Session: 13-19-01: Scientific Machine Learning (SciML) for Characterization, Modeling, and Design of Structures and Materials I

Paper Number: 173716

Physics-Informed Neural Network for Solid Mechanics Problems Involving Continuum Damage Model 

The Finite Element Method (FEM) has traditionally served as a powerful and versatile tool for solving a wide range of partial differential equations (PDEs), including those arising from solid mechanics problems for understanding and predicting the mechanical behavior of materials and structures under prescribed loading. In recent years, machine-learning (ML) and data-driven techniques have emerged as promising alternatives to finite element method for solving PDEs. We are particularly interested in Physics-Informed Neural Network (PINN), which has shown its promise in various scientific and engineering applications, such as fluid dynamics, solid mechanics, and material science. PINN is a type of neural network that combines the strengths of neural networks and physics-based equations and constitutive laws. It involves training a neural network to approximate the solution to a partial differential equation (PDE) by including the loss from governing equations and boundary conditions into the loss function, such that once the neural network is trained, both the boundary conditions and governing equations are satisfied. Since PINN directly learns the solution from data and incorporates the physics constraints during training, it is highly adaptable and can be applied to a wide range of problems without many changes between 2D and 3D formulations. Because of its mesh-free nature, it does not require mesh generation or remeshing, and handles complex geometries and adapts to irregular domains easily, which attracts increasing research interest. 

 

However, in the field of computational solid mechanics, PINNs are currently limited to simple linear elasticity, and their capability in modeling damage in materials and structures is limited. In this work, we develop a PINN and incorporate a continuum damage model (CDM) to simulate damage behavior in solids. In particular, Bonora’s nonlinear CDM model is well‑suited for ductile metals and is chosen for the current study, as it unifies nucleation, steady growth, and coalescence into a single evolution law and has been validated for alloys. The standard feed‑forward PINN enforces the PDEs, BCs, and damage evolution law via a composite loss and provides the same order of residual losses for each, ruling out the need for adaptive weighting of residuals. For the standard PINN, the normalized L2 error of damage grows dramatically over time, confirming the spectral bias of PINN. This trend depicts that the network is struggling to resolve the high‑frequency components of rapid damage increase beyond 0.3 strain. The FF‑PINN limits the error increase and constrains it to the order of 0.1% even at high strain rates. By embedding Fourier features to effectively address the PINN’s spectral bias and provide full‑range modeling of ductile damage evolution, this approach paves the way for failure prediction in complex loading scenarios and geometries.

Presenting Author: Xiang Zhang University of Wyoming

Presenting Author Biography: Dr. Xiang Zhang has been an Assistant Professor in the Mechanical Engineering Department at the University of Wyoming since 2019, leading the Computations for Advanced Materials and Manufacturing Laboratory. He earned his Ph.D. in Civil Engineering at Vanderbilt University, followed by a postdoctoral research experience in Aerospace Engineering at the University of Illinois at Urbana-Champaign. Zhang’s research interest is computational mechanics, with a particular focus on developing sophisticated multiscale/multiphysics methods in conjunction with data-driven techniques for the modeling, design, and manufacturing of high-performance materials and advanced manufacturing processes.

Authors:

Ikram Arif University of Wyoming
Min Lin University of Wyoming
Xiang Zhang University of Wyoming