We present a novel, fully three-dimensional approach to soft material characterization and constitutive modeling with relevance to soft biological tissue. Our approach leverages recent advances in experimental techniques and data-driven computation. The experimental component of this approach involves in situ mechanical loading in a magnetic field (using MRI), yielding the entire deformation tensor field throughout the specimen regardless of the possible irregularities in its three-dimensional shape. Characterization can therefore be accomplished with data at a reduced number of deformation states. We refer to this experimental technique as MR-u. Its combination with powerful approaches to inverse modeling, specifically methods of model inference, would open the door to insightful mechanical characterization for soft materials. In recent computational advances that answer this need, we have developed new, data-driven inverse techniques to infer the model that best explains the physics governing observed phenomena from a spectrum of admissible ones, while maintaining parsimony of representation. This approach is referred to as Variational System Identification (VSI). In this communication, we apply the MR–u approach to characterize soft polymers regarding them as surrogates of soft biological tissue, and using VSI, we infer the physically best-suited and parsimonious mathematical models of their mechanical response. We demonstrate the performance of our methods in the face of noisy data with physical constraints that challenge the identification of mathematical models, while attaining high accuracy in the predicted response of the inferred models.

我们提出了一种新颖的，完全三维的方法来进行软材料表征和与软生物组织相关的本构模型。我们的方法利用了实验技术和数据驱动计算的最新进展。这种方法的实验部分涉及在磁场中的原位机械载荷（使用MRI），产生整个样品的整个形变张量场，而与三维形状中可能存在的不规则性无关。因此，可以用数量减少的变形状态的数据完成表征。我们将此实验技术称为MR- u。它与强大的逆建模方法（特别是模型推断方法）相结合，将为深入研究软材料的机械特性打开一扇门。在满足此需求的最新计算进展中，我们开发了新的，数据驱动的逆向技术，以推论该模型，该模型从一系列可容许的现象中最好地解释了控制观察到的现象的物理学，同时保持了表示的简约性。这种方法称为变体系统识别（VSI）。在本通讯中，我们应用MR– u表征软聚合物的方法，将它们视为软生物组织的替代物，并使用VSI推断出物理上最适合其机械响应的最简单数学模型。我们在面对带有物理约束的嘈杂数据的情况下证明了我们方法的性能，这些挑战对数学模型的识别提出了挑战，同时在推断模型的预测响应中获得了很高的准确性。