用物理约束神经网络模拟异质材料波传播,速度快精度高。
A Physics-Informed Neural Network Framework for Elastodynamic Wave Propagation in Bimaterial Systems

- 将弹性波动方程和边界条件融入损失函数,实现物理驱动建模。
- 预测结果与有限元仿真高度一致,误差可忽略,且能外推新时间点和材料参数。
- 适合需要快速分析冲击力学问题的研究者,尤其适用于高应变率场景。
物理信息神经网络(PINNs)为求解偏微分方程提供了一种融合物理定律的框架。本文提出一种基于PINN的模型,用于模拟轴对称线性弹性条件下双材料系统的瞬态弹性波传播。以典型Split Hopkinson压力杆结构的钢-铝试样为例,将控制方程及初始、边界、界面条件直接嵌入网络的物理损失函数中。利用ANSYS Workbench显式动力学进行高保真有限元仿真作为验证数据和训练补充约束。所提框架准确预测了跨界面波的透射与反射,复现了轴向和径向位移历程、面平均响应以及主导应力和应变演化,与有限元解高度吻合。训练后的网络可在无需额外有限元计算的前提下,预测未见时间点及不同材料属性下的波响应,形成连续代理模型。网格敏感性分析验证了数值鲁棒性,多种材料组合进一步证明方法普适性。结果表明,结合物理信息神经网络与显式有限元分析,可为非均质固体中的弹性波传播提供高效精确的替代建模方案,适用于高速固体力学与冲击工程应用。
原文摘要 · Abstract (English)
Physics-informed neural networks (PINNs) provide a promising framework for solving partial differential equations while embedding the underlying physical laws directly into the learning process. This study presents a PINN-based framework for modeling transient elastodynamic wave propagation in bimaterial systems governed by the axisymmetric equations of linear elasticity. A steel-aluminum specimen representative of a Split Hopkinson Pressure Bar configuration is considered, and the governing elastodynamic equations, together with the corresponding initial, boundary, and interface conditions, are incorporated directly into the network through a physics-informed loss function. High-fidelity finite-element simulations performed using ANSYS Workbench Explicit Dynamics are used for validation and as supplementary data constraints during training. The proposed framework accurately predicts wave transmission and reflection across the bimaterial interface and reproduces axial and radial displacement histories, face-averaged responses, and the dominant stress and strain evolution with close agreement to the finite-element solutions. The trained network further demonstrates the ability to predict wave responses at previously unseen time instants and for modified material properties without requiring additional finite-element simulations, providing a continuous surrogate model for elastodynamic analysis. Mesh-sensitivity studies confirm numerical robustness, while additional material combinations demonstrate the generality of the proposed methodology. The results show that integrating physics-informed neural networks with explicit finite-element analysis provides an accurate and computationally efficient framework for elastodynamic wave propagation in heterogeneous solids, offering an effective surrogate modeling approach for high-rate solid mechanics and impact engineering applications.
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