Open Research Projects

Computational material modelling using advanced numerical techniques speeds up the design process and reduces the costs of developing new products. In the field of multi-scale modelling of heterogeneous materials, the well-established homogenisation techniques remain computationally expensive for high accuracy levels. In this project, a machine learning approach, namely the Convolutional Neural Network (CNN), is intended as a solution providing a high level of accuracy, while being computationally efficient. First step in that direction has been done previously [1] in our own group. The data set for training and testing the CNN consists of images of real micro-structures (input). Whereas, the output is the homogenised stiffness components of a given representative volume element (RVE). So far, most research in this area has mainly focused on micro-structures with isotropic components and linear elastic response.

Imaging techniques such as Electron Backscatter Diffraction (EBSD), allow the visualisation of complex crystalline structures, with their orientation in space, and motivate an extension of these CNN models to more complex micro-structures.

Thus, machine learning approaches are planned within this project for non-/linear in-/elastic anisotropic crystalline RVEs (randomly oriented in space). Hereby, the independent components of the stiffness matrix will be predicted. Furthermore, the applicability of data augmentation will be investigated to increase the available real data set and at the same time improve the generalisation capability.

Literature:

[1] F. Aldakheel, C. Soyarslan, H. S. Palanisamy, E. S. Elsayed [2023]: Machine Learning Aided Multiscale Magnetostatics, arXiv preprint arXiv:2301.12782

Fatigue is a major issue in structural engineering systems. The model-based prediction of fatigue and failure under uncertain conditions via physical based computation methods, e.g. FEM, is still a challenging task. First steps in that direction have been done previously [1,2,3] in our own group. This project is intended for further improvement of these methods. Sophisticated and goal-oriented model order reduction schemes will be developed to predict high cycle fatigue based on continuum damage mechanics concepts implemented in Finite Element Methods (high-fidelity models), which perhaps can be treated as a black-box. Besides the material properties, the loading conditions as well as the damage evolution itself will be assumed to be uncertain (e.g. random-fields or random-processes). Besides scales in space, e.g. heterogeneous meso-structures, scales in time, e.g. few random load cycles up to 10x-load cycles will be considered.

In this project, besides the physical modelling of fatigue damage in the framework of Finite Element Methods, sophisticated model order reduction techniques will be further developed in a goal-oriented manner.

Literature:

• [1] Mainak Bhattacharyya, Amélie Fau, Rodrigue Desmorat, Shadi Alameddin, David Néron, Pierre Ladevèze, Udo Nackenhorst, A kinetic two-scale damage model for high-cycle fatigue simulation using multi-temporal Latin framework, European Journal of Mechanics - A/Solids, Volume 77, 2019, 103808, ISSN 0997-7538, doi.org/10.1016/j.euromechsol.2019.103808.
• [2] Alameddin, S., Fau, A., Néron, D., Ladevèze, P., & Nackenhorst, U. (2019). Toward optimality of proper generalised decomposition bases. Mathematical and computational applications, 24(1), 30.
• [3] Zhang, W., Fau, A., Nackenhorst, U., Desmorat, R. (2020). Stochastic Material Modeling for Fatigue Damage Analysis. In: Wriggers, P., Allix, O., Weißenfels, C. (eds). Virtual Design and Validation. Lecture Notes in Applied and Computational Mechanics, vol 93. Springer, Cham. doi.org/10.1007/978-3-030-38156-1_17

Particle methods (PM) define a family of numerical methods in computational mechanics whose discretization uses discrete entities (i.e., particles) rather than piecewise meshes. The mesh independence brings exceptional abilities for simulating large deformation and material transportation. Still, PM generally is much more computationally costly than mesh-based methods since their accuracy requires a fine particle-based discretization. Studies [1, 2, 3] have shown that PM can be combined with model order reduction (MOR) techniques to alleviate the constraint on computational efficiency. However, no computational framework has been rigorously built for combining these two methods because MOR has been primarily developed for either a Lagrangian or Eulerian grid system, which is partially or entirely missing in particle-based discretization. This discrepancy prevents the coalescence of MOR and PM by bringing three challenges: (i) sampling of discrete state variables, (ii) the extreme geometrical changes of computational domains, and (iii) conformity of boundary conditions.

In this project, we intend to construct a solid computational framework to resolve the first and second challenges and mitigate the last. Considering the nature of PM’s discretization, we carry out a dual model reduction based on both Lagrangian particles and, if necessary, a reconstructed Eulerian grid system, which will work synthetically for calculating the basis of the materials’ behaviours. Also, we improve the adaptive strategy to identify the computational domains for model reduction to be meaningfully carried out. Last, we explore the approximating methods for nonconforming boundary conditions. These developments will fill the knowledge gap for particle-based reduced order modelling.

Literature:

• [1] Boukouvala F, Gao Y, Muzzio F, Ierapetritou M (2013) Reduced order discrete element method modeling. Chemical Engineering Science 95:12–26
• [2] Lee C-H, Chen J-S (2013) Proper orthogonal decomposition-based model order reduction via radial basis functions for molecular dynamics systems. International Journal for Numerical Methods in Engineering 96(10):599–627
• [3] Wallin E, Servin M (2022). Data-driven model order reduction for granular media. Computational Particle Mechanics 9: 15-28