Thermorheologically simple materials: A bayesian framework for model calibration and validation

Abstract

The dynamic properties of viscoelastic materials show highly frequency-temperature dependency and numerical methods for structural systems containing this type of material require accurate mathematical models to describe their dynamical behaviour. The material behaviour here is modelled using a constitutive equation based on fractional derivative operators and considering the temperature dependence of the material under the thermorheologically simple postulate. The quest for information about the constitutive model parameters is phrased as a statistical inverse problem under the Bayesian framework. A Markov Chain Monte Carlo (MCMC) method is used to explore the posterior density of model parameters using measured data from dynamic tests at different temperatures. The agreement between measured data and the predictive capabilities of sixteen models were quantitatively assessed using two validation metrics. Based on the validation metrics analysis it is possible to conclude that the range of temperature of the calibration data set is a key-point into the implementation of the Frequency Temperature Superposition Principle (FTSP). This was verified defining some scenarios for assessing the agreement of model predictions and the set of available experimental data. The results are quite compelling due to the fact that the proposed approach is easy-handed. Furthermore, this approach could be applied on any generic constitutive model using the FTSP.