Physics-Informed Deep-Learning For Elasticity: Forward, Inverse, and Mixed Problems

Identifying constitutive parameters for complex hyperelastic materials using physics-informed neural networks

Identifying constitutive parameters in engineering and biological materials, particularly those with intricate geometries and mechanical behaviors, remains a longstanding challenge. The recent advent of physics-informed neural networks (PINNs) offers promising solutions, but current frameworks are often limited to basic constitutive laws and encounter practical constraints when combined with experimental data. In this paper, we introduce a robust PINN-based framework designed to identify material parameters for soft materials, specifically those exhibiting complex constitutive behaviors, under large deformation in plane stress conditions. Distinctively, our model emphasizes training PINNs with multi-modal synthetic experimental datasets consisting of full-field deformation and loading history, ensuring algorithm robustness even with noisy data. Our results reveal that the PINNs framework can accurately identify constitutive parameters of the incompressible Arruda-Boyce model for samples with intricate geometries, maintaining an error below 5%, even with an experimental noise level of 5%. We believe our framework provides a robust modulus identification approach for complex solids, especially for those with geometrical and constitutive complexity.

Machine learning-enabled forward prediction and inverse design of 4D-printed active plates

Shape transformations of active composites (ACs) depend on the spatial distribution of constituent materials. Voxel-level complex material distributions can be encoded by 3D printing, offering enormous freedom for possible shape-change 4D-printed ACs. However, efficiently designing the material distribution to achieve desired 3D shape changes is significantly challenging yet greatly needed. Here, we present an approach that combines machine learning (ML) with both gradient-descent (GD) and evolutionary algorithm (EA) to design AC plates with 3D shape changes. A residual network ML model is developed for the forward shape prediction. A global-subdomain design strategy with ML-GD and ML-EA is then used for the inverse material-distribution design. For a variety of numerically generated target shapes, both ML-GD and ML-EA demonstrate high efficiency. By further combining ML-EA with a normal distance-based loss function, optimized designs are achieved for multiple irregular target shapes. Our approach thus provides a highly efficient tool for the design of 4D-printed active composites.

Identifying heterogeneous micromechanical properties of biological tissues via physics-informed neural networks

The heterogeneous micromechanical properties of biological tissues have profound implications across diverse medical and engineering domains. However, identifying the full-field heterogeneous elastic properties of soft materials using traditional computational and engineering approaches is fundamentally challenging due to difficulties in estimating local stress fields. Recently, there has been a growing interest in using data-driven models to learn full-field mechanical responses such as displacement and strain from experimental or synthetic data. However, research studies on inferring the full-field elastic properties of materials, a more challenging problem, are scarce, particularly for large deformation, hyperelastic materials. Here, we propose a physics-informed machine learning approach to identify the elastic modulus distribution in nonlinear, large deformation hyperelastic materials. We evaluate the prediction accuracies and computational efficiency of physics-informed neural networks (PINNs) on inferring the heterogeneous material parameter maps across three nonlinear materials with structural complexity that closely resemble real tissue patterns, such as brain tissue and tricuspid valve tissue. Our improved PINN architecture accurately estimates the full-field elastic properties of three hyperelastic constitutive models, with relative errors of less than 5% across all examples. This research has significant potential for advancing our understanding of micromechanical behaviors in biological materials, impacting future innovations in engineering and medicine.

Maximizing Triboelectric Nanogenerators by Physics-Informed AI Inverse Design

Triboelectric nanogenerators offer an environmentally friendly approach to harvesting energy from mechanical excitations. This capability has made them widely sought-after as an efficient, renewable, and sustainable energy source, with the potential to decrease reliance on traditional fossil fuels. However, developing triboelectric nanogenerators with specific output remains a challenge mainly due to the uncertainties associated with their complex designs for real-life applications. Artificial intelligence-enabled inverse design is a powerful tool to realize performance-oriented triboelectric nanogenerators. This is an emerging scientific direction that can address the concerns about the design and optimization of triboelectric nanogenerators leading to a next generation nanogenerator systems. This perspective paper aims at reviewing the principal analysis of triboelectricity, summarizing the current challenges of designing and optimizing triboelectric nanogenerators, and highlighting the physics-informed inverse design strategies to develop triboelectric nanogenerators. Strategic inverse design is particularly discussed in the contexts of expanding the four-mode analytical models by physics-informed artificial intelligence, discovering new conductive and dielectric materials, and optimizing contact interfaces. Various potential development levels of artificial intelligence-enhanced triboelectric nanogenerators are delineated. Finally, the potential of physics-informed artificial intelligence inverse design to propel triboelectric nanogenerators from prototypes to multifunctional intelligent systems for real-life applications is discussed.