Bayesian inference to identify parameters in viscoelasticity

Abstract

This contribution discusses Bayesian inference (BI) as an approach to identify parameters in viscoelasticity. The aims are (i) to show that the prior has a substantial influence for viscoelasticity, (ii) to show that this influence decreases for an increasing number of measurements and (iii) to show how different types of experiments influence the identified parameters and their uncertainties. The standard linear solid model is the material description of interest and a relaxation test, a constant strain-rate test and a creep test are the tensile experiments focused on. The experimental data are artificially created, allowing us to make a one-to-one comparison between the input parameters and the identified parameter values. Besides dealing with the aforementioned aims, we believe that this contribution forms a comprehensible start for those interested in applying BI in viscoelasticity.

A Tutorial on Bayesian Inference to Identify Material Parameters in Solid Mechanics

“…As these are both C 1 -continuous, their posteriors are also C 1 -continuous and hence, the MCMC algorithm to explore them is easier to implement than for elastoplasticity. The study of Rappel et al [25] shows that the effect of the prior on the mean and MAP point in viscoelasticity is larger than for elastoplasticity. The influence is especially larger for the damping parameter.…”

“…Additionally, BI provides an intrinsic statistical regularisation which makes inverse problems with limited observations solvable [11]. On the other hand, applying Bayes' theorem for material parameter identification does require the measurement noise to be 25 known, i.e. the noise distributions and their parameters must be established.…”

“…Rosić et al [23] used linear Bayesian updating via polynomial chaos expansion for an elastoplastic system. BI is also employed for the 45 identification of viscoelastic material parameters in [24,25].…”

“…(25) with s noise = 0.01 GPa. For only one stress measurement of y = 0.1576 GPa with corresponding strain = 7.25 × 10 −4 , the posterior distribution is calculated using σ π noise (ω)(a) Fitted noise distribution σ (b) The shifted noise distribution…”

Bayesian identification of Mean-Field Homogenization model parameters and uncertain matrix behavior in non-aligned short fiber composites

“…Starting from the work of [21], many works identified the parameters of material models through BI: elasticity constants of glass-fiber reinforced epoxy [22] and of carbon-epoxy unidirectional laminates [23] were inferred through vibration tests, and elasticity constants of graphite-epoxy laminates were identified from the displacement field in [24] through static tests; in the non-linear range, elasto-perfectly plastic model and cohesive zone parameters were inferred in [25], elasto-plastic material model parameters in [26,27], visco-elasticity constants in [28,29] and a hyperelastic model and its parameters in [30]; spatially varying, under the form of embedded inclusions, elasticity constants were identified in [31]; the list being non-exhaustive.…”