Fadi Aldakheel

Nima Noii, Fadi Aldakheel, Thomas Wick et al.

This work addresses an efficient Global-Local approach supplemented with predictor-corrector adaptivity applied to anisotropic phase-field brittle fracture. The phase-field formulation is used to resolve the sharp crack surface topology on the anisotropic/non-uniform local state in the regularized concept. To resolve the crack phase-field by a given single preferred direction, second-order structural tensors are imposed to both the bulk and crack surface density functions. Accordingly, a split in tension and compression modes in anisotropic materials is considered. A Global-Local formulation is proposed, in which the full displacement/phase-field problem is solved on a lower (local) scale, while dealing with a purely linear elastic problem on an upper (global) scale. Robin-type boundary conditions are introduced to relax the stiff local response at the global scale and enhancing its stabilization. Another important aspect of this contribution is the development of an adaptive Global-Local approach, where a predictor-corrector scheme is designed in which the local domains are dynamically updated during the computation. To cope with different finite element discretizations at the interface between the two nested scales, a non-matching dual mortar method is formulated. Hence, more regularity is achieved on the interface. Several numerical results substantiate our developments.

Abedulgader Baktheer, Fadi Aldakheel

Accurate lifetime prediction of structures subjected to cyclic loading is vital, especially in scenarios involving non-uniform loading histories where load sequencing critically influences structural durability. Addressing this complexity requires advanced modeling approaches capable of capturing the intricate relationship between loading sequences and fatigue lifetime. Traditional fatigue simulations are computationally prohibitive, necessitating more efficient methods. This study highlights the potential of physics-based machine learning ($φ$ML) to predict the fatigue lifetime of materials. Specifically, a FFNN is designed to embed physical constraints from experimental evidence directly into its architecture to enhance prediction accuracy. It is trained using numerical simulations generated by a physically based anisotropic continuum damage fatigue model. The model is calibrated and validated against experimental fatigue data of concrete cylinder specimens tested in uniaxial compression. The proposed approach demonstrates superior accuracy compared to purely data-driven neural networks, particularly in situations with limited training data, achieving realistic predictions of damage accumulation. Thus, a general algorithm is developed and successfully applied to predict fatigue lifetimes under complex loading scenarios with multiple loading ranges. Hereby, the $φ$ML model serves as a surrogate to capture damage evolution across load transitions. The $φ$ML based algorithm is subsequently employed to investigate the influence of multiple loading transitions on accumulated fatigue life, and its predictions align with trends observed in recent experimental studies. This work demonstrates $φ$ML as a promising technique for efficient and reliable fatigue life prediction in engineering structures, with possible integration into digital twin models for real-time assessment.

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.

Yousef Heider, Fadi Aldakheel, Wolfgang Ehlers

This work introduces a novel application for predicting the macroscopic intrinsic permeability tensor in deformable porous media, using a limited set of micro-CT images of real microgeometries. The primary goal is to develop an efficient, machine-learning (ML)-based method that overcomes the limitations of traditional permeability estimation techniques, which often rely on time-consuming experiments or computationally expensive fluid dynamics simulations. The novelty of this work lies in leveraging Convolutional Neural Networks (CNN) to predict pore-fluid flow behavior under deformation and anisotropic flow conditions. Particularly, the described approach employs binarized CT images of porous micro-structure as inputs to predict the symmetric second-order permeability tensor, a critical parameter in continuum porous media flow modeling. The methodology comprises four key steps: (1) constructing a dataset of CT images from Bentheim sandstone at different volumetric strain levels; (2) performing pore-scale simulations of single-phase flow using the lattice Boltzmann method (LBM) to generate permeability data; (3) training the CNN model with the processed CT images as inputs and permeability tensors as outputs; and (4) exploring techniques to improve model generalization, including data augmentation and alternative CNN architectures. Examples are provided to demonstrate the CNN's capability to accurately predict the permeability tensor, a crucial parameter in various disciplines such as geotechnical engineering, hydrology, and material science. An exemplary source code is made available for interested readers.