History-dependent constitutive models serve as macroscopic closures for the aggregated effects of micromechanics. Their parameters are typically learned from experimental data. With a limited experimental budget, eliciting the full range of responses needed to characterize the constitutive relation can be difficult. As a result, the data can be well explained by a range of parameter choices, leading to parameter estimates that are uncertain or unreliable. To address this issue, we propose a Bayesian optimal experimental design framework to quantify, interpret, and maximize the utility of experimental designs for reliable learning of history-dependent constitutive models. In this framework, the design utility is defined as the expected reduction in parametric uncertainty or the expected information gain. This enables in silico design optimization using simulated data and reduces the cost of physical experiments for reliable parameter identification. We introduce two approximations that make this framework practical for advanced material testing with expensive forward models and high-dimensional data: (i) a Gaussian approximation of the expected information gain, and (ii) a surrogate approximation of the Fisher information matrix. The former enables efficient design optimization and interpretation, while the latter extends this approach to batched design optimization by amortizing the cost of repeated utility evaluations. Our numerical studies of uniaxial tests for viscoelastic solids show that optimized specimen geometries and loading paths yield image and force data that significantly improve parameter identifiability relative to random designs, especially for parameters associated with memory effects.

翻译：历史相关本构模型作为微力学聚合效应的宏观闭合模型，其参数通常通过实验数据学习获得。在有限的实验预算下，要激发表征本构关系所需的全部响应范围可能较为困难。因此，数据可能被多种参数选择所解释，导致参数估计存在不确定性或不可靠性。为解决此问题，我们提出了一种贝叶斯最优实验设计框架，用于量化、解释和最大化实验设计在可靠学习历史相关本构模型中的效用。在该框架中，设计效用定义为参数不确定性的预期减少或预期信息增益。这使得利用模拟数据进行计算机内设计优化成为可能，并降低了可靠参数识别的物理实验成本。我们引入了两种近似方法，使该框架适用于具有昂贵正演模型和高维数据的先进材料测试：（i）预期信息增益的高斯近似，以及（ii）Fisher信息矩阵的代理近似。前者实现了高效的设计优化与解释，后者通过分摊重复效用评估的成本将该方法扩展至批量设计优化。我们对粘弹性固体单轴试验的数值研究表明，与随机设计相比，优化的试件几何形状与加载路径生成的图像和力数据能够显著改善参数可辨识性，尤其是与记忆效应相关的参数。