Computational homogenization of nonlinear elastic materials using neural networks

By B. A. Le, Julien Yvonnet, Qi-Chang He. 2015

362 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/9fc28c917001cef72e0340723912e60706fc0af3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Paris Perdikaris
2. Ellen Kuhl
3. Qizhi He
4. Jiun-Shyan Chen
5. Zeliang Liu
6. G. Em Karniadakis
7. Wing Kam Liu
8. Wei Chen

In Mechanics of Materials

1. Jiun-Shyan Chen
2. Qizhi He
3. Wing Kam Liu
4. Kun Wang
5. Zeliang Liu
6. Suvranu De
7. C. Brinson
8. Yu-Chin Chan

Citations in the corpus

• Deep convolutional neural networks for eigenvalue problems in mechanics (2018, background): “More traditionally, the mechanics community has been using MLPs for various pattern recognition tasks and computations for several decades now [18, 19, 20, 21, 22].”
• Meta-modeling game for deriving theoretical-consistent, micro-structural-based traction-separation laws via deep reinforcement learning (2018, methodology): “Data-driven models such as Le et al. [2015], Bessa et al. [2017], Versino et al. [2017], Kafka et al. [2018] and Wulfinghoff et al. [2018] attempted to overcome this issue via supervised machine learning (e.g. neural network [Lefik and Schrefler, 2002], symbolic regression model [Versino et al.,…”
• A Physics-Constrained Data-Driven Approach Based on Locally Convex Reconstruction for Noisy Database (2019, background): “[23] B.”
• A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality (2017, methodology): “The recent work of Yvonnet and co-workers [12–14] is of particular importance to this article because it demonstrated for the first time that a data-driven framework can be used to determine the constitutive law of nonlinear elastic heterogeneous materials.”
• Globally Approximate Gaussian Processes for Big Data With Application to Data-Driven Metamaterials Design (2019, methodology): “(cid:129) Ex1: (cid:129) Ex2 [52]: (cid:129) Ex3 [53]: (cid:129) Ex4 [54]: Tr ( ε ) , (cid:129) Ex5 [53]: For each example, two independent and unique datasets of size 30,000 are generated with Sobol sequence [50], where the fi rst one is used for training and the second for validation.”
• Geometric deep learning for computational mechanics Part I: Anisotropic Hyperelasticity (2020, background): “The concept of learning a free energy function as a mean to describe multi-scale materials has been previously explored (Le, Yvonnet, and He, 2015; Teichert, Natarajan, Van der Ven, and Garikipati, 2019).”
• Multiscale modeling meets machine learning: What can we learn? (2019, methodology): “systems. Machine learning methods have recently permeated into composites research and materials design for example to enable the homogenization of representative volume elements with neural networks [94, 63, 65, 55] or the solution of high-dimensional partial dierential equations with deep learning”
• Three-dimensional convolutional neural network (3D-CNN) for heterogeneous material homogenization (2020, methodology): “Le et al. [46] proposed a decoupled computational homogenization approach for nonlinear elastic materials using NN to approximate the effective potential.”
• Computational microstructure characterization and reconstruction: Review of the state-of-the-art techniques (2018, methodology): “Because for most composites the general form of the constitutive law is unknown, it is necessary to rely on direct numerical simulation (DNS) techniques [278–280] in multiscale FEA.”