Holistic estimation and sensitivity-based experiment design method of composite laminate first-ply failure models using statistical approaches

In this paper, a probabilistic approach is presented to simultaneously evaluate all strength and additional fitting parameters of a pre-selected composite first-ply failure model using known uniaxial and multiaxial failure stress states. The method processes all available mechanical test results in terms of failure stress states as one batch of data. For parameter fitting it implements the Maximum Likelihood Method and controlled numerical sampling techniques. The present work introduces the theoretical background as well as investigates the effect of the selection of the underlying strength distribution function type. The biggest benefit of this approach is the simultaneous handling of all available test data as well as the generality in terms of assumed strength distribution function and failure model type. In addition, the automatic evaluation of the uncertainty of all strength parameters enables introduction of a safety factor quantification related to uncertainty in material properties as one of the main contributors to scatter sources. A local sensitivity-based stress-state determination process is also introduced to design a set of input failure stresses that guarantee the identifiability of all parameters thus, ensuring robustness of the fitted constants. The entire methodology is demonstrated through the example of the Tsai-Wu model by processing experimental data and by comparing the results against the literature.