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Thermodynamics-informed multi-head attention neural networks for constitutive modelling
No full textInternational audienceWe propose a thermodynamics-informed multi-head attention neural network (TMANN) framework for predicting elastoplastic behavior under arbitrary loading paths. In contrast to earlier thermodynamics-informed networks that rely solely on internal state variables to encode loading history, the TMANN incorporates a multi-head attention mechanism that explicitly captures the material history sequence, thereby enhancing predictive accuracy and stability. The architecture comprises an attention network for predicting increments of internal state variables and a companion neural network for estimating the Helmholtz free energy at each time step. To ensure physical consistency and strengthen the model's generalization capability, the loss function explicitly enforces thermodynamic constraints, including non-negative free energy, non-negative dissipation rate, and monotonic accumulation of effective plastic strain. Furthermore, a rolling iterative prediction strategy is implemented to ensure the model's compatibility with the stepwise nature of arbitrary loading paths, as only the initial stress and strain states are known a priori. The integration of TMANN into ABAQUS through a user material subroutine verifies its practical applicability to structural simulations. The effectiveness of the proposed TMANN is validated through comparisons with classical numerical methods at both the material point level and in structural simulations. New results showcase the TMANN's robust generalization performance, maintaining high prediction accuracy under incremental loading/unloading and complex random loading scenarios
Enabling Free Growth of Thin Films by Magnetron Sputtering for Blooming Microstructures
No full textInternational audienceAbstract Magnetron sputtering is a versatile and scalable technique that enables the precise tuning of key properties, including crystalline phase, stoichiometry, and phase ratios. Despite its widespread use in producing dense non‐porous coatings on flat substrates, its potential for developing porous electroactive materials remains underexplored. Here the use of rough substrates, such as carbon nanotubes and nanosheets, revealing a dramatic change in the growth mechanism of this model systems, nickel nitride, and chromium nitride is investigated. The nanometric roughness of these carbon nanomaterials leads to distinct effects, including strong shadowing of deposited species and non‐competitive growth. This results in enhanced porous thin films with open microstructures and high available surface areas. It is then apply the experimental findings, confirmed by Monte Carlo simulations, to other thin films to demonstrate this approach extends to multiple nanorough substrate/thin film systems, thereby paving the way for designing new materials with enhanced energy conversion and storage performance
Automated classification of subsurface impact damage in thermoplastic composites using depth-resolved terahertz imaging and deep learning
No full textInternational audienceReliable detection of barely visible impact damage is critical to ensure the structural integrity of composite components in service, particularly in safetycritical applications such as pressure vessels and transportation systems. This study presents a solution for detecting such damage in woven glass fiberreinforced thermoplastic composites using terahertz (THz) time-of-flight tomography and convolutional neural networks. THz provides non-contact, non-ionizing, high-axial-resolution imaging of subsurface and back-surface damage, addressing key limitations of surface-based inspection methods. While THz imaging alone may not always permit conclusive damage identification, we bridge this gap by training neural network classifiers on depthresolved THz B-scan images using ground truth from co-located X-ray microcomputed tomography. Among several pretrained architectures tested via transfer learning, DenseNet-121 exhibits the highest accuracy. The model remains robust even when trained on truncated B-scans excluding surface indentation features, confirming its ability to detect structural anomalies located internally or on the back surface. This is particularly relevant for applications where back-side access is not feasible. Experimental validation is performed on impacted glass-fiber-reinforced thermoplastic coupons prepared in accordance with ASTM D7136, with damage severity quantified through force-displacement data and micro-tomographic analysis. Labeling for supervised learning conforms to acceptance criteria from industrial standards for composite pressure vessels (ASME BPVC Section X, CGA C-6.2), ensuring regulatory alignment and enabling deployment in quality control workflows. The proposed method minimizes the need for expert interpretation or secondary validation and offers direct applicability to in-service inspection and manufacturing quality control
Corrigendum to “Modelling tensile mechanical properties of oak timber from fibre orientation scanning for strength grading purpose” presented in 11th Hardwood conference in Sopron, Hungary, 2024
No full textCorrigendum to “Modelling tensile mechanical properties of oak timber from fibre orientation scanning for strength grading purpose” presented in 11th Hardwood conference in Sopron, Hungary, 2024International audienceThe conference paper “Modelling tensile mechanical properties of oak timber from fibre orientation scanning for strength grading purpose” (11th Hardwood Conference, Sopron, 2024) reported results from destructive tensile tests that, upon subsequent review, were found to contain errors. After a careful curation of the dataset —excluding specimens affected by malfunction events and recomputing the mechanical properties— all results involving the modulus of elasticity (MoE) and tensile strength required revision.The updated analysis is based on a dataset of 875 boards (previously 924). Consequently, Tables 1–2, Figures 3–4, and the numerical values in the text referring to mechanical properties had to be updated. For completeness, the fully revised article is provided below. Minor typographical errors have also been corrected.The most substantive changes concern the coefficients of determination (R²) that quantify the predictive performance of the proposed indicating properties for tensile strength and MoE. The R² for tensile strength prediction increases from 0.49 in the original version to 0.57 in this corrigendum, while the MoE prediction increases from 0.45 to 0.53. Accordingly, the modelling performance is better than initially reported, which does not change the article’s conclusions, but strengthens them, especially regarding the capability of this modelling approach for secondary quality oak timber strength grading.The authors apologize for these errors and hope that the consolidated results will be useful to the timber science community
An innovative modularization methodology for ETO products: case study on PLET structures
No full textInternational audienceThe offshore industry's demand for customized subsea equipment, such as Pipeline End Termination (PLET) structures, challenges traditional Engineer-to-Order (ETO) design and manufacturing process in terms of efficiency and cost.. This paper presents a new approach to identifying modularization oppurtunity in ETO products to reduce lead times and production cost while preserving customization flexibility. The research approach involves gathering detailed design and operational data, followed by applying clustering techniques, such as K-means, to group products based on relevent criteria and support early-stage modular design decisions. The methodology is tested through a case study on PLET systems, focusing on identifying similarities across different clusters. The results demonstrate that the proposed framework improves efficiency in design time, supports designers in making impactful first impressions during the design process, and enhances competitiveness in the tender phase by enabling a more structured and efficient approach to modularization
Wavelet-based enrichment for physics informed neural networks to approximate localized and heterogeneous solutions in solid mechanics
No full textInternational audienceRecent research has highlighted the potential of physics-informed neural networks (PINNs) as an efficient methodology for approximating solutions of boundary value problems in solid mechanics. Nevertheless, their ability to accurately capture highly heterogeneous solutions of complex problems remains limited and requires further investigation. The present paper explores new strategies to address this challenge. In line with existing approaches based on local refinement of collocation (training) points, a weighted version of the loss function is first proposed to better balance the physical residuals across the entire computational domain. Although this modification improves overall performance, the approximation accuracy remains unsatisfactory. To overcome this limitation, an enriched version of PINN is developed to more effectively capture locally heterogeneous distributions of state variables. Specifically, wavelet-based enrichment functions are designed to approximate local high-frequency components of the full-field solution, thereby simplifying the task of the neural network, which is then required only to approximate the global smooth component of the solution. This approach achieves satisfactory accuracy even with relatively simple neural network architectures and few collocation points, as demonstrated through several benchmark problems. Therefore, the proposed enrichment concept represents a promising direction for further improving the performance of PINNs as solvers in computational mechanics, paving the way for their application to more complex problems
A compressible pore-scale numerical simulation of hydrogen flow into brine: Application to underground hydrogen storage
No full textInternational audienceThis study investigates the dynamics of hydrogen-brine flow in idealized pore geometries, with the aim of improving underground hydrogen storage in saline aquifers. Direct numerical simulations (DNS) using Open-FOAM are carried out to assess the influence of key parameters including injection flow rate, pore geometry, dynamic contact angle, and fluid compressibility on immiscible displacement at the pore scale. Results demonstrate marked differences between compressible and incompressible models in terms of brine sweep efficiency, interface displacement patterns, and pressure drop for a given flow rate. Incompressible simulations fail to capture critical phenomena such as hydrogen bubble formation and associated pressure fluctuations. Variations in flow rate and geometric constriction significantly impact residual brine saturation and inlet pressure dynamics; lower rates reduce pressure buildup and leakage risk while increasing storage efficiency. Incorporating a dynamic contact angle reduces the capillary resistance, accelerates the flow, and mitigates pressure peaks compared to static angle models. Overall, this work demonstrates the applicability of OpenFOAM to multiphase compressible hydrogen-brine flows at the pore scale, providing application-specific validation and novel insights to guide the design and optimization of underground hydrogen storage systems.</div
Effect of pre strain on magnetic ageing in Fe-Si steels.
No full textInternational audienceThe durability and performance of electrical steels, essential for electric motors, are compromised by magnetic ageing, which mainly arises from microstructural changes such as carbide precipitation. This study examines how plastic pre-strain influences the magnetic ageing behaviour and microstructural evolution of an ultra-low carbon Fe-Si electrical steel during isothermal ageing at 200 • C. Strain quantification was performed using controlled digital image correlation; samples were pre-strained to 2% and 5% plastic deformation prior to ageing. Magnetic properties were measured with single strip testers, and microstructural changes were quantitatively analysed through SEM imaging and image analysis at different ageing intervals. The results show that increasing pre-strain significantly slows down carbide nucleation and growth kinetics, contrary to the usual expectation that dislocations accelerate precipitation. This slowdown is explained by carbon atoms segregating to dislocations, forming Cottrell atmospheres that reduce the carbon available for carbide formation. Although magnetic losses increase with pre-strain due to enhanced domain wall pinning by dislocations, overall magnetic ageing is reduced because precipitate formation is suppressed. A modified precipitation model that includes dislocation density and carbon segregation effects successfully predicts the experimental data. These findings provide new insights into the complex relationship between plastic deformation, precipitation kinetics, and magnetic ageing in electrical steels, guiding strategies to improve motor efficiency and lifespan
高阶材料常数：基于张量不变性的对称关系
No full textInternational audienceHöherordentliche Materialkonstanten bestimmen die nichtlineare Elastizität, feldvorgespannte Elektromechanik, Akustoelastizität sowie zahlreiche moderne Anwendungen in der nichtlinearen Akustik, piezoelektrischen Wandlung und in kristallinen Funktionsmaterialien. Dennoch ist selbst für gut untersuchte Kristalle die Symmetriereduktion höherer Tensoren in der Literatur fragmentiert, oft unvollständig hergeleitet oder in uneinheitlichen Konventionen dargestellt.Dieses Buch stellt einen einheitlichen, auf Invarianz beruhenden Ansatz zur systematischen Ableitung von Symmetrierelationen materialabhängiger Tensoren in kristallinen Medien vor. Ausgehend von exakten Tensortransformationsgesetzen und Punktgruppengeneratoren werden alle zulässigen Tensorkomponenten und ihre linearen Abhängigkeiten ohne heuristische Annahmen oder implizite Vereinfachungen bestimmt. Die Methode ist rangunabhängig und gilt einheitlich für verschiedene physikalische Kopplungen, wodurch kanonische reduzierte Formen entstehen, die transparent, reproduzierbar und konsistent sind.Ein vollständig ausgearbeitetes trigonal-symmetrisches Referenzbeispiel, basierend auf früheren Arbeiten des Autors in Annalen der Physik, validiert den Ansatz. Anschließend wird die Methode systematisch auf alle kristallographischen Punktgruppen erweitert und in übersichtlichen Zusammenfassungstabellen zusammengeführt.Higher-order material constants govern nonlinear elasticity, bias-field electromechanics, acoustoelasticity, and a wide range of modern applications in nonlinear acoustics, piezoelectric transduction, and engineered crystalline media. Yet even for well-studied crystals, the symmetry reduction of higher-rank tensors remains scattered across the literature, derived incompletely, or presented in incompatible conventions.This book provides a unified, invariance-based framework for deriving symmetry relations of material tensors in crystalline media. Starting from exact tensor transformation laws and point-group generators, all admissible tensor components and their linear relations are obtained systematically—without heuristic assumptions or undocumented shortcuts. The method applies uniformly across tensor ranks and physical couplings, yielding canonical reduced forms that are transparent, reproducible, and internally consistent.A fully worked trigonal benchmark, grounded in the author’s earlier Annalen der Physik study of biased piezoelectric crystals, validates the approach. The treatment then extends exhaustively across all crystallographic point groups and culminates in consolidated summary tables for rapid reference.This volume provides a rigorous generator-based invariance procedure applicable at arbitrary tensor rank, explicit symmetry reductions for elastic, piezoelectric, dielectric, electrostrictive, and higher-order coupled tensors, complete coverage of all crystallographic point groups and the isotropic limit, and a consistent Voigt and generalized-Voigt convention designed to eliminate sign and indexing ambiguities.Intended as both a reference and a methodological guide, this book offers a dependable foundation for researchers and engineers working with higher-order constitutive models in crystalline and multiphysics media.Las constantes materiales de orden superior gobiernan la elasticidad no lineal, la electromecánica bajo campos de polarización, la acustoelasticidad y numerosas aplicaciones modernas en acústica no lineal, transducción piezoeléctrica y medios cristalinos diseñados. Sin embargo, incluso para cristales bien estudiados, la reducción por simetría de tensores de alto orden sigue estando dispersa en la literatura, a menudo incompleta o presentada bajo convenciones incompatibles.Este libro introduce un marco unificado basado en la invariancia tensorial para derivar sistemáticamente las relaciones de simetría de los tensores de propiedades materiales en medios cristalinos. A partir de leyes exactas de transformación tensorial y generadores de grupos puntuales, se obtienen rigurosamente todas las componentes admisibles y sus relaciones lineales, sin recurrir a suposiciones heurísticas ni atajos no documentados. El método se aplica de forma uniforme a cualquier rango tensorial y a diversos acoplamientos físicos, produciendo formas reducidas canónicas, transparentes y reproducibles.Un ejemplo completamente desarrollado para la simetría trigonal, basado en el trabajo previo del autor publicado en Annalen der Physik, valida el enfoque. El tratamiento se extiende posteriormente a todos los grupos puntuales cristalográficos y culmina en tablas resumen para consulta rápida.Les constantes matérielles d’ordre supérieur gouvernent l’élasticité non linéaire, l’électromécanique sous champ biaisé, l’acoustoélasticité et de nombreuses applications modernes en acoustique non linéaire, transduction piézoélectrique et milieux cristallins ingénierés. Pourtant, même pour des cristaux bien étudiés, la réduction par symétrie des tenseurs de rang élevé demeure dispersée dans la littérature, souvent incomplète ou formulée selon des conventions incompatibles.Cet ouvrage propose un cadre unifié fondé sur l’invariance tensorielle pour dériver systématiquement les relations de symétrie des tenseurs de constantes matérielles dans les milieux cristallins. À partir des lois exactes de transformation tensorielle et des générateurs des groupes ponctuels, l’ensemble des composantes admissibles et de leurs relations linéaires est obtenu sans hypothèses heuristiques ni raccourcis non documentés. La méthode s’applique uniformément à tous les rangs tensoriels et aux différents couplages physiques, conduisant à des formes réduites canoniques transparentes, reproductibles et cohérentes.Une étude de référence entièrement développée pour la symétrie trigonale, fondée sur les travaux antérieurs de l’auteur publiés dans Annalen der Physik sur les cristaux piézoélectriques sous champ biaisé, valide la démarche. Le traitement est ensuite étendu de manière exhaustive à l’ensemble des groupes ponctuels cristallographiques et aboutit à des tableaux de synthèse facilitant l’utilisation pratique des résultats.Cet ouvrage fournit ainsi une procédure d’invariance rigoureuse applicable à tout rang tensoriel, des réductions explicites pour les constantes élastiques, piézoélectriques, diélectriques, électrostrictives et autres couplages d’ordre supérieur, une couverture complète des symétries cristallographiques jusqu’à la limite isotrope, ainsi qu’une convention Voigt et Voigt généralisée cohérente visant à éliminer toute ambiguïté de signe ou d’indexation.Conçu à la fois comme ouvrage de référence et comme guide méthodologique, ce livre constitue une base fiable pour les chercheurs et ingénieurs travaillant sur des modèles constitutifs d’ordre supérieur dans les milieux cristallins et multiphysiques.उच्च-क्रम भौतिक स्थिरांक गैर-रेखीय प्रत्यास्थता, पक्षपाती क्षेत्र विद्युत-यांत्रिकी, ध्वनि-प्रत्यास्थता तथा गैर-रेखीय ध्वनिकी, पाईजोइलेक्ट्रिक ट्रांसडक्शन और अभियांत्रिक क्रिस्टलीय माध्यमों में अनेक आधुनिक अनुप्रयोगों को नियंत्रित करते हैं। इसके बावजूद, सुविख्यात क्रिस्टलों के लिए भी उच्च-क्रम टेन्सरों का सममिति-आधारित अपसारण साहित्य में बिखरा हुआ, अपूर्ण अथवा असंगत परंपराओं में प्रस्तुत पाया जाता है।यह पुस्तक क्रिस्टलीय माध्यमों में भौतिक टेन्सरों के सममिति संबंधों को व्यवस्थित रूप से प्राप्त करने हेतु टेन्सर अपरिवर्तनीयता पर आधारित एकीकृत ढांचा प्रस्तुत करती है। सटीक टेन्सर रूपांतरण नियमों और बिंदु-समूह जनकों से प्रारंभ करते हुए, सभी अनुमत टेन्सर घटक और उनके रैखिक संबंध कठोरता से प्राप्त किए जाते हैं, बिना किसी हीयुरिस्टिक अनुमान या अव्यक्त सरलीकरण के।高次材料定数は、非線形弾性、バイアス場下の電気機械結合、音弾性効果、ならびに非線形音響、圧電変換、設計結晶材料における多くの現代的応用を支配している。しかし、十分に研究された結晶であっても、高次テンソルの対称性縮約は文献中に散在しており、不完全または互換性のない規約で示されることが多い。本書は、テンソル不変性に基づく統一的枠組みを提示し、結晶媒体における材料テンソルの対称関係を体系的に導出する。正確なテンソル変換則と点群生成元から出発し、すべての許容テンソル成分およびそれらの線形関係を、ヒューリスティックな仮定や暗黙的近似なしに厳密に求める。Hogere-orde materiaalconstanten bepalen niet-lineaire elasticiteit, elektromecanica onder biasvelden, acousto-elasticiteit en talrijke moderne toepassingen in niet-lineaire akoestiek, piëzo-elektrische transductie en ontworpen kristallijne media. Desondanks blijft de symmetriereductie van hogere-rang tensoren, zelfs voor goed bestudeerde kristallen, versnipperd in de literatuur, vaak onvolledig afgeleid of gepresenteerd in onderling incompatibele conventies.Dit boek introduceert een uniform, op tensorinvariantie gebaseerd raamwerk voor de systematische afleiding van symmetrierelaties van materiaaltensoren in kristallijne media. Vertrekkend van exacte tensortransformatiewetten en puntgroepgeneratoren worden alle toegestane tensorcomponenten en hun lineaire relaties strikt afgeleid, zonder heuristische aannames of ongedocumenteerde vereenvoudigingen.As constantes de materiais de ordem superior governam a elasticidade não linear, a eletromecânica sob campos de polarização, a acustoelasticidade e diversas aplicações modernas em acústica não linear, transdução piezoelétrica e meios cristalinos engenheirados. No entanto, mesmo para cristais amplamente estudados, a redução por simetria de tensores de alta ordem permanece dispersa na literatura, frequentemente incompleta ou apresentada em convenções incompatíveis.Este livro apresenta um arcabouço unificado baseado na invariância tensorial para a derivação sistemática das relações de simetria de tensores de propriedades materiais em meios cristalinos. A partir de leis exatas de transformação tensorial e geradores de grupos pontuais, todas as componentes admissíveis e suas relações lineares são obtidas de forma rigorosa, sem pressupostos heurísticos ou simplificações implícitas. O método aplica-se uniformemente a qualquer ordem tensorial e a diferentes acoplamentos físicos, resultando em formas reduzidas canônicas, transparentes e reproduzíveis.Высшие материальные константы определяют нелинейную упругость, электромеханику при наличии смещающих полей, акустоэластичность и широкий спектр современных приложений в нелинейной акустике, пьезоэлектрической трансдукции и инженерных кристаллических средах. Тем не менее даже для хорошо изученных кристаллов редукция тензоров высокого ранга по симметрии остаётся фрагментированной в литературе, часто выводится неполно или представляется в несовместимых конвенциях.В данной книге предлагается единый подход, основанный на тензорной инвариантности, для систематического вывода симметрийных соотношений материальных тензоров в кристаллических средах. Исходя из точных законов тензорного преобразования и генераторов точечных групп, все допустимые компоненты тензоров и их линейные соотношения выводятся строго и прозрачно — без эвристических предположений и недокументированных упрощений. Метод применяется одинаково для любых тензорных рангов и физических связей, приводя к каноническим редуцированным формам, которые являются воспроизводимыми и внутренне согласованными.Полностью разработанный эталонный пример для тригональной симметрии, основанный на предыдущей работе автора в Annalen der Physik по пьезоэлектрическим кристаллам под действием смещающих полей, подтверждает корректность метода. Далее изложение охватывает все кристаллографические точечные группы и завершается сводными таблицами для быстрого практического использования.高阶材料常数控制着非线性弹性、偏置场电机耦合、声弹性以及非线性声学、压电换能和工程化晶体介质中的诸多现代应用。然而，即便对于研究充分的晶体，高阶张量的对称约化仍然零散地分布于文献中，往往推导不完整，或采用彼此不兼容的约定。本书提出了一种基于张量不变性的统一框架，用于系统地推导晶体介质中材料张量的对称关系。从精确的张量变换定律和点群生成元出发，严格地获得所有允许的张量分量及其线性关系，避免了启发式假设和未说明的简化。该方法对不同张量阶数和物理耦合形式具有统一适用性，得到的约化形式清晰、可重复且内部一致。书中通过一个完整的三方晶系实例验证了该方法，该实例基于作者先前发表于 Annalen der Physik 的偏置压电晶体研究。随后，方法被系统地推广至所有晶体学点群，并最终汇总为便于快速查阅的对称约化表格
Corrigendum to “Thermodynamics-informed multi-head attention neural networks for constitutive modelling” [Int. J. Solids Struct. 328 (2026) 113845]
No full textInternational audienceThe authors regret that the fourth affiliation (d) is incorrect in the published version. The correct affiliation has been used above. We consider this error to be significant as the failure to correctly state an author’s affiliation may result in legal/professional repercussions to the said author. The authors would like to apologise for any inconvenience caused