaviors [1]. While they are traditionally used to simulate the performance of future structures and systems, their application also extends to advanced tasks, such as reliability assessment [2], remaining useful life (RUL) prediction [3, 4], and system-level optimization [5] for existing structures. The predictive performance of these models depends on how accurately they represent the underlying physical phenomena, which is influenced by the selected approximations and parameter choices [6, 7]. In particular, material behavior, governed by constitutive laws, is sensitive to these input parameters, which play a critical role in analyzing the underlying physical processes [8]. These parameters are typically determined through experimental testing, which includes both standardized and non-standardized procedures. While standardized tests provide baseline values suitable for general use, non-standard tests are often required to investigate localized phenomena and nonlinear behavior. However, the parameters obtained from such tests are highly sensitive to size effect and specimengeometry, which can complicate the interpretation and limit the general applicability of the derived parameters. This work focuses on the identification of input parameters that govern the elastic, plastic hardening, and failure behavior of aluminum alloy specimens. Some parameters may reflect intrinsic material properties, while others may be model-dependent, relying on the specific type of model. To identify these parameters, this work goes beyond standardized laboratory tests by examining non-standard tests using notched specimens, which introduce stress concentrations and weaken the material. To extract these parameters from non-standard tests, a Bayesian inverse procedure [6,9] is applied with an embedded strong discontinuity Q6 ED model [10,11] on laboratory samples tested until failure. Furthermore, the study demonstrates the capability of Bayesian identification to derive material parameters from experimental tests not originally intended for their targeted calibration, or when it is not possible to test ideal specimens. The process of determining parameter values to align model predictions with experimental measurements of a particular problem is known as parameter identification or model calibration [6,8], which aims to find parameters independent of sample size, geometry, and boundary conditions to ensure the applicability of the model to a wide range of engineering problems [8]. A traditional approach to parameter identification relies on standardized tests and direct laboratory measurements that are related to specific parameters. In the context of material failure, different tests are recommended to determine the necessary material parameters. For example, uniaxial tension and splitting tests are commonly used to determine material strength, while three and four-point notched bending tests are employed to evaluate fracture energy [12]. However, beyond the dependence on the test design, several challenges arise from this approach [12,13]. As numerical models are increasingly complex with a range of parameters, finding the proper measurements becomes challenging. Even when such measurements exist, the sheer volume of collected data can influence the results. For example, in [14], it was shown that fracture energy values depend on the timing of test termination. Additionally, the obtained results can also be affected by the nonlinear processes occurring within the material during testing. Stress concentrations caused by notches, holes and imperfections can lead to inaccuracies and the general applicability can thus be influenced by the size and shape of these notches [15,16].