Lu Zhang

Human tissues are highly organized structures with collagen fiber arrangements varying from point to point. Anisotropy of the tissue arises from the natural orientation of the fibers, resulting in location-dependent anisotropy. Heterogeneity also plays an important role in tissue function. It is therefore critical to discover and understand the distribution of fiber orientations from experimental mechanical measurements such as digital image correlation (DIC) data. To this end, we introduce the Heterogeneous Peridynamic Neural Operator (HeteroPNO) approach for data-driven constitutive modeling of heterogeneous anisotropic materials. Our goal is to learn a nonlocal constitutive law together with the material microstructure, in the form of a heterogeneous fiber orientation field, from load-displacement field measurements. We propose a two-phase learning approach. First, we learn a homogeneous constitutive law in the form of a neural network-based kernel function and a nonlocal bond force. This captures the complex homogeneous material responses from data. Second, we reinitialize the learnt bond force and train it together with the kernel and the fiber orientation field for each material point. Due to the inherent properties of the state-based peridynamic framework that we use, our HeteroPNO-learned material models are guaranteed to be objective and to satisfy the balances of linear and angular momenta. The effects of heterogeneity and the nonlinearity of the constitutive relationship are captured by the nonlocal kernel function, enabling physical interpretability. These features enable our HeteroPNO architecture to learn a constitutive model for biological tissue with anisotropic, heterogeneous response undergoing large deformation. To demonstrate the applicability of our approach, we apply the HeteroPNO in learning a material model and fiber orientation field from DIC measurements in biaxial testing. We evaluate the learnt fiber architecture, which is found to be consistent with observations from polarized spatial frequency domain imaging. The framework is capable of providing displacement and stress field predictions for new and unseen loading instances.

Multifunctional metamaterials (MMM) bear promise as next-generation material platforms supporting miniaturization and customization. Despite many proof-of-concept demonstrations and the proliferation of deep learning assisted design, grand challenges of inverse design for MMM, especially those involving heterogeneous fields possibly subject to either mutual meta-atom coupling or long-range interactions, remain largely under-explored. To this end, we present a data-driven design framework, which streamlines the inverse design of MMMs involving heterogeneous fields. A core enabler is implicit Fourier neural operator (IFNO), which predicts heterogeneous fields distributed across a metamaterial array, thus in general at odds with homogenization assumptions, in a parameter-/sample-efficient fashion. Additionally, we propose a standard formulation of inverse problem covering a broad class of MMMs, and gradient-based multitask concurrent optimization identifying a set of Pareto-optimal architecture-stimulus (A-S) pairs. Fourier multiclass blending is proposed to synthesize inter-class meta-atoms anchored on a set of geometric motifs, while enjoying training-free dimension reduction and built-it reconstruction. Interlocking the three pillars, the framework is validated for light-bylight programmable plasmonic nanoantenna, whose design involves vast space jointly spanned by quasi-freeform supercells, maneuverable incident phase distributions, and conflicting figure-of-merits involving on-demand localization patterns. Accommodating all the challenges without a-priori simplifications, our framework could propel future advancements of MMM.