Yousef Heider

Yuqing He, Yousef Heider, Bernd Markert

This manuscript presents a practical method for incorporating trained Neural Networks (NNs) into the Finite Element (FE) framework using a user material (UMAT) subroutine. The work exemplifies crystal plasticity, a complex inelastic non-linear path-dependent material response, with a wide range of applications in ABAQUS UMAT. However, this approach can be extended to other material behaviors and FE tools. The use of a UMAT subroutine serves two main purposes: (1) it predicts and updates the stress or other mechanical properties of interest directly from the strain history; (2) it computes the Jacobian matrix either through backpropagation or numerical differentiation, which plays an essential role in the solution convergence. By implementing NNs in a UMAT subroutine, a trained machine learning model can be employed as a data-driven constitutive law within the FEM framework, preserving multiscale information that conventional constitutive laws often neglect or average. The versatility of this method makes it a powerful tool for integrating machine learning into mechanical simulation. While this approach is expected to provide higher accuracy in reproducing realistic material behavior, the reliability of the solution process and the convergence conditions must be paid special attention. While the theory of the model is explained in [Heider et al. 2020], exemplary source code is also made available for interested readers [https://doi.org/10.25835/6n5uu50y]

Phu Thien Nguyen, Yousef Heider, Dennis M. Kochmann et al.

The ultimate aim of the study is to explore the inverse design of porous metamaterials using a deep learning-based generative framework. Specifically, we develop a property-variational autoencoder (pVAE), a variational autoencoder (VAE) augmented with a regressor, to generate structured metamaterials with tailored hydraulic properties, such as porosity and permeability. While this work uses the lattice Boltzmann method (LBM) to generate intrinsic permeability tensor data for limited porous microstructures, a convolutional neural network (CNN) is trained using a bottom-up approach to predict effective hydraulic properties. This significantly reduces the computational cost compared to direct LBM simulations. The pVAE framework is trained on two datasets: a synthetic dataset of artificial porous microstructures and CT-scan images of volume elements from real open-cell foams. The encoder-decoder architecture of the VAE captures key microstructural features, mapping them into a compact and interpretable latent space for efficient structure-property exploration. The study provides a detailed analysis and interpretation of the latent space, demonstrating its role in structure-property mapping, interpolation, and inverse design. This approach facilitates the generation of new metamaterials with desired properties. The datasets and codes used in this study will be made open-access to support further research.