Fully capturing this behavior in traditional homogenized tissue testing requires the excitation of multiple deformation modes, i.e. combined triaxial shear tests and biaxial stretch tests. Inherently, such multimodal experimental protocols necessitate multiple tissue samples and extensive sample manipulations. Intrinsic inter-sample variability and manipulation-induced tissue damage might have an adverse effect on the inversely identified tissue behavior. In this work, we aim to overcome this gap by focusing our attention to the use of heterogeneous deformation profiles in a parameter estimation problem. More specifically, we adapt EUCLID, an unsupervised method for the automated discovery of constitutive models, towards the purpose of parameter identification for highly nonlinear, orthotropic constitutive models using a Bayesian inference approach and three-dimensional continuum elements. We showcase its strength to quantitatively infer, with varying noise levels, the material model parameters of synthetic myocardial tissue slabs from a single heterogeneous biaxial stretch test. This method shows good agreement with the ground-truth simulations and with corresponding credibility intervals. Our work highlights the potential for characterizing highly nonlinear and orthotropic material models from a single biaxial stretch test with uncertainty quantification.

翻译：在传统的均质化组织测试中，要完全捕捉这种行为需要激发多种变形模式，即结合三轴剪切试验和双轴拉伸试验。本质上，这种多模式实验方案需要多个组织样本和大量的样本操作。样本间固有的变异性以及操作引起的组织损伤可能对逆向识别的组织行为产生不利影响。在这项工作中，我们旨在通过将注意力集中在参数估计问题中利用非均匀变形场来克服这一局限。更具体地说，我们调整了EUCLID（一种用于自动发现本构模型的无监督方法），将其用于高度非线性、正交各向异性本构模型的参数识别，采用贝叶斯推断方法和三维连续体单元。我们展示了该方法在不同噪声水平下，从单一非均匀双轴拉伸试验中定量推断合成心肌组织板材料模型参数的能力。该方法与真实模拟结果及相应的可信区间显示出良好的一致性。我们的工作突显了通过单次双轴拉伸试验结合不确定性量化来表征高度非线性和正交各向异性材料模型的潜力。