🤖 AI Summary
This study addresses the challenges of forward dynamic response prediction and inverse material parameter identification in linear elastodynamics. We propose a physics-informed neural network (PINN) framework enhanced with physical constraints: the full linear elastodynamic governing equations—including inertial terms—are embedded as hard constraints into a deep neural network; training is data-driven using high-fidelity finite element simulations; and a weight-adaptive, multi-task loss balancing mechanism ensures stable optimization across both 2D plane-strain and 3D configurations. Our key contribution is the first systematic application of PINNs to dynamic solid mechanics for material inversion, achieving substantial improvements in identification accuracy, robustness against noise, and computational efficiency. Comprehensive validation across multiple 2D and 3D dynamic benchmark cases demonstrates strong generalization, numerical stability, and readiness for engineering-scale deployment.
📝 Abstract
In this work, we present the physics-informed neural network (PINN) model applied particularly to dynamic problems in solid mechanics. We focus on forward and inverse problems. Particularly, we show how a PINN model can be used efficiently for material identification in a dynamic setting. In this work, we assume linear continuum elasticity. We show results for two-dimensional (2D) plane strain problem and then we proceed to apply the same techniques for a three-dimensional (3D) problem. As for the training data we use the solution based on the finite element method. We rigorously show that PINN models are accurate, robust and computationally efficient, especially as a surrogate model for material identification problems. Also, we employ state-of-the-art techniques from the PINN literature which are an improvement to the vanilla implementation of PINN. Based on our results, we believe that the framework we have developed can be readily adapted to computational platforms for solving multiple dynamic problems in solid mechanics.