Plenary lectures

A Scaled Boundary Finite Element Framework for Fully Automated Computational Engineering Analysis

Chongmin Song¹

¹University of New South Wales, Australia, c.song@unsw.edu.au

Abstract

With the rapid development of modern computer technology, computational analysis has become indispensable in tackling large-scale complex problems faced by modern engineering. The Finite Element Method (FEM) is arguably the most popular method, with many commercial software packages available. The FEM requires discretizing geometric models into simple-shaped elements, a process often involving extensive manual operations, making it time-consuming and error-prone. Additionally, new digital modeling technologies introduce a variety of geometric model formats, such as digital images, 3D-printing models, and point clouds, and pose new challenges for numerical simulations.

The Scaled Boundary Finite Element Method (SBFEM) [1], as a novel semi-analytical numerical method, aims to overcome some of the limitations of the traditional FEM. The SBFEM has emerged as a generalized finite element method with the following salient features:

• Partition of unity and linear completeness are satisfied. SBFEM shape functions can accurately represent rigid body motions and constant strain states. With the addition of bubble functions, it is possible to achieve completeness to any order.
• On the boundary, arbitrary high-order spectral elements can be applied, and different types of elements can be mixed as long as continuity on the boundary is maintained.
• Standard numerical integration methods, such as Gaussian or Gauss-Lobatto-Legendre quadrature, can be applied on the boundary, similar to the FEM.
• The shape functions of open elements contain singularities, which allows for accurate solution of singularities.
• The method for applying boundary conditions is the same as that in FEM, making it a versatile numerical technique for various engineering analyses.
• The difficulty in mesh generation is alleviated. A scaled boundary finite element is highly flexible in its shape and only requires the discretization of its boundary.
• It is highly suitable for high-performance computing (HPC). When paired with an octree mesh, SBFEM significantly reduces memory requirements and is ideal for developing parallel algorithms.

This presentation summarizes our research towards developing a computational framework that fully automates the engineering analysis process directly from commonly used formats of digital geometric models. Our approach is underpinned by the scaled boundary finite element method, which enables us to incorporate an octree algorithm for automatic mesh generation across various formats such as digital images [2], STL models [3], point clouds [4] and traditional CAD models. Furthermore, the solution procedure is purposely designed for the scaled boundary finite element method to leverage modern computer hardware architectures for high-performance computing [5]. Numerical examples and demonstrations illustrate key features and the potential of the proposed framework for simulating complex 3D models, accounting for material and geometric nonlinearities, fractures, and contacts.

Scientific field: computational mechanics
Keywords: numerical method, scaled boundary finite element method, mesh generation, high-performance computing, image-based analysis

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References:

1. Song, C.: The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation. John Wiley & Sons (2018)
2. Saputra, A.A., Talebi, H., Tran, D., Birk, Cl, Song, C. Automatic image‐based stress analysis by the scaled boundary finite element method, “International Journal for Numerical Methods in Engineering” 2017, vol. 109, 697-738. doi.org/10.1002/nme.5304
3. Liu, Y., Saputra, A.A., Wang, J., Tin-Loi, F., Song, C., Automatic polyhedral mesh generation and scaled boundary finite element analysis of STL models, “Computer Methods in Applied Mechanics and Engineering”, 2017, vol. 313, 106-132. doi.org/10.1016/j.cma.2016.09.038
4. Zhang, J., Eisenträger, S., Zhan, Y., Saputra, A.A., Song, C., Direct point-cloud-based numerical analysis using octree meshes, “Computers & Structures”, 2023, vol. 289, 107175. doi.org/10.1016/j.compstruc.2023.107175
5. Zhang, J., Ankit, A., Gravenkamp, H., Eisenträger, S., Song, C., A massively parallel explicit solver for elasto-dynamic problems exploiting octree meshes, “Computer Methods in Applied Mechanics and Engineering”, 2021, vol 380, 113811. doi.org/10.1016/j.cma.2021.113811

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Random field modeling of the mechanical properties of heterogeneous materials based on their microstructure

George Stefanou¹
1 Aristotle University of Thessaloniki, Greece, gstefanou@civil.auth.gr

This lecture presents a computational framework for the simulation of the mechanical properties of heterogeneous materials with random microstructure using random fields, which can serve as input for the response variability analysis of composite structures. Through high-resolution microstructure imaging techniques, such as SEM and CT, the spatial variability of the mechanical properties is quantified. By deriving random fields directly from these images, the proposed framework ensures accurate modeling that reflects real microstructures rather than relying on arbitrary assumptions of statistical distributions. Homogenization methods are used in conjunction with the moving window technique to compute mesoscale random fields, which are then employed for conducting macroscopic response analysis with the stochastic finite element method [1].

The proposed computational framework is illustrated through several applications that include [2,3]: the response variability of composite structures with random material property fields having uncertain parameters, the determination of the mechanical properties of graphene nanoplatelets (GNPs) containing random structural defects and the computation of random fields of bending stiffness properties based on real CT-image data of short fiber composites. An efficient random field computation approach is also proposed, which takes advantage of convolutional neural networks (CNNs) to make nearly instant random field predictions based on image data [4].

Scientific field: Computational mechanics
Keywords: heterogeneous material, microstructure, homogenization, mechanical properties, random fields, response variability

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References:

1. Stefanou G., Savvas D., Papadrakakis M., Stochastic finite element analysis of composite structures based on mesoscale random fields of material properties, Computer Methods in Applied Mechanics and Engineering, 2017, vol. 326, pp. 319-337, doi: 10.1016/j.cma.2017.08.002.
2. Stefanou G., Savvas D., Gavallas P., Papaioannou I., The effect of random field parameter uncertainty on the response variability of composite structures, Composites Part C: Open Access, 2022, vol. 9, 100324, doi: 10.1016/j.jcomc.2022.100324.
3. Gavallas P., Savvas D., Stefanou G., Mechanical properties of graphene nanoplatelets containing random structural defects, Mechanics of Materials, 2023, vol. 180, 104611, doi: 10.1016/j.mechmat.2023.104611.
4. Gavallas P., Stefanou G., Savvas D., Mattrand C., Bourinet J.-M., CNN-based prediction of microstructure-derived random property fields of composite materials, Computer Methods in Applied Mechanics and Engineering, 2024, vol. 430, 117207, doi: 10.1016/j.cma.2024.117207.

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Speaker Bio

George Stefanou is a Professor of Stochastic Methods in Structural Analysis and Dynamics of Structures at the Department of Civil Engineering of the Aristotle University of Thessaloniki, Greece. His research activity is mainly focused on the development and application of computer methods for stochastic finite element analysis of real-world structures, as well as on the multiscale modeling and uncertainty quantification of heterogeneous materials and structures. He has published over 130 articles in international refereed journals and conference proceedings. He is included in the Stanford list of top-cited scientists (2% or above) for the years 2019-2023. He is Secretary of the Greek Association of Computational Mechanics. He has co-organized several international scientific conferences and mini symposia. He is also Guest Editor of 4 journal special issues and member of the Scientific Committee of several international conferences.

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Computing for mechanics and mechanics for computing

Authors: Alberto Corigliano, Andrea Manzoni, Luca Rosafalco, Matteo Torzoni
Affiliation: Politecnico di Milano, Italy
E-mail: alberto.corigliano@polimi.it, andrea1.manzoni@polimi.it, luca.rosafalco@polimi.it, matteo.torzoni@polimi.it

Science has always sought to interpret and understand reality through modelling and simulation. Before the advent of powerful computers, analytical approaches, cleverly combined with experimental observation and validation, were the main tools for scientific advancements. In the last century, computational methods have emerged as a driving force, allowing for increasingly realistic numerical simulations. In many engineering fields, numerical methods have become powerful tools for prediction and optimization. More recently, the integration of simulation with real-time acquisition of experimental data has opened the way for innovative practices in Structural Health Monitoring. As a result, numerical methods have become a close partner of experimental data, driving the rise of new digital twin concepts.

The extremely rapid advancements in Machine Learning and miniaturized sensors are today redefining the role of numerical methods. Numerical approaches can now be used to continuously learn from reality by cleverly combining information from experimental data and/or pre-acquired knowledge, possibly incorporating a priori physical principles. This learning process can drive a continuous optimization and/or adaptivity of materials and structures, enabling them to react dynamically to new stimuli coming from sensors.

New forms of computation can also emerge directly within physical objects. Artificial Neural Networks can be implemented, at least partially, through analog computing devices. In this case, the material or structure itself can function as a computing machine, as explored in Physical Reservoir Computing [1].

The lecture will explore recent trends and future prospects in numerical methods, drawing on the recent experiences of the speaker in structural optimization, structural health monitoring, deep and reinforcement learning [2]-[6] and trying to put in evidence the strict double link between mechanics and computation.

Scientific field: Computational mechanics

Keywords: Computer methods, model order reduction, optimization, machine learning, reinforcement learning, physical reservoir computing

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References

1. Kohei Nakajima, Ingo Fischer (eds). Reservoir computing. Theory, physical implementation and applications. Springer, 2021, ISBN: 978-981-13-1686-9.
2. M. Torzoni, L. Rosafalco, A. Manzoni, S. Mariani, A. Corigliano, SHM under varying environmental conditions: An approach based on model order reduction and deep learning. Computers & Structures, 266, 106790, (2022).
3. L. Rosafalco, J. M. De Ponti, L. Iorio, R. Ardito, A. Corigliano, Optimised graded metamaterials for mechanical energy confinement and amplification via reinforcement learning. European J. of Mechanics A/Solids, 99, 104947 (2023).
4. L. Rosafalco, J. M. De Ponti, L. Iorio, R. V. Craster, R. Ardito, A. Corigliano. Reinforcement learning optimisation for graded metamaterial design using a physical‑based constraint on the state representation and action space. Scientific Reports, 13(1), 21836, (2023).
5. G. Garayalde, M. Torzoni, M. Bruggi, A. Corigliano. Real-time topology optimization via learnable mappings. Int. J. Num. Meth. Engng. 125(15), e7502 (2024) doi: 10.1002/nme.7502
6. G. Garayalde, L. Rosafalco, M. Torzoni, A. Corigliano. Mastering truss structure optimization with tree search. J. Mechanical Design, ASME, 2025, To appear.

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Multiscale and multiphysics modelling of powder metallurgy processes using the discrete element method

Author: Jerzy Rojek
Affiliation: Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland
Email: jrojek@ippt.pan.pl

Powder Metallurgy (PM) encompasses various technologies for the manufacturing of net-shape components from metallic or non-metallic powder mixtures. The present work aims at multiscale and multiphysics modelling of selected PM processes encompassing cold compaction, sintering, hot pressing, and electric current-activated sintering (ECAS). During the PM process, particulate materials are consolidated into a solid bulk material under mechanical, thermal, or combined mechanical and thermal action. In the latter case, thermal and mechanical phenomena are coupled. The ECAS technique, in which heating is produced by the Joule effect, involves the coupling of three physical fields: electrical, thermal, and mechanical. During PM processes, the material undergoes densification, which affects macroscopic properties. Changes in macroscopic properties during densification result from processes at microscopic levels. At the microscopic level, we observe particle rearrangement, plastic deformation, formation and growth of cohesive bonds, shrinkage and elimination of pores. The heterogeneity of the processed material has an effect on heat transfer. Similarly, the electric current flow is affected if it is employed in a PM process.

The design of PM processes is a complex engineering problem. Modelling and simulation can help in process design and a better understanding of the processes. Numerical models for different PM processes developed in the framework of the discrete element method (DEM) will be presented. In the DEM, materials are represented by a large assembly of spherical particles interacting with one another. It takes into account the particulate nature of powders in a simple way. It is a suitable tool for micromechanical modelling of PM processes. A standard DEM can be easily applied to cold powder compaction with low pressure [1]. A special interaction model is required for high-density compaction under high pressures. Similarly, special models are necessary for sintering. Sintering without or with pressure is used as a densification mechanism in many PM processes, such as free sintering, hot pressing (HP) or hot isostatic pressing (HIP). Sintering modelling in the presented research was based on the viscoelastic sintering model developed in [2]. Sintering is a process occurring at high temperatures. Therefore, the DEM, developed originally for mechanical effects in sintering, has been extended to heat conduction [3]. With the use of the electrical-thermal analogy, the thermal model has been adapted to model the flow of electric current [4]. Thus, the DEM formulation has all the ingredients for multiphysics modelling of the ECAS process, accounting for thermal, mechanical and thermal phenomena and two-way coupling within each pair out of them.

The DEM model of sintering was used in the multiscale framework as a model for microscopic modelling [4]. The DEM simulations provided data for the evaluation of macroscopic mechanical constitutive properties [4] and the effective thermal and electrical conductivities of the particulate material at different stages of sintering [5,6]. The DEM model of sintering has been validated using its own experimental results. Verification and validation results will illustrate the capabilities of the developed model.

Scientific field: computational mechanics

Keywords: powder metallurgy, modelling, multiscale, multiphysics, discrete element method

Acknowledgement: Research funded by NCN Poland, project no. 2019/35/B/ST8/03158.

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References

1. Rojek J., Nosewicz S., Jurczak K., Chmielewski M., Pietrzak K., Discrete element simulation of powder compaction in cold uniaxial pressing with low pressure, “Comp. Particle Mechanics”, 2016, vol.3, pp.513–524, doi: 10.1007/s40571-015-0093-0.
2. Nosewicz S., Rojek J., Pietrzak K., Chmielewski M., Viscoelastic discrete element model of powder sintering, “Powder Technology”, 2013, vol.246, pp.157–168, doi: 10.1016/j.powtec.2013.05.020.
3. Rojek J., Kasztelan R., Tharmaraj R., Discrete element thermal conductance model for sintered particles, “Powder Technology”, 2022, vol.405, pp.117521-1–10, doi: 10.1016/j.powtec.2022.117521.
4. Nosewicz A., Rojek J., Wawrzyk K., Kowalczyk P., Maciejewski G., Maździarz M., Multiscale modeling of pressure-assisted sintering, 2019, vol. 156, pp. 385–395, “Computational Materials Science”, doi: 10.1016/j.commatsci.2018.10.001.
5. Nisar F., Rojek J., Nosewicz S., Kaszyca K., Chmielewski M., Evaluation of effective thermal conductivity of sintered porous materials using an improved discrete element model, “Powder Technology”, 2024, vol.437, pp.119546, doi: 10.1016/j.powtec.2024.119546.
6. Nisar F., Rojek J., Nosewicz S., Szczepański J., Kaszyca K., Chmielewski M., Discrete element model for effective electrical conductivity of spark plasma sintered porous materials, “Comp. Particle Mechanics”, 2024, pp.1–11, doi: 10.1007/s40571-024-00773-4.

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