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：历史依赖本构模型是微观力学聚合效应的宏观闭合表达，其参数通常通过实验数据学习。在有限实验预算下，获取表征本构关系所需的全部响应范围可能较为困难，导致数据能被多种参数组合合理解释，进而产生不确定或不可靠的参数估计。为解决这一问题，我们提出了一种贝叶斯最优实验设计框架，用于量化、解释并最大化实验设计在历史依赖本构模型可靠学习中的效用。该框架将设计效用定义为参数不确定性的期望降低或期望信息增益，从而能够利用模拟数据进行计算机内设计优化，减少可靠参数识别所需物理实验的成本。我们引入两种近似方法，使该框架适用于具有昂贵正向模型和高维数据的先进材料测试：(i) 期望信息增益的高斯近似，以及(ii) 费舍信息矩阵的替代模型近似。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，将方法扩展至批量设计优化。针对粘弹性固体的单轴实验数值研究表明，相较于随机设计，优化后的试样几何形状与加载路径所获得的图像及力数据显著提升了参数可辨识性，尤其涉及记忆效应的参数。