Innovative Application of Physics-Informed Neural Networks in Composite Laminated Theory

This article introduces the open-source project PINN_CLT, which applies Physics-Informed Neural Networks (PINN) to Classical Lamination Theory (CLT). By integrating physical constraints to solve composite material mechanics problems, it brings new possibilities to the fields of materials science and structural engineering. PINN minimizes both data fitting errors and residuals of physical control equations, enabling data-efficient and physically consistent predictions, especially with advantages in solving inverse problems.

Classical Lamination Theory (CLT) is the core framework of composite material mechanics. Since the mid-20th century, it has been the foundation of structural design in aerospace, automotive, and other fields, predicting the properties of laminated plates by superposing the mechanical behaviors of layers. Traditional CLT analysis relies on analytical solutions and finite elements, but faces challenges such as high computational cost and cumbersome iterative optimization in complex geometries, nonlinear materials, or inverse problems.

Unlike traditional neural networks, PINN minimizes both data fitting errors and residuals of physical control equations during training, and can output physically consistent results even with sparse data. In PINN_CLT, the equilibrium equations, constitutive relations, and boundary conditions of lamination theory are encoded as constraints in the loss function. Its advantages include: high data efficiency, physically consistent results, support for solving inverse problems, and provision of continuous solution representations.

The project is based on a deep learning framework, with a fully connected neural network as its core. It takes spatial coordinates (x,y,z) as input and outputs displacement components (u,v,w), using the tanh activation function in hidden layers. The loss function includes data fitting terms, control equation residual terms, boundary condition terms, and constitutive relation constraint terms, balancing multi-objective optimization through an adaptive weight strategy.

In the aerospace field, PINN can quickly evaluate the stress and deformation of composite laminated plates; in material characterization, it can infer the properties of layered materials through surface strain/displacement without destructive testing; it also supports uncertainty quantification, estimating the uncertainty range of prediction results through Bayesian PINN, providing a basis for reliability design.

PINN_CLT faces challenges such as low training efficiency (due to complex loss functions) and high-dimensional problems (curse of dimensionality caused by multiple layers). Future directions include multi-scale modeling, nonlinear expansion, experimental verification, and real-time applications (deploying embedded systems for structural health monitoring).

PINN_CLT is a microcosm of the integration of AI and traditional engineering, demonstrating the combination of domain knowledge and data-driven methods. With the advancement of deep learning technology, such physics-informed methods are expected to play a transformative role in materials science, fluid mechanics, and other fields, and are worthy of attention from composite material researchers.