Human tissues are highly organized structures with specific collagen fiber
arrangements varying from point to point. The effects of such heterogeneity
play an important role for tissue function, and hence it is of critical to
discover and understand the distribution of such fiber orientations from
experimental measurements, such as the digital image correlation data. To this
end, we introduce the heterogeneous peridynamic neural operator (HeteroPNO)
approach, for data-driven constitutive modeling of heterogeneous anisotropic
materials. The goal is to learn both a nonlocal constitutive law together with
the material microstructure, in the form of a heterogeneous fiber orientation
field, from loading field-displacement field measurements. To this end, we
propose a two-phase learning approach. Firstly, we learn a homogeneous
constitutive law in the form of a neural network-based kernel function and a
nonlocal bond force, to capture complex homogeneous material responses from
data. Then, in the second phase we reinitialize the learnt bond force and the
kernel function, and training them together with a fiber orientation field for
each material point. Owing to the state-based peridynamic skeleton, our
HeteroPNO-learned material models are objective and have the balance of linear
and angular momentum guaranteed. Moreover, the effects from heterogeneity and
nonlinear constitutive relationship are captured by the kernel function and the
bond force respectively, enabling physical interpretability. As a result, our
HeteroPNO architecture can learn a constitutive model for a biological tissue
with anisotropic heterogeneous response undergoing large deformation regime.
Moreover, the framework is capable to provide displacement and stress field
predictions for new and unseen loading instances.

我们介绍了异质的 Peridynamic 神经算子 (HeteroPNO) 方法，用于数据驱动的异质各向异性材料的本构建模。该方法可以从加载场 - 位移场测量中学习非局部本构定律和材料微结构，包括异质的纤维方向场，以实现生物组织的各向异性响应的本构模型学习和预测。