A deep energy method for finite deformation hyperelasticity

By Vien Minh Nguyen-Thanh, Xiaoying Zhuang, Timon Rabczuk. 2020

306 citations recorded by the source corpus.

Abstract We present a deep energy method for finite deformation hyperelasticitiy using deep neural networks (DNNs). The method avoids entirely a discretization such as FEM. Instead, the potential energy as a loss function of the system is directly minimized. To train the DNNs, a backpropagation dealing with the gradient loss is computed and then the minimization is performed by a standard optimizer. The learning process will yield the neural network's parameters (weights and biases). Once the network is trained, a numerical solution can be obtained much faster compared to a classical approach based on finite elements for instance. The presented approach is very simple to implement and requires only a few lines of code within the open-source machine learning framework such as Tensorflow or Pytorch. Finally, we demonstrate the performance of our DNNs based solution for several benchmark problems, which shows comparable computational efficiency such as FEM solutions.

Subfields: Biomedical Engineering, Mechanics of Materials, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2b2fefd30e43154c8469ce7897188b342e0acc0d

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In Biomedical Engineering

In Mechanics of Materials

In Statistical and Nonlinear Physics

Citations in the corpus

Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacture (2020, methodology): “Due to these advantages, many variations of the PINN approach have been successfully used to solve PDEs in a wide range of engineering applications [24, 29–37].”
Deep Autoencoder based Energy Method for the Bending, Vibration, and Buckling Analysis of Kirchhoff Plates (2020, methodology): “…methods, a variety of numerical methods have been developed including the ﬁnite element method [2, 3], boundary element method [4, 5], meshfree method [6, 7], isogeometric analysis (IGA) formulations [8], numerical manifold method [9, 10, 11] and recently deep learning based methods [12, 13, 14].”