[Jumeaux numériques physiques de maçonnerie antique basés sur les techniques de construction originelles : le cas des nuraghi sardes]
A short review is provided regarding modern technical tools allowing to build digital twins for modelling ancient stone masonry structures and their physical behaviour. The objective of such tools is to assess the structural safety of cultural heritage masonry structures. The present work focuses on the particular case of Sardinian nuraghi, which are ancient corbelled stone masonry structures whose typical form is a truncated cone. As a starting point we consider a careful historical analysis of the construction techniques of those nuraghi. From this analysis, we address the choice of theoretical and numerical tools apt to construct a digital twin of complex nuraghi, in addition to delineating future challenges in building digital twins capable of simulating any physical process which may be relevant to ancient buildings.
Le présent article passe en revue les outils techniques modernes aptes à modéliser les structures antiques en maçonnerie et leur comportement physique. L’utilisation de ces outils vise à estimer la sûreté structurelle d’ouvrages en maçonnerie faisant partie du patrimoine culturel. Le présent article considère le cas particulier des nuraghi sardes : il s’agit de structures antiques en maçonnerie construites en encorbellement et présentant une forme typique de cône tronqué. Le point de départ consiste en une étude historique attentive des techniques de construction de ces structures. De cette étude sont ensuite déduits quels types d’outils théoriques et numériques semblent adaptés à la construction de jumeaux numériques pour des nuraghi complexes, ainsi que les défis à relever pour que de tels jumeaux puissent modéliser n’importe quel phénomène physique pouvant affecter ces structures antiques.
Révisé le :
Accepté le :
Publié le :
Mots-clés : Jumeaux numériques, maçonneries antiques, patrimoine culturel, nuraghi, modélisation multiphysique, météorisation
Chuong Anthony Tran 1 ; Emilio Barchiesi 1 ; Roberto Busonera 1 ; Mustafa Erden Yildizdag 1 ; Ilaria Trivelloni 1 ; Emilio Turco 1

@article{CRMECA_2025__353_G1_791_0, author = {Chuong Anthony Tran and Emilio Barchiesi and Roberto Busonera and Mustafa Erden Yildizdag and Ilaria Trivelloni and Emilio Turco}, title = {Physical digital twins for ancient stone masonry informed of original construction techniques: the case of {Sardinian} nuraghi}, journal = {Comptes Rendus. M\'ecanique}, pages = {791--813}, publisher = {Acad\'emie des sciences, Paris}, volume = {353}, year = {2025}, doi = {10.5802/crmeca.308}, language = {en}, }
TY - JOUR AU - Chuong Anthony Tran AU - Emilio Barchiesi AU - Roberto Busonera AU - Mustafa Erden Yildizdag AU - Ilaria Trivelloni AU - Emilio Turco TI - Physical digital twins for ancient stone masonry informed of original construction techniques: the case of Sardinian nuraghi JO - Comptes Rendus. Mécanique PY - 2025 SP - 791 EP - 813 VL - 353 PB - Académie des sciences, Paris DO - 10.5802/crmeca.308 LA - en ID - CRMECA_2025__353_G1_791_0 ER -
%0 Journal Article %A Chuong Anthony Tran %A Emilio Barchiesi %A Roberto Busonera %A Mustafa Erden Yildizdag %A Ilaria Trivelloni %A Emilio Turco %T Physical digital twins for ancient stone masonry informed of original construction techniques: the case of Sardinian nuraghi %J Comptes Rendus. Mécanique %D 2025 %P 791-813 %V 353 %I Académie des sciences, Paris %R 10.5802/crmeca.308 %G en %F CRMECA_2025__353_G1_791_0
Chuong Anthony Tran; Emilio Barchiesi; Roberto Busonera; Mustafa Erden Yildizdag; Ilaria Trivelloni; Emilio Turco. Physical digital twins for ancient stone masonry informed of original construction techniques: the case of Sardinian nuraghi. Comptes Rendus. Mécanique, Volume 353 (2025), pp. 791-813. doi: 10.5802/crmeca.308
[1] Conservazione e restauro strutturale dei beni architettonici, CittàStudi, 2017, 448 pages
[2] Conservation-oriented integrated approach for structural stability assessment of complex historic masonry structures, J. Eng. Res., Volume 13 (2024) no. 2, pp. 1551-1593 | DOI
[3] Structural restoration of monuments: recommendations and advances in research and practice, Proceedings of the 1st International Conference on Restoration of Heritage Masonry Structures (2006), p. 16
[4] The ISCARSAH guidelines on the analysis, conservation and structural restoration of architectural heritage, SAHC 2021: 12th International Conference on Structural Analysis of Historical Constructions, International Centre for Numerical Methods in Engineering (CIMNE) (2021), pp. 1629-1640
[5] Conservation of building and decorative stone, Routledge, 2007, 478 pages | DOI
[6] Conservation of historic buildings, Routledge, 2007, 404 pages | DOI
[7] Structural damage and remedial measures for the temples of Angkor, Cambodia, Struct. Eng. Int., Volume 11 (2001) no. 4, pp. 234-236 | DOI
[8] Modeling strategies for the computational analysis of unreinforced masonry structures: review and classification, Arch. Comput. Methods Eng., Volume 27 (2020), pp. 1153-1185 | DOI
[9] Computations on historic masonry structures, Prog. Struct. Eng. Mater., Volume 4 (2002) no. 3, pp. 301-319 | DOI
[10] Computational modeling of masonry structures using the discrete element method, IGI Global, 2016, 300 pages | DOI
[11] Simulations of masonry-infilled reinforced concrete frame failure, Eng. Comput. Mech., Volume 166 (2013) no. 4, pp. 179-193 | DOI
[12] Finite element model for masonry, J. Struct. Div., Volume 104 (1978) no. 8, pp. 1267-1285 | DOI
[13] Out-of-plane strength reduction of unreinforced masonry walls because of in-plane damages, Earthq. Eng. Struct. Dyn., Volume 44 (2015) no. 13, pp. 2157-2176 | DOI
[14] Uses and limits of the equivalent frame model on existing unreinforced masonry buildings for assessing their seismic risk: a review, J. Build. Eng., Volume 10 (2017), pp. 166-182 | DOI
[15] A mathematical description of macroscopic behaviour of brick masonry, Int. J. Solids Struct., Volume 29 (1992) no. 5, pp. 531-546 | DOI | Zbl
[16] Three-dimensional Cosserat homogenization of masonry structures: elasticity, Acta Geot., Volume 3 (2008), pp. 71-83 | DOI
[17] Shell elements for sequentially linear analysis: lateral failure of masonry structures, Eng. Struct., Volume 31 (2009) no. 7, pp. 1382-1392 | DOI
[18] Robust modeling of RC structures with an ‘event-by-event’ strategy, Eng. Fract. Mech., Volume 75 (2008) no. 3-4, pp. 590-614 | DOI
[19] Dynamics of structures, Computers and Structures, 2003, 739 pages
[20] Variational principles are a powerful tool also for formulating field theories, Variational models and methods in solid and fluid mechanics (Francesco dell’Isola; Sergey Garvrilyuk, eds.), Springer, 2011, pp. 1-15 | Zbl
[21] Least action and virtual work principles for the formulation of generalized continuum models, Discrete and continuum models for complex metamaterials (Francesco dell’Isola; David J. Steigmann, eds.), Cambridge University Press, 2020, pp. 327-394 | DOI
[22] The method of virtual power in continuum mechanics. Part 2: Microstructure, SIAM J. Appl. Math., Volume 25 (1973) no. 3, pp. 556-575 | DOI | Zbl
[23] The method of virtual power in the mechanics of continuous media, I: Second-gradient theory, Math. Mech. Complex Syst., Volume 8 (2020) no. 2, pp. 153-190 | DOI | MR | Zbl
[24] The principle of virtual power: from eliminating metaphysical forces to providing an efficient modelling tool, Contin. Mech. Thermodyn., Volume 25 (2013) no. 2, pp. 127-146 | DOI | MR | Zbl
[25] The influence of different geometries of matrix/scaffold on the remodeling process of a bone and bioresorbable material mixture with voids, Math. Mech. Solids, Volume 22 (2017) no. 5, pp. 969-987 | DOI | MR | Zbl
[26] Bio-inspired design of a porous resorbable scaffold for bone reconstruction: a preliminary study, Biomimetics, Volume 6 (2021) no. 1, p. 18 | DOI
[27] A bone remodeling model involving two mechanical stimuli originated from shear and normal load conditions within the 3D continuum mechanics framework, Contin. Mech. Thermodyn., Volume 37 (2025) no. 1, p. 7 | DOI
[28] Simulating bone healing with bio-resorbable scaffolds in a three-dimensional system: insights into graft resorption and integration, C. R. Méc., Volume 353 (2025) no. G1, pp. 479-497 | DOI
[29] Higher-gradient continua: The legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives, Math. Mech. Solids, Volume 22 (2017) no. 4, pp. 852-872 | DOI | MR | Zbl
[30] Analytical continuum mechanics à la Hamilton–Piola least action principle for second gradient continua and capillary fluids, Math. Mech. Solids, Volume 20 (2015) no. 4, pp. 375-417 | DOI | Zbl
[31] A Biot-Cosserat two-dimensional elastic nonlinear model for a micromorphic medium, Contin. Mech. Thermodyn., Volume 32 (2020) no. 5, pp. 1357-1369 | DOI | MR
[32] Identification of a geometrically nonlinear micromorphic continuum via granular micromechanics, Z. Angew. Math. Phys., Volume 72 (2021), pp. 1-21 | Zbl
[33] The method of virtual power in continuum mechanics: application to coupled fields, Acta Mech., Volume 35 (1980) no. 1, pp. 1-70 | DOI | MR | Zbl
[34] Minimization variational principles for acoustics, elastodynamics and electromagnetism in lossy inhomogeneous bodies at fixed frequency, Proc. R. Soc. A: Math. Phys. Eng. Sci., Volume 465 (2009) no. 2102, pp. 367-396 | DOI | MR | Zbl
[35] Anisotropic and dispersive wave propagation within strain-gradient framework, Wave Motion, Volume 63 (2016), pp. 120-134 | DOI | Zbl
[36] A class of one dimensional periodic microstructures exhibiting effective Timoshenko beam behavior, ESAIM, Control Optim. Calc. Var., Volume 29 (2023), pp. 53-80 | DOI | Zbl
[37] A beam model for duoskelion structures derived by asymptotic homogenization and its application to axial loading problems, Eur. J. Mech. A Solids, Volume 98 (2023), 104848 | Zbl
[38] Asymptotic comparison of the strain-gradient and micromorphic models when loading forces are widely spread, Theoretical analyses, computations, and experiments of multiscale materials: a tribute to Francesco dell’Isola (Ivan Giorgio; Luca Placidi; Emilio Barchiesi; Bilen Emek Abali; Holm Altenbach, eds.), Springer, 2022, pp. 253-272 | DOI | Zbl
[39] Linear pantographic sheets: asymptotic micro-macro models identification, Math. Mech. Complex Syst., Volume 5 (2017) no. 2, pp. 127-162 | DOI | Zbl
[40] Equilibria of axial-transversely loaded homogenized duoskelion beams, Math. Mech. Complex Syst., Volume 12 (2024) no. 3, pp. 283-309 | DOI | MR | Zbl
[41] Multi-scale approaches to micro-structured materials modeling, Comprehensive mechanics of materials (First Edition) (Vadim Silberschmidt, ed.), Elsevier, 2024, pp. 98-135 | DOI
[42] Plane bias extension test for a continuum with two inextensible families of fibers: a variational treatment with Lagrange multipliers and a perturbation solution, Int. J. Solids Struct., Volume 81 (2016), pp. 1-12 | DOI
[43] Advances in pantographic structures: design, manufacturing, models, experiments and image analyses, Contin. Mech. Thermodyn., Volume 31 (2019) no. 4, pp. 1231-1282 | DOI
[44] Large in-plane elastic deformations of bi-pantographic fabrics: asymptotic homogenization and experimental validation, Math. Mech. Solids, Volume 25 (2020) no. 3, pp. 739-767 | DOI | Zbl
[45] Analysis of transmission and reflection characteristics of linear plane waves in pantographic lattices, Z. Angew. Math. Phys., Volume 74 (2023) no. 5, p. 178 | DOI | MR | Zbl
[46] An approach to the mechanics of pantographic structures through swarm dynamics, Math. Mech. Solids (2024), 36 pages | DOI
[47] Towards the synthesis of planar beams whose deformation energy depends on the third gradient of displacement, Math. Mech. Complex Syst., Volume 12 (2024) no. 4, pp. 573-597 | DOI | Zbl
[48] Existence of weak solutions in elasticity, Math. Mech. Solids, Volume 18 (2013) no. 2, pp. 204-217 | DOI | MR | Zbl
[49] Linear pantographic sheets: existence and uniqueness of weak solutions, J. Elasticity, Volume 132 (2018), pp. 175-196 | DOI | Zbl
[50] On existence and uniqueness of weak solutions for linear pantographic beam lattices models, Contin. Mech. Thermodyn., Volume 31 (2019) no. 6, pp. 1843-1861 | DOI
[51] Continuum models for pantographic blocks with second gradient energies which are incomplete, Mech. Res. Commun., Volume 125 (2022), 103988 | DOI
[52] The theory of elastic and viscoelastic micropolar liquids, J. Appl. Math. Mech., Volume 63 (1999) no. 5, pp. 755-767 | DOI
[53] Additive manufacturing introduced substructure and computational determination of metamaterials parameters by means of the asymptotic homogenization, Contin. Mech. Thermodyn., Volume 33 (2021) no. 4, pp. 993-1009 | DOI | MR
[54] Strain-gradient modeling and computation of 3-d printed metamaterials for verifying constitutive parameters determined by asymptotic homogenization, Theoretical analyses, computations, and experiments of multiscale materials: a tribute to Francesco dell’Isola (Ivan Giorgio; Luca Placidi; Emilio Barchiesi; Bilen Emek Abali; Holm Altenbach, eds.), Springer, 2022, pp. 343-357 | DOI | Zbl
[55] On the dependence of standard and gradient elastic material constants on a field of defects, Math. Mech. Solids, Volume 25 (2020) no. 1, pp. 35-45 | DOI | MR | Zbl
[56] Computation of brittle fracture propagation in strain gradient materials by the FEniCS library, Math. Mech. Solids, Volume 26 (2020) no. 3, pp. 325-340 | DOI | MR | Zbl
[57] A variational approach for a nonlinear 1-dimensional second gradient continuum damage model, Contin. Mech. Thermodyn., Volume 27 (2015), pp. 623-638 | DOI | MR | Zbl
[58] A variational approach for a nonlinear one-dimensional damage-elasto-plastic second-gradient continuum model, Contin. Mech. Thermodyn., Volume 28 (2016), pp. 119-137 | MR | Zbl | DOI
[59] Thermomechanics-based nonlinear rate-dependent coupled damage-plasticity granular micromechanics model, Contin. Mech. Thermodyn., Volume 27 (2015) no. 4, pp. 787-817 | DOI | MR | Zbl
[60] Hemivariational continuum approach for granular solids with damage-induced anisotropy evolution, Math. Mech. Solids, Volume 26 (2021) no. 5, pp. 738-770 | DOI | Zbl | MR
[61] Emergence of critical state in granular materials using a variationally-based damage-elasto-plastic micromechanical continuum model, Int. J. Numer. Anal. Methods Geomech., Volume 48 (2024) no. 13, pp. 3369-3391 | DOI
[62] A parametric study on a granular micromechanics continuum-based hemivariational approach: unraveling the emergence of critical states in granular materials, Math. Mech. Complex Syst., Volume 13 (2025) no. 1, pp. 25-54 | DOI | MR | Zbl
[63] A procedure for the experimental identification of the strain gradient characteristic length, Z. Angew. Math. Phys., Volume 75 (2024) no. 3, pp. 1-14 | Zbl | MR
[64] Strain-gradient finite elasticity solutions to rigid bar pull-out test, Contin. Mech. Thermodyn., Volume 36 (2024) no. 3, pp. 607-617 | DOI | MR
[65] Chirality in 2D Cosserat media related to stretch-micro-rotation coupling with links to granular micromechanics, Int. J. Solids Struct., Volume 202 (2020), pp. 28-38 | DOI
[66] A new block-based approach for the analysis of damage in masonries undergoing large deformations, Contin. Mech. Thermodyn., Volume 35 (2023) no. 4, pp. 1625-1654 | DOI | MR
[67] Validation of a hemi-variational block-based approach to the modelling of common in-plane failures in masonry structures, Sixty shades of generalized continua: dedicated to the 60th birthday of Prof. Victor A. Eremeyev (Holm Altenbach; Arkadi Berezovski; Francesco dell’Isola; Alexey Porubov, eds.), Springer, 2023, pp. 191-210 | DOI
[68] A hemivariational damageable elastoplastic vertex-spring model for masonry analysis, Math. Mech. Solids, Volume 30 (2025) no. 1, pp. 57-72 | DOI
[69] Towards the Galerkin approximation of tetraskelion metamaterials, Contin. Mech. Thermodyn., Volume 37 (2025) no. 1, 6 pages | MR
[70] Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models, Z. Angew. Math. Phys., Volume 67 (2016), pp. 1-28 | MR | Zbl
[71] Pantographic lattices with non-orthogonal fibres: experiments and their numerical simulations, Compos. B. Eng., Volume 118 (2017), pp. 1-14 | DOI
[72] How swarm robot dynamic can describe mechanical systems, International Conference on Robots for Space Applications in Orbital Stations, Springer (2023), pp. 148-159
[73] Rules governing swarm robot in continuum mechanics, Math. Mech. Solids, Volume 27 (2022) no. 10, pp. 1930-1949 | DOI | Zbl
[74] Flocking rules governing swarm robot as tool to describe continuum deformation, Dynamics, strength of materials and durability in multiscale mechanics (Advanced Structured Materials), Springer, 2021 no. 137, pp. 223-243 | DOI | Zbl
[75] Position-based dynamic of a particle system: a configurable algorithm to describe complex behaviour of continuum material starting from swarm robotics, Contin. Mech. Thermodyn., Volume 30 (2018) no. 5, pp. 1069-1090 | DOI | Zbl
[76] Revisiting digital twins: origins, fundamentals, and practices, Front. Eng. Manage., Volume 9 (2022) no. 4, pp. 668-676 | DOI
[77] Application of digital 3D models on urban planning and highway design, WIT Trans. Built Environ., Volume 30 (1997), pp. 391-402
[78] A brief overview on crack patterns, repair and strengthening of historical masonry structures, Materials, Volume 16 (2023) no. 5, 1882, 22 pages | DOI
[79] On the vulnerability of historical masonry structures: analysis and mitigation, Mater. Struct., Volume 40 (2007), pp. 723-743 | DOI
[80] Advancing cultural heritage structures conservation: integrating BIM and cloud-based solutions for enhanced management and visualization, Heritage, Volume 6 (2023) no. 12, pp. 7316-7342 | DOI
[81] A seismic behavior and rehabilitation of the historic masonry minaret by experimental and numerical methods, Asian J. Civ. Eng, Volume 18 (2017) no. 5, pp. 807-822
[82] Stability analysis of leaning historic masonry structures, Autom. Constr., Volume 92 (2018), pp. 199-213 | DOI
[83] I nuraghi: torri preistoriche di Sardegna, Edizioni “La Zattera”, 1962, 206 pages
[84] La civiltà dei Sardi: dal neolitico all’età dei nuraghi, Edizioni “La Zattera”, 1963
[85] La civiltà nuragica, Carlo Delfino editore, 1982, 352 pages
[86] Il nuraghe, Civiltà nuragica, Electa, 1985, pp. 45-109
[87] Sardinia’s nuraghi: four millennia of becoming, World Archaeol., Volume 30 (1998) no. 1, pp. 59-71 | DOI
[88] L’alba dei nuraghi, Fabula, 2006, 279 pages
[89] Il bronzo medio della Sardegna, Atti della XLIV Riunione scientifica: la preistoria e la protostoria della Sardegna (Cagliari, Barumini, Sassari, 23-28 novembre 2009), Istituto italiano di preistoria e protostoria, 2009, pp. 123-130
[90] Il bronzo recente della Sardegna, Atti della XLIV Riunione scientifica: la preistoria e la protostoria della Sardegna (Cagliari, Barumini, Sassari, 23-28 novembre 2009), Istituto italiano di preistoria e protostoria, 2009, pp. 131-140
[91] Il bronzo finale della Sardegna, Atti della XLIV Riunione scientifica: la preistoria e la protostoria della Sardegna (Cagliari, Barumini, Sassari, 23-28 novembre 2009), Istituto italiano di preistoria e protostoria, 2009, pp. 141-154
[92] I Nuraghi. Le torri dell’isola, L’isola delle torri: Giovanni Lilliu e la Sardegna nuragica (Marco Minoja; Gianfranca Salis; Luisanna Usai, eds.), Carlo Delfino editore, 2015, pp. 76-83
[93] Le origini della civiltà nuragica, L’isola delle torri: Giovanni Lilliu e la Sardegna nuragica (Marco Minoja; Gianfranca Salis; Luisanna Usai, eds.), Carlo Delfino editore, 2015, pp. 70-75
[94] I nuraghi, La Sardegna nuragica, storia e monumenti (Alberto Moravetti; Paolo Melis; Lavinia Foddai; Elisabetta Alba, eds.), Carlo Delfino editore, 2017
[95] Dal nuraghe a corridoio al nuraghe complesso, Il tempo dei nuraghi. La Sardegna dal XVIII all’VIII secolo aC, Ilisso Nuoro, 2018, pp. 54-60
[96] A prehistory of Sardinia 2300–500 BC, Monographs in Mediterranean Archaeology, Sheffield Academic Press, 1996 no. 5, 224 pages
[97] The nuragic civilization, Carlo Delfino editore, 2003, 96 pages
[98] Evoluzione tipologica delle camere dei nuraghi: un’approssimazione morfometrica, Atti della XLIV Riunione scientifica: la preistoria e la protostoria della Sardegna (Cagliari, Barumini, Sassari, 23-28 novembre 2009), Istituto italiano di preistoria e protostoria, 2012, pp. 671-678
[99] Appunti sulla civiltà nuragica, L’isola delle torri: Giovanni Lilliu e la Sardegna nuragica (Marco Minoja; Gianfranca Salis; Luisanna Usai, eds.), Carlo Delfino editore, 2015, pp. 37-57
[100] Considerazioni sui protonuraghi, La Sardegna nuragica, storia e monumenti (Alberto Moravetti; Paolo Melis; Lavinia Foddai; Elisabetta Alba, eds.), Carlo Delfino editore, 2017, pp. 11-27
[101] Nuraghi, santuari, tombe monumentali, L’età del bronzo recente in Italia. Atti del Congresso Nazionale di Lido di Camaiore, 26-29 ottobre 2000, M. Baroni (2004), p. 383-98
[102] L’edilizia nell’antichità, Carocci editore, 1990, 226 pages
[103] An investigation into the construction of Sardinian nuraghi, Pap. Br. Sch. Rome, Volume 55 (1987), pp. 1-74 | DOI
[104] Discrete element analysis on the Sardinian “Nuraghe”, STRUMAS V, International Symposium on Computer Methods in Structural Masonry, Rome (2001), pp. 719-728
[105] 4D recording and analysis: The case study of Nuraghe Oes (Giave, Sardinia), Appl. Archaeol. Cult. Heritage, Volume 2 (2015) no. 4, pp. 233-239 | DOI
[106] 3D modelling approach to enhance the characterization of a Bronze Age nuragic site, Minerals, Volume 14 (2024) no. 5, p. 489 | DOI
[107] On a hemi-variational formulation for a 2D elasto-plastic-damage strain gradient solid with granular microstructure, Math. Eng., Volume 5 (2022), pp. 1-24 | DOI
[108] Emergence of bimodulus (tension-compression asymmetric) behavior modeled in granular micromechanics framework, Math. Mech. Solids (2025) | DOI
[109] Maximum mechano-damage power release-based phase-field modeling of mass diffusion in damaging deformable solids, Z. Angew. Math. Phys., Volume 73 (2022) no. 1, p. 35 | DOI | MR | Zbl
[110] Fluid diffusion related aging effect in a concrete dam modeled as a Timoshenko beam, Math. Mech. Complex Syst., Volume 11 (2023) no. 2, pp. 313-334 | DOI | MR | Zbl
[111] Application of mechanical modelling strategies to the hygrothermal analysis of masonry walls, European Congress on Computational Methods in Applied Sciences and Engineering, European Congress on Computational Methods in Applied Sciences and Engineering (2024), p. 12
[112] Moisture and temperature effects on masonry structures: the civic tower of Pavia as a case study, International Brick and Block Masonry Conference, Springer (2025), pp. 845-865 | DOI
[113] A variational formulation for three-dimensional linear thermoelasticity with ’thermal inertia’, Meccanica, Volume 59 (2024), pp. 1745-1756 | DOI | MR | Zbl
[114] New variational-Lagrangian irreversible thermodynamics with application to viscous flow, reaction–diffusion, and solid mechanics, Adv. Appl. Mech., Volume 24 (1984), pp. 1-91 | DOI | MR | Zbl
[115] Numerical and analytical studies of kinetics, equilibrium, and stability of the chemical reaction fronts in deformable solids, Ph. D. Thesis, Technische Universität Berlin (Germany) (2021)
Cité par Sources :
Commentaires - Politique