Simulation of hyperelastic materials in real-time using deep learning
Simulation of hyperelastic materials in real-time using deep learning
复制标题
DOI：
10.1016/j.media.2019.101569
复制
发表时间：
2020-01-01
影响因子：
10.9
通讯作者：
Cotin, Stephane
中科院分区：
文献类型：
--
作者：
Mendizabal, Andrea;Marquez-Neila, Pablo;Cotin, Stephane
有限元法是求解工程问题最常用的数值方法之一。由于其计算成本，已经引入了各种想法，以减少计算时间，如区域分解，并行计算，自适应网格，模型降阶。在本文中，我们提出了U-Mesh：一种基于U-Net架构的数据驱动方法，该架构近似于接触力和由FEM算法计算的位移场之间的非线性关系。我们证明，深度学习是基于人工神经网络的最新机器学习方法之一，可以通过其以紧凑形式编码高度非线性模型的能力来增强计算力学。我们的方法被应用到三个基准的例子：悬臂梁，L形和肝脏模型受到移动点状负载。并与本征正交分解（POD）方法进行了比较。结果表明，U-Mesh可以在各种几何形状和拓扑结构、网格分辨率和输入力的数量上进行非常快速的模拟，并且误差非常小。(C)2019 Elsevier B. V.版权所有。
The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition, parallel computing, adaptive meshing, and model order reduction. In this paper we present U-Mesh: A data-driven method based on a U-Net architecture that approximates the non-linear relation between a contact force and the displacement field computed by a FEM algorithm. We show that deep learning, one of the latest machine learning methods based on artificial neural networks, can enhance computational mechanics through its ability to encode highly nonlinear models in a compact form. Our method is applied to three benchmark examples: a cantilever beam, an L-shape and a liver model subject to moving punctual loads. A comparison between our method and proper orthogonal decomposition (POD) is done through the paper. The results show that U-Mesh can perform very fast simulations on various geometries and topologies, mesh resolutions and number of input forces with very small errors. (C) 2019 Elsevier B.V. All rights reserved.