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.

线性粘弹性本构理论通常表示为涉及四阶张量和延迟时间的 Prony 级数。从实验中获得此类本构模型中涉及的项的数值是一个不适定问题，因为许多参数集可以充分拟合实验数据。考虑到粘弹性结构响应的模拟所涉及的计算时间与粘弹性系数的数量成比例，设计产生最少参数数量的识别策略将是相当有意义的。我们在这项工作中提出了一个基于贝叶斯推理的框架来实现这一目标。我们已将我们的方法应用于三维实验数据，并在独立数据集上验证了所获得的本构理论，用于两种不同的粘弹性材料。我们的结果证明了我们方法的稳健性和充分性。