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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Hybrid Analytical-Numerical Monte Carlo Approaches for Stochastic Response Determination of Systems Endowed with Fractional Derivative Elements

By P.D. Spanos

L.B. Ryon Chair in Engineering
Houston, USA

Abstract

Nonlinear dynamic systems are widely used to model complex physical phenomena, in which system behavior cannot be adequately captured by linear differential equations. If these systems are subjected to stochastic excitations of various origins, predicting their response becomes a challenging task. The complexity  increases   further  with the introduction of fractional derivative elements, which are often employed to model hereditary phenomena, and memory effects. Such features are prevalent in many physical and engineering systems, where the dynamic behavior is inherently non-local. While the fractional derivative operator provides a more accurate representation of these systems, it also introduces significant analytical and computational challenges [1].

Fractional derivatives extend the concept of integer-order differentiation, allowing for non-integer orders that offer greater flexibility in modeling real-world systems. They have been successfully applied in various fields, including viscoelasticity, control theory, electrical systems, biology and bioengineering, and anomalous diffusion.

In the context of stochastic dynamics, Statistical Linearization (SL) [2], perturbation techniques [3], and, for lightly damped systems subjected to broad-band random excitations, Stochastic Averaging (SA) [4], have proven to be efficient and versatile tools for determining   response statistical quantities  such as mean, variance, and higher-order moments, for a variety of nonlinearities and   of stochastic excitations, as well as the temporal evolution of relevant response statistics.

In the presence of fractional derivative terms, the aforementioned standard methods are typically adapted to handle numerically the associated additional complexity. Common approaches include finite difference schemes, Harmonic Balancing (HB), perturbation and path integral techniques, wavelet-based representations, and system augmentation methods, all of which  support an efficient treatment of fractional derivatives.

Despite their versatility and computational efficiency of the SL and SA techniques, they often fail to accurately and readily determine the Power Spectral Density (PSD) of nonlinear system responses.

In context with the preceding comments a perspective on the concept of conditional spectrum is first presented in the lecture by relying on a suite of pertinent Monte Carlo numerical simulations, as delineated in the paper such as [5-8].

The discussion continues with a generalization of the SL technique for determining the non-stationary response statistics of a broad class of lightly damped nonlinear oscillators comprising fractional derivative terms ,and subjected to broad-band stochastic excitation. The approach involves a pre-processing step in which the HB technique is applied exclusively to the fractional derivative term, yielding response-amplitude-dependent equivalent damping and stiffness parameters. These parameters are then averaged using the probability density function (PDF) of the response amplitude, which is assumed to follow a Rayleigh distribution with time-dependent parameters. Thus,, the expected values of the equivalent quantities are expressed as functions of the system response variance. The covariance Lyapunov equation corresponding to the equivalent system is then numerically solved to obtain non-stationary estimates of auto-correlation and cross-correlation functions for displacement and velocity responses. These estimates are subsequently used to derive analogous expressions for the fractional derivative term, and the integer-order state variables of the oscillator.

Further, in addressing the limitation of SL and SA to capture the spectral response of the class of nonlinear systems under investigation, an interpretation of the conditional spectrum [9, 10] concept is presented  under the assumption of an ergodic system response. Specifically, the Fokker–Planck–Kolmogorov equation is formulated for a system exhibiting both damping and stiffness nonlinearities combined  a fractional derivative term. In the stationary case, solving this equation yields a refined PDF for the response amplitude, serving as the foundation for examining the system stationary displacement and velocity spectra for  varying levels of nonlinearity. In this context, it is shown that an appropriately approximated stationary PDF of the oscillator’s response amplitude, combined with a specific corrective term, can yield, for the first time, highly accurate spectral response estimates. The approach proves particularly effective in accurately capturing the shape and resonance shifts in the stationary power spectrum of the state variables of the considered nonlinear memory-dependent systems. Specifically, the oscillator's response spectrum is interpreted as a superposition of individual surrogate linearized oscillators, each corresponding to distinct amplitude levels. To ensure that each oscillator achieves the expected stationary response variance at its respective amplitude level, an adjustment term is incorporated in the original conditional spectrum formulation, ensuring that each individual oscillator exhibits the expected response variance. This adjustment accounts for potential deviations from stationarity within specific amplitude intervals due to variations in initial conditions. Further comparison between the results obtained using the proposed method, and a suit of additional Monte Carlo simulations     demonstrate  its accuracy and reliability for  a wide range of fractional derivative orders and nonlinearities.

In conclusion, the discussed approach  is found to be particularly attractive due to its applicability to a broad class of nonlinear systems  endowed    with fractional  derivative  elements, subject to stochastic excitations, as well as its capacity to efficiently compute key response statistics  and  spectral  features at a low computational cost.

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References

[4] Podlubny, I.: Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of their Solution and some of their Applications. Academic Press, San Diego (1999).

[2] Roberts, J.B., Spanos, P.D.: Random Vibration and Statistic Linearization. Dover Publications Inc., Mineola, New York (1999).

[3] Momani, S., Odibat, Z.: Homotopy perturbation method for nonlinear partial differential equations of fractional order. Phys. Lett. A 365, 345–350 (2007).

[4] Roberts, J.B., Spanos, P.D.: Stochastic averaging: an approximate method of solving random vibration problems. Int. J. Nonlin. Mech. 21 (2), 111–134 (1986).

[5] Spanos, P.D., Kougioumtzoglou, I.A., Soize, C.: On the determination of the power spectrum of randomly excited oscillators via stochastic averaging: an alternative perspective. Probabilist. Eng. Mech. 26 (1), 10–15 (2011).

[6] Pomaro, B., Spanos, P.D.: Extended statistical linearization approach for estimating non-stationary response statistics of systems comprising fractional derivative elements. Probabilist. Eng. Mech. 74, 103471 (2023).

[7] Pomaro, B, Spanos, P.D.: A Perspective on conditional spectrum-based determination of response statistics of nonlinear systems. Probabilist. Eng. Mech. 78, 103704 (2024).

[8] Spanos, P.D., Pomaro, B.: Stochastic response spectrum determination of nonlinear systems endowed with fractional derivative elements. In press in Nonlinear Dynamics.

[9] Bouc, R.: The power spectral density of response for a strongly nonlinear random random oscillator. J. Sound Vib. 175, 317–331 (1994).

[10] Miles, R.N.: Spectral response of a bilinear oscillator. J. Sound Vib. 163, 319–326 (1993).

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BIO

Professor Spanios is a Caltech alumnus with a Ph.D degree in Applied Mechanics and with minor I in Applied Mathematics and minor II in Business Economics; and with an MS degree in Civil Engineering . Also, he holds a 5-year diploma in Mechanical Engineering and Engineering Sciences for NTU in Athens, Greece. His interests are in the area of dynamical systems with emphasis on probabilistic (risk and reliability),Monte Carlo numerical simulations, non-linear, and signal-processing aspects; and with applications to structural- , aerospace- , offshore- , bio-, and materials- engineering.. He has supervised the MS theses of more than 75 students and the Ph.D. theses of more than 60 students. His research findings have been disseminated in more than 400 papers in archival journals, technical conferences, and industrial reports. He is Editor-in-Chief of the International Journal of Non-Linear Mechanics, and of the Journal of Probabilistic Engineering Mechanics. He is a Distinguished/ Honorary Member of both ASCE and ASME. He is a member of the academies NAE and AAAS (USA); and a corresponding/foreign member of NA/NAE of Hellas, Europe, Canada, China, India, and Russia. He is a Registered Professional Engineer (TX), and a Licensed CE/ME Engineer (GR) His work has been supported by NSF, DOE, ONR, AFOSR, NASA and by many industrial consortia. He has received numerous awards from NSF, ASCE, ASME, IASSAR,Eurodyn,EuAS, and Rice University (teaching prize). Since 1988, he holds the LB Ryon Endowed Chair in Engineering at Rice University in Houston, Texas.

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Aleatory and epistemic uncertainties in engineering analysis

Michael Beer

Institute for Risk and Reliability, Leibniz Universität Hannover, Germany, beer@irz.uni-hannover.de

Department of Civil and Environmental Engineering, University of Liverpool, UK

International Joint Research Center for Engineering Reliability and Stochastic Mechanics (ERSM) & International Joint Research Center for Resilient Infrastructure (ICRI), Tongji University, China

Abstract

Analyzing engineering structures and systems we are challenged by complexity, nonlinearities and uncertainties, which call for highly efficient models and analysis technologies to provide realistic results at reasonable computational cost. An efficient and effective quantification of both aleatory and epistemic uncertainties is essential in this regard. To address aleatory uncertainties, a class of covariance models is discussed. It is shown that an optimal spectral representation can be derived to meet the key physics behind fluctuating engineering quantities and simultaneously to improve the efficiency of spectral stochastic analyses significantly. The discussion is the expanded to the consideration of epistemic uncertainties. It is highlighted that their appropriate consideration in an engineering analysis is a key requirement for proper design and operation of our structures and systems. The quantification of epistemic uncertainties is discussed elucidating the capabilities of the concepts. Clearly, the first consideration should be devoted to a probabilistic modelling, naturally through subjective probabilities, expressing some belief, which can be integrated into a fully probabilistic framework in a coherent manner with potent Bayesian approaches. While this pathway is already widely established and used, the potential of set-theoretical approaches and imprecise probabilities has only been utilized to some extent. Those approaches, however, attract increasing attention in cases when available information is not rich enough to meaningfully specify subjective probability distributions or when only bounding information on probabilistic models is available. They offer a complementing perspective providing additional insight for reliability assessment and decision-making. Their conceptual features facilitate a modelling at a reasonable level of detail and capturing the remaining epistemic uncertainty in a set-valued manner. This approach allows for an optimal balance between model detailedness and imprecision of results to still derive useful decisions. However, it is also associated with quite extensive numerical cost when applied in a crude way. To address this issue, a numerically efficient analysis technology is presented, which does not only resolve the additional burden of processing both aleatory and epistemic uncertainties, but also time-dependent reliability problems without the typical multiple repetition of the reliability analysis. Engineering examples show the practical applicability as well as the gain in using the proposed concepts.

 

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Speaker Bio

Michael Beer is Professor and Head of the Institute for Risk and Reliability, Leibniz Universität Hannover, Germany. He is also part time Professor at the University of Liverpool and guest Professor at Tongji University and Beijing University of Science and Technology, China. He obtained a doctoral degree from Technical University Dresden, Germany, and worked for Rice University, National University of Singapore, and the University of Liverpool, UK. Dr. Beer’s research is focused on uncertainty quantification in engineering with emphasis on imprecise probabilities. Dr. Beer is Editor in Chief of the ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A Civil Engineering and Part B Mechanical Engineering. He is also Editor in Chief (joint) of the Encyclopedia of Earthquake Engineering, Associate Editor of Information Sciences, and Editorial Board Member of Engineering Structures and several other international journals. He has won several awards including the Alfredo Ang Award on Risk Analysis and Management of Civil Infrastructure of ASCE. Dr. Beer is the Chairman of the European Safety and Reliability Association (ESRA) and a Co-Chair of Risk and Resilience Measurements Committee (RRMC), Infrastructure Resilience Division (IRD), ASCE. He is serving on the Executive Board of the International Safety and Reliability Association (IASSAR), on the Executive Board of the European Association of Structural Dynamics (EASD), and on the Board of Directors of the International Association for Probabilistic Safety Assessment and Management (IAPSAM). He is a Fellow of the Alexander von Humboldt-Foundation and a Member of ASCE (EMI), ASME, CERRA, IACM and GACM.

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Heterogeneous Materials: Characterization, Reconstruction, Simulation, and Application

Chenfeng Li

Zienkiewicz Institute for Modelling, Data & AI, Swansea University, UK

Heterogeneous materials consist of multiple phase randomly distributed throughout a medium, leading to complex structures that influence their behaviour and performance. Examples include voids and minerals in rocks, aggregates and cement paste in concrete, inclusions and fibres in composites, and polycrystalline grain structures in alloys. The intricate and stochastic nature of these materials plays a crucial role in their processing, mechanical properties, and overall performance in engineering applications. Traditionally, researchers have relied on experimental techniques, theoretical models, and numerical simulations to analyze heterogeneous materials. However, with the rapid advancements in artificial intelligence (AI), integrating physics-based modelling, data analytics, and machine learning has opened new frontiers in this field. AI-driven approaches enhance our ability to characterize, reconstruct, and simulate heterogeneous materials with unprecedented accuracy, offering deeper insights into their microstructural behaviours and potential applications. This lecture will explore these aspects in detail, focusing on porous media and alloy materials as key case studies.

The microstructure of heterogeneous materials can be effectively captured through advanced microscopic imaging techniques, including optical microscopy, scanning electron microscopy, and micro-computed tomography. These methods provide high-resolution images that reveal the intricate internal structures of materials. To quantitatively describe the randomness and complexity of thee microstructures, researcher employ various statistical descriptors, such as N-point correlation functions, lineal path functions, and tortuosity. These descriptors help in understanding the spatial distribution of phases and structural anisotropy. Extensive research has been conducted on the characterization of porous materials, polycrystalline metals, and composite structures, leading to a broad spectrum of statistical metrics available in the literature. However, a fundamental challenge remains: selecting the most relevant statistical descriptors for a given material system. Since different descriptors capture distinct features and are often interdependent, an optimal selection strategy is necessary to maximize their effectiveness in material analysis and prediction models.

Despite the power of microscopic imaging, direct imaging has limitations due to constraints in sample availability and the inherent resolution and field-of-view restriction o imaging systems. In many cases, only 2D cross-sectional images can be acquired, whereas a full 3D representation of the microstructure is essential for accurate quantitative analysis. Microstructure reconstruction addresses this challenge by generating digital 3D models that statistically replicate the features observed in the original material. A variety of digital reconstruction techniques have been developed, ranging from stochastic methods and optimization-based approaches to more advanced AI-driven generative models. The latest advancements in deep learning have significantly enhanced the accuracy and efficiency of digital reconstruction, enabling researchers to generate high-fidelity 3D microstructures from limited 2D image data. 

Once high-resolution digital microstructures are available, physics-based simulations can be performed to investigate the intricate relationships between processing conditions, microstructural evolution, material properties and overall performance. These simulations vary depending on the material system under study, employing techniques such as finite element analysis for mechanical behaviour prediction, lattice Boltzmann methods for fluid flow in porous media, and phase-field modelling for microstructural evolution in alloys. This lecture will highlight key methodologies used in the study of porous materials and polycrystalline metals, demonstrating their effectiveness through real-world case studies. The integration of AI-enhanced microstructure characterization, digital reconstruction, and physics-based simulations is transforming material science, paving the way for more precise material design and optimization.

Scientific Field: Computational Mechanics, Materials Science

Keywords: Heterogeneous Materials, Microstructure, Porous Media, Alloy

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References:

1. B.B. Chen, D.F. Li, P. Davies, R. Johnston, X.Y. Ge, and C.F. Li, Recent Progress of Digital Reconstruction in Polycrystalline Materials, Archives of Computational Methods in Engineering, In Press.
2. S.Q. Cui, J.L. Fu, S. Cen, H.R. Thomas, and C.F. Li, The Correlation Between Statistical Descriptors of Heterogeneous Materials, Computer Methods in Applied Mechanics and Engineering, 384 (2021) 113948.
3. X. Li, Z.L. Liu, S.Q. Cui, C.C. Luo, C.F. Li, and Z. Zhuang, Predicting the Effective Mechanical Properties of Heterogeneous Materials Through Image-Based Modeling and Deep Learning, Computer Methods in Applied Mechanics and Engineering, 347 (2019) 735-753.

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BIO

Chenfeng Li FLSW, Professor of Civil Engineering, is internationally recognized for his pioneering research in engineering computation, data analytics, uncertainty quantification, and risk assessment. He has developed innovated computational solutions to tackle technical challenges across diverse engineering domains, including civil infrastructure, materials science, manufacturing, and energy sectors. His profound expertise is highly sought after by leading organizations in infrastructure and construction, such as ARUP, Costain, Bauer, Soletanche Bachy, among others. The impact of his research is evidenced by significant contributions to industrial guides and large-scale industrial applications. Within Swansea University, he serves as the Co-director for the Zienkiewicz Institute for Modelling, Data and AI. Additionally, he serves as a Non-executive Director for the trade organization Temporary Works Forum and the Editor-in-Chief of Engineering Computations.

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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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Data-driven self-healing concrete model and analysis

Nicholas Fantuzzi¹, Dimitra Tsimpli², Francesco Fabbrocino²

¹ DICAM Department, University of Bologna, Italy, nicholas.fantuzzi@unibo.it

² Engineering Department, Pegaso Telematic University, Italy, dimitra.tsimpli@unipegaso.it, francesco.fabbrocino@unipegaso.it

Abstract

The constituents of concrete have a high CO2 emission impact, especially due to cement. Most of the CO2 production of the concrete is produced from the burning of fossil fuels to heat up the kiln and when during the calcination process when the limestone is heated. The main solution for the de carbonization of concrete involves improving the energy efficiency of kilns, switching from fossil fuel to biomass, carbon capturing and storage and finally switching to clinker substitutes. At the same time, it is known that the main indicator of a degraded concrete structure is the presence of cracks in the structural elements. The formation of cracks is critical to the life cycle assessment of a concrete structure. Autogenous effect of self-healing concrete is attributed to the calcium hydroxide carbonation, and the swelling of cement and calcium silicate particles from further hydration. The present analysis focuses on the investigation of the self-healing properties provided by fly ash, hydrated lime powder and silica fume on concrete mixes. These fillers provide advantages both in terms of tension strength as well as healing properties. A Classification/Regression model is trained on a dataset, and results are analyzed based on the present dataset. Results are verified providing accuracy and data dispersion on a synthetic dataset reaching allowable accuracy ranges to be considered for practical engineering design purposes.

Acknowledgements: The authors acknowledge the support of PRIN 2022 PNRR, Project P202278LFC (CUP J53D23015620001) which is funded by the European Union - NextGenerationEU.

 Scientific field: [one of: solid mechanics OR fluid mechanics OR solid/fluid interaction OR computational mechanics OR biomechanics OR advanced materials OR trans-disciplinary engineering OR ANN mini-symposium OR other]

Keywords: [self-healing concrete, data-driven analysis, machine learning, statistical analysis, training, testing]

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References:

[1] Chen G., Tang W., Chen S., Wang S., Cui H., Prediction of self-healing of engineered cementitious composite using machine learning approaches, “Applied Sciences”, 2022, vol. 12, no. 7, pp. 3605 doi: 10.3390/app12073605.

[2] Stuckrath C., Serpell R., Valenzuela L.M., Lopez M., Quantification of chemical and biological calcium carbonate precipitation: Performance of self-healing in reinforced mortar containing chemical admixtures, “Cement & Concrete Composites”, 2014, vol. 50, pp. 10-15, doi: 10.1016/j.cemconcomp.2014.02.005.

[3] Davies R., Teall O., Pilegis M., Kanellopoulos A., Sharma T., Jefferson A., Gardner D., Al-Tabbaa A., Paine K., Lark R., Large Scale Application of Self-Healing Concrete: Design, Construction, and Testing. “Frontiers in Materials”, 2018, vol. 5, pp. 51, doi: 10.3389/fmats.2018.00051.

[4] Althoey F., Amin M.N., Khan K., Usman M.M., Khan M.A., Javed M.F., Sabri M.M., Alrowais R., Maglada A.M., Machine learning based computational approach for crack width detection of self-healing concrete, “Case Studies in Construction Materials”, 2022, vol. 17, pp. e01610, doi: 10.1016/j.cscm.2022.e01610.

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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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Refinement of Hybrid Analyses Reveals Unexpected Load-Carrying Mechanisms of NATM- and TBM-Driven Tunnels

Christian Hellmich, Raphael Scharf, Ali Razgordanisharahi, Maximilian Sorgner, Bernd Moritz, Thomas Pilgerstorfer, Markus Brantner, Bernhard Pichler

Affiliations

1. TU Wien (Vienna University of Technology), Vienna, Austria

2. ÖBB Infrastruktur GmbH, Graz, Austria

3. Geoconsult, Puch bei Hallein, Austria

4. IGT-engineering, Salzburg, Austria

Contact Emails: christian.hellmich@tuwien.ac.at, raphael.scharf@tuwien.ac.at, ali.razgordanisharahi@tuwien.ac.at, bernhard.pichler@tuwien.ac.at

Abstract

In geotechnical engineering, the ground surrounding a tunnel opening is largely unknown. This makes precise and realistic mechanical modeling nearly impossible. Hence, accurately quantifying the forces acting on a tunnel shell is a formidable challenge. To address this, hybrid methods [1,4] have been proposed within the framework of the New Austrian Tunneling Method (NATM) [2]. These methods combine mechanical models for the aging viscoelastic tunnel shell, made of shotcrete, with geodetic measurement data [3] that provide displacement vectors at selected points on the inner tunnel surface. By increasingly refining interpolation strategies [1,4] of the point-specific displacements along the tunnel shell circumference, and applying the corresponding boundary conditions to a structural mechanical model of the shell, the utilization degree – a key indicator of the shell’s mechanical competence – can be quantified [1,4]. Recently [5] this approach has been substantially refined and extended in its application in two major ways:

First, rather than arbitrarily choosing displacement interpolation functions, the mathematical structure of the displacement fields was derived from viscoelastic shell theory [6]. This approach uses shell equilibrium conditions based on the principle of virtual power [7,8], along with a rate-type aging viscoelastic material law [9] in the Laplace-Carson space. This theory-based method allows for the translation of point-based displacement measurements into normal forces, bending moments, stresses, and ground pressure-related traction forces acting on the shell. When applying this refined concept to the top heading of the Stein tunnel [10], this tunnel shell was found to be highly flexible, even undergoing plastic moment deformation [11]. This behavior was rarely, if ever, observed in the context of NATM tunneling.

Secondly, a hybrid method for Tunnel Boring Machine (TBM)-driven segmental tunnels has been developed. Strains recorded at specific points from vibrating wire sensors placed at two reinforcement layers are first translated – using a viscoelastic model – into stresses [12]. These stresses are then integrated into bending moments and normal forces, which are subsequently interpolated along the shell circumference. This approach allows for (i) the assessment of mechanical competence of the longitudinal joints (the weakest portions of the tunnel shell), and (ii) through shell equilibrium conditions, the determination of ground pressure and shear traction at the shell-ground interface. When applied to construction lot KAT3 of the Koralm tunnel [13] in southern Austria, the tunnel shell, despite being segmental, behaves like a pseudo-monolithic structure. However, maximum bending moments are observed off the spring-line, indicating that ground-loosening forces are acting on the tunnel crown. This phenomenon may be linked to variations in the effectiveness of the grout bond between the tunnel shell and the surrounding ground.

Scientific field: Solid Mechanics

Keywords: Tunnel engineering, Viscoelasticity, Monitoring, Long-term assessment

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References

1. C. Hellmich, J. Macht, H. Mang. A hybrid method for determination of the level of utilization of shotcrete shells, Felsbau, 17(5), 422-425, 1999.
2. H. Lauffer. The development of the NATM–a historical review, Geomechanics and Tunnelling, 3(6), 763-772, 2010.
3. W. Schubert, A. Steindorfer, E. Button. Displacement monitoring in tunnels-an overview, Felsbau, 20(3), 7-15, 2002.
4. M. Brandtner, B. Moritz, P. Schubert. On the challenge of evaluating stress in a shotcrete lining...
5. C. Hellmich, B. Pichler, R. Heissenberger, B. Moritz. 150 years reliable railway tunnels– Extending the hybrid method...
6. R. Scharf, B. Pichler, R. Heissenberger, B. Moritz, C. Hellmich, Data-driven analytical mechanics of aging viscoelastic shotcrete tunnel shells...
7. P. Germain. The method of virtual power in continuum mechanics. Part 2: Microstructure. SIAM Journal on Applied Mathematics, 25(3), 556-575, 1973.
8. R. Höller, M. Aminbaghai, L. Eberhardsteiner, J. Eberhardsteiner, R. Blab, B. Pichler, C. Hellmich. Rigorous amendment of Vlasov's theory for thin elastic plates on elastic Winkler foundations...
9. S. Scheiner, C. Hellmich. Continuum microviscoelasticity model for aging basic creep of early-age concrete...
10. J. Benedikt, H. Wagner, T. Herzeg. The St. Kanzian Chain of Tunnels–Tunnelling under very varied and extremely difficult conditions...
11. R. Scharf, M. Brandtner, B. Moritz, B. Pichler, C. Hellmich, C. Refined hybrid structural analysis shows plastic flexibility enhancement in NATM tunnel shell...
12. A. Razgordanisharahi, M. Sorgner, T. Pilgerstorfer, B. Moritz, C. Hellmich, B. Pichler, Realistic long-term stress levels in a deep segmented tunnel lining...
13. B. Moritz, H. Wagner, K. Mussger, D. Handke, G. Harer. Criteria for the selection of tunnelling method through the example of the Koralm Tunnel...

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BIO

Christian Hellmich is full professor at Technische Universität Wien (TUW, Vienna, Austria), directing there the Institute for Mechanics of Materials and Structures. At TUW, he received his (civil) engineering diploma (1995), his Dr.techn. (PhD, 1999), and his habilitation (2004). Being on leave from his academic position at TUW, he was Postdoctoral Fellow at M.I.T. from 2000 to 2002; and over the years, he has held several short-term visiting professorships in France, Italy, and Germany.

Together with collaborators across the globe, he has developed (micro)structural bio-chemomechanical models, in terms of theoretical foundations, computational realization, as well as experimental validation and developments for various biological and man-made systems; including bone and soft tissues, cement and concrete, wood and wood composites, rock and soil, brick, steel, rubber, graphene, DNA, as well as metal-, mineral-, polymer-, and glass-based biomaterials. These mathematical models are employed in concrete, tunnel, pipeline, and biomedical engineering.

Also trained as a violinist, he has been active at the crossroads of Science and Arts, from which he takes a broad cultural perspective on the nature of universities and their role in society. This is also reflected by his interdisciplinary work integrating engineers, physicists, chemists, biologists, and medical doctors.

Christian Hellmich has co-authored 185 peer-reviewed publications; and about the same amount of book chapters and proceedings papers; he has given more than 300 presentations at international conferences and universities, often as invited, keynote, or plenary speaker. He serves in editorial roles for several peer-reviewed journals, including Journal of Engineering Mechanics (ASCE), Mechanics of Materials, and AIP Applied Physics Reviews.

He has provided extensive reviewing and advisory service for various universities and science foundations, including his role as a panel member for the European Research Council (ERC). He has also served in the Engineering Mechanics Institute of the American Society of Civil Engineers (EMI-ASCE), in particular so in the Board of Governors and in various technical committees, as president of the International Association for Concrete Creep (IA-CONCREEP), as president of the Austrian Chapter of the European Society of Biomechanics (ESB), as symposium organizer for the Materials Research Society (MRS), and in the Board of Directors of the Young Academy of the Austrian Academy of Sciences (ÖAW).

His activities have been recognized through several national and international awards, such as the Kardinal Innitzer Advancement Award of the Archdiocese of Vienna (2004), the Science Recognition Award of the Region of Lower Austria (2005), the Zienkiewicz Award of the European Community on Computational Methods in Applied Sciences (ECCOMAS, 2008), an ERC grant (2010), and the Walter L. Huber Research Prize of ASCE (2012); moreover, he was named Fellow of EMI (2014), Fellow of the European Alliance of Medical and Biological Engineering & Sciences (EAMBES, 2019), corresponding member of ÖAW (2019), and Fellow of the Society of Engineering Science (SES, 2023).

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