Heterogeneous Peridynamic Neural Operators: Discover Biotissue Constitutive Law and Microstructure From Digital Image Correlation Measurements
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. 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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Peridynamic Neural Operators: A Data-Driven Nonlocal Constitutive Model for Complex Material Responses
Neural operators, which can act as implicit solution operators of hidden governing equations, have recently become popular tools for learning the responses of complex real-world physical systems. Nevertheless, most neura…
Monotone Peridynamic Neural Operator for Nonlinear Material Modeling with Conditionally Unique Solutions
Data-driven methods have emerged as powerful tools for modeling the responses of complex nonlinear materials directly from experimental measurements. Among these methods, the data-driven constitutive models present advan…
A data-driven peridynamic continuum model for upscaling molecular dynamics
Nonlocal models, including peridynamics, often use integral operators that embed lengthscales in their definition. However, the integrands in these operators are difficult to define from the data that are typically avail…
Beyond empirical models: Discovering new constitutive laws in solids with graph-based equation discovery
Constitutive models are fundamental to solid mechanics and materials science, underpinning the quantitative description and prediction of material responses under diverse loading conditions. Traditional phenomenological …
Learning Memory and Material Dependent Constitutive Laws
We propose and study a neural operator framework for learning memory- and material microstructure-dependent constitutive laws for heterogeneous materials. We work in the two-scale setting where homogenization theory prov…