Machine Learning Seminar presentation
Topic: Data-driven constitutive laws for hyperelasticity modeling in eigenspace using algorithmic differentiation coupling FEniCS-Pytorch model: application to RVEs
Speaker: Minh Vu Chau, FSTM, University of Luxembourg
Time: Wednesday, 2021.02.17, 10:00 CET
How to join: Please contact Jakub Lengiewicz
Macroscale constitutive behavior of heterogeneous hyperelastic materials can be obtained from the microstructure by a homogenization process using multilevel finite elements (FE2) analysis. Although various advancements have been made, FE2 still remains a computationally expensive method. Alternatively, artificial neural networks (ANN) have been proposed as an efficient data-driven method for constitutive modeling, accepting either synthetic data from computational homogenization solutions or experimental datasets. In this presentation, we would like to introduce the Neural Network in which the constitutive relation of hyperelastic materials is achieved via computational homogenization, and is independent upon the used coordinate system.
At the microscopic scale, a synthetic training dataset is acquired from numerical simulation of RVE using the FEniCS framework. Subsequently, a multivariable regression analysis using ANN is conducted with eigenvalues of strain-stress pairs used as inputs and outputs. After successful training, this ANN is then plugged back into the algorithmic differentiation framework by embedding Pytorch inside FeniCS which creates a coupling symbolic FEniCS-Pytorch model such that it will capture the constitutive relationship of the material. Some technical notes on how to successfully combine multiple sub-losses functions into one total loss are also discussed if we have enough time.