On the tri-dimensional constitutive theory identification of linearly viscoelastic solids based on Bayesian framework

Abstract

Linearly viscoelastic constitutive theories are usually expressed as a Prony series involving fourth order tensors and retardation times. Obtaining the numerical values of the terms involved in such constitutive models from experiments is an ill-posed problem in the sense that many parameter sets can adequately fit experimental data. Considering that the computational time involved in the simulation of the response of viscoelastic structures scales with the number of viscoelastic coefficients, it would be of considerable interest to devise identification strategies yielding the minimum number of parameters. We propose in this work a framework based on the Bayesian inference to reach this objective. We have applied our methodology to three-dimensional experimental data and validated the obtained constitutive theory on an independent data set, for two different viscoelastic materials. Our results demonstrated the robustness and adequacy of our method.