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For the study, the experimental data and the McNab–Foster model are used. It is shown that an artificially formed specific inhomogeneity in the distribution of hydrogen concentrations significantly affects the shape of thermal desorption spectra and in turn the results of their interpretation based on the Choo–Lee plot and the Kissinger formula. Large errors are possible in the binding energies determined by means of the thermal desorption spectra, provided that the skin layer is formed artificially when the samples are charged with hydrogen. It is shown that the standard description of thermal desorption of hydrogen based upon the one-dimensional model leads to errors. The three-dimensional formulation of problem of hydrogen diffusion in cylindrical sample results in a broken line in the Choo–Lee plot rather than a straight line obtained in the framework of one-dimensional formulation. Comparison of experimental data with the 3D simulation data convinces that effect of the skin layer on the thermal desorption spectra is associated only with the diffusion of hydrogen at the sites of the crystal lattice in the McNab–Foster model.\n",{"EN":149},"Necessity of 3D modeling for simulation of impact of skin effect of hydrogen charging on the binding energy of traps determined from the thermal desorption spectra",{"VOID":151},"[\"737173416755035233\"]",{"VOID":153},"Cailletet, L.: First report of h embrittlement of metals. Compt. Rend 58, 327 (1864)\nGraham, T.: XVIII: on the absorption and dialytic separation of gases by colloid septa. Philos. Trans. R. Soc. Lond. 156, 399–439 (1866). https:\u002F\u002Fdoi.org\u002F10.1098\u002Frstl.1866.0018\nJohnson, W.H.: II: on some remarkable changes produced in iron and steel by the action of hydrogen and acids. Proc. R. Soc. 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Eng., A 742, 712–721 (2019). https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.msea.2018.09.048\nWu, R., Ahlström, J., Magnusson, H., Frisk, K., Martinsson, A., Kimab, S.: Charging, Degassing and Distribution of Hydrogen in Cast Iron. Svensk kärnbränslehantering (SKB) (2015)\nPolyanskiy, V., Belyaev, A., Alekseeva, E., Polyanskiy, A., Tretyakov, D., Yakovlev, Y.A.: Phenomenon of skin effect in metals due to hydrogen absorption. Continuum Mech. Thermodyn. 31(6), 1961–1975 (2019). https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs00161-019-00839-2\nAlekseeva, E.L., Belyaev, A.K., Polyanskiy, A.M., Polyanskiy, V.A., Varshavchik, E.A., Yakovlev, Y.A.: Surface vs diffusion in TDS of hydrogen. In: E3S Web of Conferences, vol. 121, p. 01012 (2019). https:\u002F\u002Fdoi.org\u002F10.1051\u002Fe3sconf\u002F201912101012. EDP Sciences\nPolyanskiy, V.A., Belyaev, A.K., Chevrychkina, A.A., Varshavchik, E.A., Yakovlev, Y.U.A.: Impact of skin effect of hydrogen charging on the Choo–Lee plot for cylindrical samples. Int. J. Hydrog. Energy 46(9), 6979–6991 (2021). https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.ijhydene.2020.11.192\nLiu, Y., Wang, M., Liu, G.: Hydrogen trapping in high strength martensitic steel after austenitized at different temperatures. Int. J. Hydrogen Energy 38(33), 14364–14368 (2013). https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.ijhydene.2013.08.121\nTakashima, K., Han, R., Yokoyama, K., Funakawa, Y.: Hydrogen embrittlement induced by hydrogen charging during deformation of ultra-high strength steel sheet consisting of ferrite and nanometer-sized precipitates. 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Energy 43(50), 22685–22693 (2018). https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.ijhydene.2018.10.121\nZheng, Y., Zhang, L., Shi, Q., Zhou, C., Zheng, J.: Effects of hydrogen on the mechanical response of X80 pipeline steel subject to high strain rate tensile tests. Fatigue Fract. Eng. Mater. Struct. 43(4), 684–697 (2020). https:\u002F\u002Fdoi.org\u002F10.1111\u002Fffe.13151\nFick, A.: Ueber Diffusion. Ann. Phys. 170(1), 59–86 (1855)\nArrhenius, S.: Über die dissociationswärme und den einfluss der temperatur auf den dissociationsgrad der elektrolyte. Z. Phys. Chem. 4U(1), 96–116 (1889). https:\u002F\u002Fdoi.org\u002F10.1515\u002Fzpch-1889-0408\nDarken, L.S., Smith, R.P.: Behavior of hydrogen in steel during and after immersion in acid. Corrosion 5(1), 1–16 (1949)\nMcNabb, A., Foster, P.K.: A new analysis of the diffusion of hydrogen in iron and ferrite. Trans. Metallic. Soc. 227, 618–627 (1963)\nPressouyre, G.: A classification of hydrogen traps in steel. Metall. Trans. 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Hydrogen Energy 39(30), 17381–17390 (2014). https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.ijhydene.2014.07.080\nBelyaev, A.K., Polyanskiy, A.M., Polyanskiy, V.A., Sommitsch, C., Yakovlev, Y.A.: Multichannel diffusion vs tds model on example of energy spectra of bound hydrogen in 34CrNiMo6 steel after a typical heat treatment. Int. J. Hydrogen Energy 41(20), 8627–8634 (2016). https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.ijhydene.2016.03.198\nAndronov, D.Y., Arseniev, D.G., Polyanskiy, A.M., Polyanskiy, V.A., Yakovlev, Y.A.: Application of multichannel diffusion model to analysis of hydrogen measurements in solid. Int. J. Hydrogen Energy 42(1), 699–710 (2017). https:\u002F\u002Fdoi.org\u002F10.1016\u002Fj.ijhydene.2016.10.126\nFrolova, K.P., Vilchevskaya, E.N., Polyanskiy, V.A., Yakovlev, Y.A.: Modeling the skin effect associated with hydrogen accumulation by means of the micropolar continuum. Continuum Mech. 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The parameters for the modified Nakamura–Ziabicki model, which depend on the local cooling rates, are identified based on fitting the model to flash DSC (differential scanning calorimetry with high cooling rates) and standard DSC non-isothermal cooling experiments. 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Sci. 42(5), 940–950 (2002). https:\u002F\u002Fdoi.org\u002F10.1002\u002Fpen.11003",{"doi":644},"10.1002\u002Fpen.11003",{"id":646,"createTime":647,"updateTime":648,"relativeEntities":649,"slug":650,"properties":651,"entityType":156,"verifyStatus":157,"verifyTime":662,"verifyNote":159,"languages":22,"translateLanguages":22,"viewCount":23,"primaryUrl":663,"fullTextUrl":22,"authors":664,"publicationType":223,"publisherRelationship":695,"citationCount":22,"citationInfo":22,"publishDate":751,"publishYear":752,"citationAnalyzeStatus":21,"lastCitationAnalyze":753,"indexDatabases":754,"openAccess":22,"references":22,"isForceReanalyzing":285},"58a68b63-c997-43c4-815e-88aad2e8f812","2024-01-10T06:17:43.439+00:00","2026-07-21T16:10:05.059+00:00",[],"The-computation-of-the-dynamics-of-the-martensitic-transformation",{"abstract":652,"title":654,"gsPaper":656,"references":658,"doi":660},{"EN":653},"We present numerical computations for the dynamics of the development of twinned martensitic microstructure and for the propagation of the austeniticfinely twinned martensitic interface. Our computations approximated a threedimensional model for the dynamics of the In-20.7 at% T1 alloy which used the stress tensor derived from the Ericksen-James energy density.",{"EN":655},"The computation of the dynamics of the martensitic transformation",{"VOID":657},"[\"12903534346598867710\"]",{"VOID":659},"J. M. Ball, P. J. Holmes, R. D. James, R. L. Pego, and P. J. Swart,On the dynamics of fine structure, J. Nonlinear Sci. 1 (1990), 17–70\nJ. M. Ball and R. D. James,Fine phase mixtures as minimizers of energy, Arch. Rational Mech. Anal. 100 (1987), 13–52\nJ. M. Ball and R. D. James,Proposed experimental tests of a theory of fine microstructure and the two-well problem, Phil. Trans. R. Soc. Lond. A 338 (1992), 389–450\nZ.S. Basinski and J.W. Christian,Experiments on the martensitic transformation in single crystals of indium-thallium alloys, Acta Met. 2 (1954), 148–166\nM. W. Burkart and T. A. Read,Diffusionless phase change in the indium-thallium system, Trans. AIME J. 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Luskin,Optimal order estimates for the numerical approximation of the solution of a variational problem with a double well potential, Math. Comp. 57 (1991), 621–637\nC. Collins, M. Luskin, and J. Riordan,Computational images of crystalline microstructure, Computing Optimal Geometries (J. Taylor, ed.), AMS Special Lectures in Mathematics and AMS Videotape Library, Amer. Math. Soc., Providence, 1991, pp. 16–18\nC. Collins, M. Luskin, and J. Riordan,Computational results for a two-dimensional model of crystalline microstructure, in Microstructure and Phase Transitions (James, Kinderlehrer, and Luskin,eds.), IMA Volumes in Mathematics and its Applications, Springer-Verlag, New York, vol. 54, 1993, pp. 51–56\nJ. L. Ericksen,Some constrained elastic crystals, Material Instabilities in Continuum Mechanics and Related Problems, J. M. Ball, ed., Oxford Univ. Press, 1987, pp. 119–137\nJ. L. Ericksen,Constitutive theory for some constrained elastic crystals, Int. J. Solids and Structures 22 (1986), 951–964\nG. Golub and C. Van Loan,Matrix computations, Second Ed, Johns Hopkins Univ, Baltimore, 1989\nR. James,Basic principles for the improvement of shape-memory and related materials, Smart Materials, Structures, and Mathematical Issues, C. Rogers, ed., Technomic Publishing Co., 1989, pp. 156–163\nD. Kinderlehrer,Remarks about equilibrium configurations of crystals, Material Instabilities in Continuum Mechanics and Related Problems, J. M. Ball, ed., Oxford University Press, 1987, pp. 217–242\nR. Kohn,Relaxation of a double-well energy, Continuum Mechanics and Thermodynamics 3 (1991), 193–236\nM. Luskin,Numerical analysis of microstructure for crystals with a nonconvex energy density, in Progress in Partial differential eequations: the Metz Surveys (M. Chipot and J. Saint Jean Paulin, eds.), Pitman Research Notes in Mathematics Series, #249, Longman House, UK, 1991, pp. 156–165\nR. Pego,Phase transitions in one-dimensional nonlinear viscoelasticity, Arch. Rational Mech. Anal. 97 (1987), 353–394\nR. Rannacher and S. Turek,Simple nonconforming quadrilateral Stokes element, Nummer. Meth. for PDEs 8 (1992), 97–111\nP. Rybka,Dynamical modeling of phase transitions by means of viscoelasticity in many dimensions, Proc. Roy. Soc. Edinburgh 121A (1992), 101–138\nP. J. Swart and P. J. Holmes,Energy minimization and the formation of microstructure in dynamic anti-plane shear, Arch. Rational Mech. 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All the contributions to growth of solute chemicals and nutrients are here resumed in one scalar descriptor, the biochemical energy of the system. The free energy of the system accounts for both strain and biochemical storage. The exploitation of a dissipation inequality by standard means provides admissible couplings between growth, tension and energy. Specific admissible constitutive equations lead back, in some cases, to classical models.",{"EN":765},"Growth and dissipation in biological tissues",{"VOID":767},"[\"15993670124400910322\"]",{"VOID":769},"Ambrosi D. and Guana F. (2007). Stress-modulated growth. Math. Mech. Solids 12(3): 319–342\nAteshian, G.A.: On the theory of reactive mixtures for modelling biological growth. Biomechan. Model. Mechanobiol. (2007, in press)\nCermelli P., Fried E. and Sellers S. (2001). Configurational stress, yield and flow in rate-independent plasticity. Proc. R. Soc. Lond. 457: 1447–1467\nDiCarlo A. and Quiligotti S. (2002). Growth and balance. Mech. Res. Commun. 29: 449–456\nFusi L., Farina A. and Ambrosi D. (2006). Mathematical modelling of a solid–liquid mixture with mass exchange between constituents. Math. Mech. Solids 11(6): 575–595\nGarikipati K., Arruda E.M., Grosh K., Narayanan H. and Calve S. (2004). A continuum treatment of growth in biological tissue: the coupling of mass transport and mechanics. J. Mech. Phys. Solids 52(7): 1595–1625\nGuillou A. and Ogden R. (2006). Growth in soft biological tissue and residual stress development. In: Holzapfel, G.A. and Ogden, R.W. (eds) Mechanics of biological tissue., pp. Springer, Heidelberg\nHan B., Bai X.H., Lodyga M., Xu J., Yang B.B., Keshavjee S., Post M. and Liu M. (2004). Conversion of mechanical forces into biochemical signalling. J. Biol. Chem. 279(52): 54793–54801\nHu Y., Bock G., Wick G. and Xu Q. (1998). Activation of PDGF receptor a in vascular smooth muscle cells by mechanical stress. FASEB J. 12: 1135–1142\nHumphrey J.D. (2003). Continuum biomechanics of soft biological tissues. Proc. R. Soc. 459: 3–46\nLiu S.Q. and Fung Y.C. (1989). Relationship between hypertension, hypertrophy and opening angle of zero-stress state of arteries following aortic constriction. J. Biomech. Eng. 111: 325–335\nMichaelis M. and Menten M. (1913). Die Kinetik der Invertinwirkung. Biochem. Z. 49: 333–369\nMurray J.D. (2004). Mathematical biology, 3rd edn. Springer, Heidelberg\nRodriguez E.K., Hoger A. and McCulloch A. (1994). Stress dependent finite growth in soft elastic tissues. J. Biomech. 27: 455–467\nRachev A., Stergiopulos N. and Meister J.J. (1996). Theoretical study of dynamics of arterial wall remodeling in response to changes in blood pressure. J. Biomech. 29(5): 635–642\nRachev A., Stergiopulos N. and Meister J.-J. (1998). A model for geometric and mechanical adaptation of arteries to sustained hypertension. J. Biomech. Eng. 120: 9–17\nTaber L.A. (1995). Biomechanics of growth, remodeling and morphogenesis. Appl. Mech. Rev. 48(8): 487–545\nTaber L.A. (1998). A model for aortic growth based on fluid shear and fiber stresses. J. Biomech. Eng. 120: 348–354\nZhu C., Bao G. and Wang N. (2000). Cell mechanics: mechanical response, cell adhesion, and molecular deformation. A. Rev. Biomed. 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P., Le Tallec P., Perlat J.P., Perthame B.: Entropy condition for the ES BGK model of Boltzmann equation for mono and polyatomic gases. Eur. J. Mech. B Fluids 19, 813–830 (2000)",{},{"id":22,"text":985,"url":22,"identifiers":986},"Arkeryd L.: Stability in L 1 for the spatially homogeneous equation. Arch. Rat. Mech. Anal. 103(2), 151–167 (1988)",{},{"id":22,"text":988,"url":22,"identifiers":989},"Bahi, Y.: Contribution la simulation numrique des coulements en gaz rarfis. Phd Thesis, University Pierre et Marie Curie, Paris (1997)",{},{"id":22,"text":991,"url":22,"identifiers":992},"Bhatnagar P.L., Gross E.P., Krook M.: A model for collision processes in gases. Phys. Rev. 94, 511 (1954)",{},{"id":994,"text":995,"url":996,"identifiers":997},"4c68646b-0035-4279-8000-0006b275d4fa","Borgnakke C., Larsen P.S.: Statistical collision model for Monte–Carlo simulation of polyatomic gas mixtures. J. Comp. Phys. 18, 405–420 (1975)","https:\u002F\u002Flink.springer.com\u002F10.1007\u002Fs10440-022-00541-7",{"doi":998},"10.1007\u002Fs10440-022-00541-7",{"id":22,"text":1000,"url":22,"identifiers":1001},"Bourgat J.F., Desvillettes L., Le Tallec P., Perthame B.: Microreversible collisions for polyatomic gases and Boltzmann’s theorem. Eur. J. Mech. B Fluids 13(2), 237–254 (1994)",{},{"id":994,"text":1003,"url":996,"identifiers":1004},"Brull S., Schneider J.: A new approach of the ellipsoidal statistical model. Cont. Mech. Thermodyn. 20(2), 63–74 (2008)",{"doi":998},{"id":994,"text":1006,"url":996,"identifiers":1007},"Cercignani, C.: The Boltzmann Equation and Its Applications, pp. 40–103. Scottish Academic Press, Edinburgh (1988)",{"doi":998},{"id":22,"text":1009,"url":22,"identifiers":1010},"Chapman, S., Cowling, T.G.: The Mathematical Theory of Non-Uniform Gases, 3rd Edn. Cambridge Mathematical Library (1970)",{},{"id":22,"text":1012,"url":22,"identifiers":1013},"Csiszár I.: I-divergence geometry of probability distributions and minimization problems Sanov property. Ann. Probab. 3, 146–158 (1975)",{},{"id":994,"text":1015,"url":996,"identifiers":1016},"Collet J.F.: Extensive Lyapounov functionals for moment-preserving evolution equations. C. R. A. S. Ser. I 334, 429–434 (2002)",{"doi":998},{"id":22,"text":1018,"url":22,"identifiers":1019},"Desvillettes L.: Sur un Modèle de type Borgnakke-Larsen Conduisant des lois d’Energie Non-linéaires en Température pour les Gaz Parfaits Polyatomiques. Ann. Fac. Sci. Toulouse Sér. 6(2), 257–262 (1997)",{},{"id":994,"text":1021,"url":996,"identifiers":1022},"Goldstein, D., Sturtevant, B., Broadwell, J.E.: Investigation of the motion of discrete-velocity gases, In: Muntz, E.P., Weaver, D.P., Campbell, D.H. (Eds.) Rarefied gas dynamics: theoretical and computational techniques, progress in astronautics and aeronautics, vol. 118, pp. 100–117 (1989)",{"doi":998},{"id":994,"text":1024,"url":996,"identifiers":1025},"Holway, L.H.: Kinetic theory of shock structure using an ellipsoidal distribution function. In: Rarefied Gas Dynamics [Proceedings Fourth International Symposium, University Toronto (1964)], vol. I. Academie Press, New York, pp. 193–215 (1966)",{"doi":998},{"id":994,"text":1027,"url":996,"identifiers":1028},"Kusker I.: A model for rotational energy exchange in polyatomic gases. Physica A 158, 784–800 (1989)",{"doi":998},{"id":994,"text":1030,"url":996,"identifiers":1031},"Le Tallec P.: A hierarchy of hyperbolic models linking Boltzmann to Navier Stokes equations for polyatomic gases. ZAMM 80(11–12), 779–790 (2000)",{"doi":998},{"id":1033,"text":1034,"url":1035,"identifiers":1036},"3a69c0c0-61d4-46b1-8f3d-5ac1b710c3d6","Levermore C.D.: Moment closure hierarchies for kinetic theories. J. Stat. Phys. 83, 1021–1065 (1996)","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002FBF02179552",{"doi":1037},"10.1007\u002FBF02179552",{"id":994,"text":1039,"url":996,"identifiers":1040},"Michel P., Schneider J.: Approximation simultanée de réels par des nombres rationnels et noyau de collision de l’équation de Boltzmann. CRAS-série 1 Maths. 330(9), 857–862 (2000)",{"doi":998},{"id":22,"text":1042,"url":22,"identifiers":1043},"Mieussens, L.: Modèles à vitesses discrètes et méthodes numériques pour l’équation de Boltzmann BGK. Phd Thesis (1999)",{},{"id":22,"text":1045,"url":22,"identifiers":1046},"Mieussens L.: Discrete velocity models and implicit scheme for the BGK equation rarefied gas dynamic. M3AS 10(8), 1121–1149 (2000)",{},{"id":994,"text":1048,"url":996,"identifiers":1049},"Junk M.: Domain of definition of Levermore’s five-moment system. J. Stat. Phys. 93, 1143–1167 (1998)",{"doi":998},{"id":22,"text":1051,"url":22,"identifiers":1052},"Junk M.: Maximum entropy for reduced moment problems. M3AS 10, 1121–1149 (2000)",{},{"id":994,"text":1054,"url":996,"identifiers":1055},"Rogier F., Schneider J.: A direct method for solving the Boltzmann equation. TTSP 23(1–3), 313–338 (1994)",{"doi":998},{"id":994,"text":1057,"url":996,"identifiers":1058},"Pullin D.I.: Kinetic models for polyatomic molecules with phenomenological energy exchange. Phys. Fluids 21, 209–216 (1978)",{"doi":998},{"id":22,"text":1060,"url":22,"identifiers":1061},"Schneider J.: Entropic approximation in kinetic theory. M2AN 38(3), 541–561 (2004)",{},{"id":994,"text":1063,"url":996,"identifiers":1064},"Palczewski A., Schneider J., Bobylev A.: A consistency result for a discrete-velocity model of the Boltzmann equation. SIAM. J. Numer. Anal. 34(5), 1865–1883 (1997)",{"doi":998},{"id":994,"text":1066,"url":996,"identifiers":1067},"Toscani G.: Remarks on entropy and equilibrium states. Appl. Math. Lett. 12(7), 19–25 (1999)",{"doi":998},{"id":1069,"text":1070,"url":1071,"identifiers":1072},"b379a4a9-1564-4bc9-81ed-fd2798333d29","Villani C.: Fisher information estimates for Boltzmann’s collision operator. J. Maths Pures Appl. 77, 821–837 (1998)","https:\u002F\u002Fwww.sciencedirect.com\u002Fscience\u002Farticle\u002Fpii\u002FS002178249880010X",{"doi":1073},"10.1016\u002Fs0021-7824(98)80010-x",{"id":1075,"text":1076,"url":1077,"identifiers":1078},"58fa62cc-0b2d-499b-a19c-61c7f37fe7bd","Wennberg, B.: Stability and Exponential Convergence for the Boltzmann Equation. Phd thesis, Chalmers University Tech. (1993)","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002FBF00375152",{"doi":1079},"10.1007\u002FBF00375152",{"id":1081,"createTime":1082,"updateTime":1083,"relativeEntities":1084,"slug":1085,"properties":1086,"entityType":156,"verifyStatus":157,"verifyTime":1097,"verifyNote":159,"languages":22,"translateLanguages":22,"viewCount":23,"primaryUrl":1098,"fullTextUrl":22,"authors":1099,"publicationType":223,"publisherRelationship":1153,"citationCount":23,"citationInfo":1209,"publishDate":1212,"publishYear":1210,"citationAnalyzeStatus":21,"lastCitationAnalyze":1213,"indexDatabases":1214,"openAccess":22,"references":22,"isForceReanalyzing":285},"8da5b0bb-f502-43b1-80f0-dd8180c77150","2023-12-11T10:35:05.368+00:00","2026-07-19T06:14:55.122+00:00",[],"An-asymptotic-membrane-model-for-wrinkling-of-very-thin-films",{"abstract":1087,"title":1089,"gsPaper":1091,"references":1093,"doi":1095},{"EN":1088},"In this work, a formal deduction of a two-dimensional membrane theory, similar to Landau–Lifshitz model, is performed via an asymptotic development of the weak formulation of the three-dimensional equations of elasticity. Some interesting aspects of the deduced model are investigated, in particular the property of obtaining a hyperbolic equation for the out-of-plane displacement under a certain class of boundary conditions and loads. Some simple cases are analyzed to show the relevant aspects of the model and the phenomenology that can be addressed. In particular, it is shown how this mathematical formulation is capable to describe instabilities well known as wrinkling, often observed for the buckling of very thin membranes.",{"EN":1090},"An asymptotic membrane model for wrinkling of very thin films",{"VOID":1092},"[\"7531898453803461184\"]",{"VOID":1094},"Friedrichs, K.O., Dressler, R.F.: A boundary-layer theory for elastic plates. Commun. Pure Appl. Math. 14(1), 1–33 (1961)\nCiarlet, P.G., Destuynder, P.: Une justification du modèle bi-harmonique en théorie des plaques. C. R. Acad. Sci. Paris 285, 851–854 (1977)\nLandau, L.D., Lifshitz, E.M.: Theory of Elasticity, 3rd edn. Pergamon Press, Oxford, UK (1986)\nVandeparre, H., Piñeirua, M., Brau, F., Roman, B., Bico, J., Gay, C., Bao, W., Lau, C.N., Reis, P.M., Damman, P.: Wrinkling hierarchy in constrained thin sheets from suspended graphene to curtains. Phys. Rev. Lett. 106(22), 224301 (2011)\nHure, J., Roman, B., Bico, J.: Stamping and wrinkling of elastic plates. Phys. Rev. Lett. 109(5), 054302 (2012)\nTakei, A., Brau, F., Roman, B., Bico, J.: Stretch-induced wrinkles in reinforced membranes: From out-of-plane to in-plane structures. EPL (Europhys. Lett.) 96(6), 64001 (2011)\nAltenbach, H., Eremeyev, V.A.: On the shell theory on the nanoscale with surface stresses. Int. J. Eng. Sci. 49(12), 1294–1301 (2011)\nAltenbach, H., Eremeyev, V.A., Morozov, N.F.: Linear theory of shells taking into account surface stresses. In Doklady Physics 54(12), 531 (2009). (SP MAIK Nauka\u002FInterperiodica)\nAutieri, C.: Antiferromagnetic and xy ferro-orbital order in insulating SrRuO3 thin films with SrO termination. J. Phys. Condens. Matter 28(42), 426004 (2016)\nGiorgio, I., Corte, A.Della, dell’Isola, F., Steigmann, D.J., Steigmann, D.J.: Buckling modes in pantographic lattices. C. R. Mecanique 344(7), 487–501 (2016)\nGiorgio, I., Grygoruk, R., dell’Isola, F., Steigmann, D.J.: Pattern formation in the three-dimensional deformations of fibered sheets. Mech. Res. Commun. 69, 164–171 (2015)\nAlibert, J.J., Seppecher, P., dell’Isola, F.: Truss modular beams with deformation energy depending on higher displacement gradients. Math. Mech. Solids 8(1), 51–73 (2003)\nSeppecher, P., Alibert, J.J., dell’Isola, F.: Linear elastic trusses leading to continua with exotic mechanical interactions. J. Phys. Conf. Ser. 319, 012018 (2011)\nMadeo, A., Ferretti, M., dell’Isola, F., Boisse, P.: Thick fibrous composite reinforcements behave as special second-gradient materials: three-point bending of 3D interlocks. Zeitschrift für angewandte Mathematik und Physik 66(4), 2041–2060 (2015)\nMillet, O., Hamdouni, A., Cimetière, A., Elamri, K.: Analyse dimensionnelle de l’équation de navier et application à la théorie des plaques minces. Journal de Physique III 7(10), 1909–1925 (1997)\nMillet, O., Hamdouni, A., Cimetière, A.: Dimensional analysis and asymptotic expansions of equilibrium equations in nonlinear elasticity. Part I: the membrane model. Arch. Mech. 50(6), 953–973 (1998)\nMillet, O., Hamdouni, A., Cimetière, A.: Dimensional analysis and asymptotic expansions of equilibrium equations in nonlinear elasticity. Part II: the two-dimensional von karman model. Arch. Mech. 50(6), 975–1001 (1998)\nMillet, O., Hamdouni, A., Cimetière, A.: Construction d’un modèle eulérien de plaques en grands déplacements par méthode asymptotique. Comptes Rendus de l’Académie des Sciences-Series IIB-Mechanics-Physics-Chemistry-Astronomy 325(5), 257–261 (1997)\nMillet, O., Hamdouni, A., Cimetière, A.: A classification of thin plate models by asymptotic expansion of non-linear three-dimensional equilibrium equations. Int. J. Non-Linear Mech. 36(1), 165–186 (2001)\nHamdouni, A., Millet, O.: Classification of thin shell models deduced from the nonlinear three-dimensional elasticity. Part I: the shallow shells. Arch. Mech. 55(2), 135–176 (2003)\nHamdouni, A., Millet, O.: Classification of thin shell models deduced from the nonlinear three-dimensional elasticity. Part II: the strongly curved shells. Arch. Mech. 55(2), 177–220 (2003)\nAudoly, B., Roman, B., Pocheau, A.: Secondary buckling patterns of a thin plate under in-plane compression. Eur. Phys. J. B Condens. Matter Complex Syst. 27(1), 7–10 (2002)\nAudoly, B.: Stability of straight delamination blisters. Phys. Rev. Lett. 83(20), 4124 (1999)\nHutchinson, J.W., He, M.Y., Evans, A.G.: The influence of imperfections on the nucleation and propagation of buckling driven delaminations. J. Mech. Phys. Solids 48(4), 709–734 (2000)\nAudoly, B., Boudaoud, A.: Buckling of a stiff film bound to a compliant substrate-Part I: formulation, linear stability of cylindrical patterns, secondary bifurcations. J. Mech. Phys. Solids 56(7), 2401–2421 (2008)\nAudoly, B., Boudaoud, A.: Buckling of a stiff film bound to a compliant substrate-Part II: a global scenario for the formation of herringbone pattern. J. Mech. Phys. Solids 56(7), 2422–2443 (2008)\nAudoly, B., Boudaoud, A.: Buckling of a stiff film bound to a compliant substrate-Part III: herringbone solutions at large buckling parameter. J. Mech. Phys. Solids 56(7), 2444–2458 (2008)\nRivlin, R.S.: Plane strain of a net formed by inextensible cords. In: Collected Papers of RS Rivlin, pp. 511–534. Springer, New York (1997)\ndell’Isola, F., Della Corte, A., Greco, L., Luongo, A.: 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. 81, 1–12 (2016)\nPlacidi, L., Greco, L., Bucci, S., Turco, E., Rizzi, N.L.: A second gradient formulation for a 2D fabric sheet with inextensible fibres. Zeitschrift für angewandte Mathematik und Physik 67(5), 114 (2016)\nPlacidi, L., Andreaus, U., Della Corte, A., Lekszycki, T.: Gedanken experiments for the determination of two-dimensional linear second gradient elasticity coefficients. Zeitschrift für angewandte Mathematik und Physik 66(6), 3699–3725 (2015)\nPlacidi, L., Andreaus, U., Giorgio, I.: Identification of two-dimensional pantographic structure via a linear D4 orthotropic second gradient elastic model. J. Eng. Math. 103, 1–21 (2016)\nAlibert, J.J., Della Corte, A.: Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof. Zeitschrift für angewandte Mathematik und Physik 66(5), 2855–2870 (2015)\nTurco, E., dell’Isola, F., Cazzani, A., Rizzi, N.L.: Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models. Zeitschrift für Angewandte Mathematik und Physik 67(4), 1–28 (2016)\nTurco, E.: Discrete is it enough? The revival of Piola–Hencky keynotes to analyze three-dimensional Elastica. Contin. Mech. Thermodyn. pp. 1–19 (2018). https:\u002F\u002Fdoi.org\u002F10.1007\u002Fs00161-018-0656-4",{"VOID":1096},"10.1007\u002Fs00161-018-0676-0","2024-05-15T20:47:42.477+00:00","http:\u002F\u002Flink.springer.com\u002F10.1007\u002Fs00161-018-0676-0",[1100,1125,1138],{"id":1101,"sortIndex":23,"researcher":22,"roles":1102,"affiliations":1103,"properties":1120,"displayName":1122,"givenName":22,"familyName":22},"bdfad1a9-79e4-46f0-98cc-22b39f2dd94d",[165],[1104,1112],{"id":1105,"sortIndex":23,"affiliation":1106,"properties":22},"1858654e-27ae-4afc-88a9-4113565514d7",{"id":1105,"createTime":22,"updateTime":22,"relativeEntities":1107,"slug":22,"properties":1108,"entityType":22,"verifyStatus":22,"verifyTime":22,"verifyNote":22,"languages":22,"translateLanguages":22,"viewCount":22,"url":22,"parentIds":1111,"statistic":22},[],{"title":1109},{"VI":1110},"Laboratoire des Sciences de l’Ingénieur pour l’Environnement UMR - 7356 CNRS, Université de La Rochelle, La Rochelle, France",[],{"id":1113,"sortIndex":100,"affiliation":1114,"properties":22},"fff9ede9-77b1-4812-b555-2dbf3c4054ad",{"id":1113,"createTime":22,"updateTime":22,"relativeEntities":1115,"slug":22,"properties":1116,"entityType":22,"verifyStatus":22,"verifyTime":22,"verifyNote":22,"languages":22,"translateLanguages":22,"viewCount":22,"url":22,"parentIds":1119,"statistic":22},[],{"title":1117},{"VI":1118},"M&MoCS, Università degli Studi dell’Aquila, L’Aquila, Italy",[],{"title":1121,"gsAuthor":1123},{"VI":1122},"Antonio Battista",{"VOID":1124},"[\"ROyVRNgAAAAJ\"]",{"id":1126,"sortIndex":100,"researcher":22,"roles":1127,"affiliations":1128,"properties":1135,"displayName":1137,"givenName":22,"familyName":22},"24da2c44-0834-4f8f-b7cd-1a3ec283236d",[165],[1129],{"id":1105,"sortIndex":23,"affiliation":1130,"properties":22},{"id":1105,"createTime":22,"updateTime":22,"relativeEntities":1131,"slug":22,"properties":1132,"entityType":22,"verifyStatus":22,"verifyTime":22,"verifyNote":22,"languages":22,"translateLanguages":22,"viewCount":22,"url":22,"parentIds":1134,"statistic":22},[],{"title":1133},{"VI":1110},[],{"title":1136},{"VI":1137},"Aziz 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Millet",{"VOID":1152},"[\"WFf_y44AAAAJ\"]",{"url":1098,"publisher":1154,"properties":1204},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":1155,"slug":10,"properties":1156,"entityType":20,"verifyStatus":21,"verifyTime":22,"verifyNote":22,"languages":22,"translateLanguages":22,"viewCount":23,"subjectFields":1160,"manageAffiliations":1173,"indexDatabases":1184,"url":22,"thumbnailPath":22,"statistic":1199,"gsStatistic":22,"type":134,"analyzePriority":22},[],{"issn":1157,"title":1158,"eissn":1159},{"VOID":15},{"EN":17},{"VOID":13},[1161,1165,1169],{"id":26,"createTime":22,"updateTime":22,"relativeEntities":1162,"label":1163,"description":1164,"parentId":22,"standard":22,"scholarHubFieldId":22},[],{"EN":29},{},{"id":32,"createTime":22,"updateTime":22,"relativeEntities":1166,"label":1167,"description":1168,"parentId":22,"standard":22,"scholarHubFieldId":22},[],{"EN":35},{},{"id":38,"createTime":22,"updateTime":22,"relativeEntities":1170,"label":1171,"description":1172,"parentId":22,"standard":22,"scholarHubFieldId":22},[],{"EN":41},{},[1174,1179],{"id":45,"createTime":22,"updateTime":22,"relativeEntities":1175,"slug":22,"properties":1176,"entityType":22,"verifyStatus":22,"verifyTime":22,"verifyNote":22,"languages":22,"translateLanguages":22,"viewCount":22,"url":22,"parentIds":1178,"statistic":22},[],{"title":1177},{"EN":49},[],{"id":52,"createTime":22,"updateTime":22,"relativeEntities":1180,"slug":22,"properties":1181,"entityType":22,"verifyStatus":22,"verifyTime":22,"verifyNote":22,"languages":22,"translateLanguages":22,"viewCount":22,"url":22,"parentIds":1183,"statistic":22},[],{"title":1182},{"EN":56},[58],[1185,1192],{"id":61,"indexDatabase":1186,"url":74,"indexYears":22,"academicFieldIds":1191,"indexDatabaseRanking":22},{"id":63,"createTime":22,"updateTime":22,"relativeEntities":1187,"label":1188,"description":1189,"key":70,"publicationTags":1190,"standard":22},[],{"EN":66,"VI":66},{"EN":68,"VI":69},[72,73],[76,77],{"id":79,"indexDatabase":1193,"url":90,"indexYears":91,"academicFieldIds":1198,"indexDatabaseRanking":96},{"id":81,"createTime":22,"updateTime":22,"relativeEntities":1194,"label":1195,"description":1196,"key":87,"publicationTags":1197,"standard":22},[],{"EN":84,"VI":84},{"EN":84,"VI":86},[89],[93,94,95],{"impactFactor":23,"impactFactorByYear":1200,"i10Index":100,"i10IndexLast5Year":23,"totalPublication":101,"totalPublicationByYear":1201,"totalCitation":129,"totalCitationByYear":1202,"totalCitationPerPublication":131,"totalCitationPerPublicationByYear":1203,"hindexLast5Year":100,"hindex":100},{"2011":99},{"1989":103,"1990":104,"1991":105,"1992":106,"1993":107,"1994":103,"1995":108,"1996":103,"1997":107,"1998":109,"1999":104,"2000":103,"2001":110,"2002":111,"2003":112,"2004":110,"2005":113,"2006":109,"2007":114,"2008":110,"2009":115,"2010":114,"2011":116,"2012":117,"2013":118,"2014":119,"2015":120,"2016":121,"2017":122,"2018":123,"2019":124,"2020":125,"2021":126,"2022":127,"2023":128,"2024":109},{"2009":129},{"2009":133},{"pages":1205,"volume":1207},{"VOID":1206},"189-207",{"VOID":1208},"31",{"total":23,"publishYear":1210,"statisticByYear":1211},2018,{},"2018-05-09","2026-07-19T06:14:55.121+00:00",[72,96],{"id":1216,"createTime":1217,"updateTime":1218,"relativeEntities":1219,"slug":1220,"properties":1221,"entityType":156,"verifyStatus":157,"verifyTime":1232,"verifyNote":159,"languages":22,"translateLanguages":22,"viewCount":23,"primaryUrl":1233,"fullTextUrl":22,"authors":1234,"publicationType":223,"publisherRelationship":1294,"citationCount":23,"citationInfo":1350,"publishDate":1352,"publishYear":1210,"citationAnalyzeStatus":977,"lastCitationAnalyze":1353,"indexDatabases":1354,"openAccess":22,"references":22,"isForceReanalyzing":285},"c7565e29-1437-4e8a-8145-02cec1b65ed8","2024-02-18T11:20:42.567+00:00","2026-07-18T09:51:06.941+00:00",[],"On-the-wave-dispersion-in-microstructured-solids",{"abstract":1222,"title":1224,"gsPaper":1226,"references":1228,"doi":1230},{"EN":1223},"In this paper, elastic wave propagation in a one-dimensional micromorphic medium characterized by two internal variables is investigated. The evolution equations are deduced following two different approaches, namely using: (i) the balance of linear momentum and the Clausius–Duhem inequality, and (ii) an assumed Lagrangian functional (including a gyroscopic coupling) together with a variational principle. The dispersion relation is obtained and the possibility of the emerging band gaps is shown in such microstructured materials. Some numerical simulations are also performed in order to highlight the dispersive nature of the material under study.",{"EN":1225},"On the wave dispersion in microstructured solids",{"VOID":1227},"[\"7123590042635457595\"]",{"VOID":1229},"Alessandroni, S., dell’Isola, F., Porfiri, M.: A revival of electric analogs for vibrating mechanical systems aimed to their efficient control by PZT actuators. Int. J. Solids Struct. 39(20), 5295–5324 (2002)\nAlibert, J.J., Seppecher, P., dell’Isola, F.: Truss modular beams with deformation energy depending on higher displacement gradients. Math. Mech. Solids 8(1), 51–73 (2003)\nAltenbach, H., Eremeyev, V.A.: On the constitutive equations of viscoelastic micropolar plates and shells of differential type. Math. Mech. Complex Syst. 3(3), 273–283 (2015)\nAndrianov, I.V., Bolshakov, V.I., Danishevs’kyy, V.V., Weichert, D.: Higher order asymptotic homogenization and wave propagation in periodic composite materials. Proc. R. Soc. Lond. A Math. Phys. Eng. Sci. 464(2093), 1181–1201 (2008)\nArnol’d, V.I.: Mathematical Methods of Classical Mechanics. Springer, Berlin (2013)\nAskes, H., Metrikine, A.V., Pichugin, A.V., Bennett, T.: Four simplified gradient elasticity models for the simulation of dispersive wave propagation. Philos. Mag. 88(28–29), 3415–3443 (2008)\nAuffray, N., dell’Isola, F., Eremeyev, V.A., Madeo, A., Rosi, G.: Analytical continuum mechanics à la Hamilton–Piola least action principle for second gradient continua and capillary fluids. Math. Mech. Solids 20(4), 375–417 (2015)\nBerezovski, A., Engelbrecht, J., Berezovski, M.: Waves in microstructured solids: a unified viewpoint of modeling. Acta Mech. 220(1–4), 349–363 (2011)\nBerezovski, A., Engelbrecht, J., Maugin, G.A.: Generalized thermomechanics with dual internal variables. Arch. Appl. Mech. 81(2), 229–240 (2011)\nBertram, A., Glüge, R.: Gradient materials with internal constraints. Math. Mech. Complex Syst. 4(1), 1–15 (2016)\nBiswas, R., Poh, L.H.: A micromorphic computational homogenization framework for heterogeneous materials. J. Mech. Phys. Solids 102, 187–208 (2017)\nBloch, A.: XXXVIII: A new approach to the dynamics of systems with gyroscopic coupling terms. Lond. Edinb. Dublin Philos. Mag. J. Sci. 35(244), 315–334 (1944)\nBorn, M., Huang, K.: Dynamical Theory of Crystal Lattices. Oxford University Press, Oxford (1954)\nBoutin, C., dell’Isola, F., Giorgio, I., Placidi, L.: Linear pantographic sheets: asymptotic micro-macro models identification. Math. Mech. Complex Syst. 5(2), 127–162 (2017)\nBrillouin, L.: Wave Propagation in Periodic Structures: Electric Filters and Crystal Lattices. Dover Publications, Mineola (1946)\nCapriz, G.: Continua with Microstructure. Springer, Berlin (1989)\nChen, W., Fish, J.: A dispersive model for wave propagation in periodic heterogeneous media based on homogenization with multiple spatial and temporal scales. Trans. ASME J. Appl. Mech. 68(2), 153–161 (2001)\nCrandall, S.H.: Dynamics of Mechanical and Electromechanical Systems. McGraw-Hill, New York (1968)\nDe Masi, A., Merola, I., Presutti, E., Vignaud, Y.: Potts models in the continuum. Uniqueness and exponential decay in the restricted ensembles. J. Stat. Phys. 133(2), 281–345 (2008)\ndell’Isola, F., Andreaus, U., Placidi, L.: At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: an underestimated and still topical contribution of Gabrio Piola. Math. Mech. Solids 20(8), 887–928 (2015)\ndell’Isola, F., Corte, A.D., Giorgio, I.: Higher-gradient continua: the legacy of Piola, Mindlin, Sedov and Toupin and some future research perspectives. Math. Mech. Solids 22(4), 852–872 (2017)\ndell’Isola, F., Cuomo, M., Greco, L., Della Corte, A.: Bias extension test for pantographic sheets: numerical simulations based on second gradient shear energies. J. Eng. Math. 103(1), 127–157 (2017)\ndell’Isola, F., Della Corte, A., Esposito, R., Russo, L.: Some cases of unrecognized transmission of scientific knowledge: from antiquity to Gabrio Piola’s peridynamics and generalized continuum theories. In: Generalized Continua as Models for Classical and Advanced Materials, pp. 77–128. Springer (2016)\ndell’Isola, F., Seppecher, P., Della Corte, A.: The postulations á la D’Alembert and á la Cauchy for higher gradient continuum theories are equivalent: a review of existing results. Proc. R. Soc. 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Appl. Math. Mech. (Z. Angew. Math. Mech.) 97(4), 477–506 (2017)\nEugster, S.R., et al.: Exegesis of sect. II and III. A from “Fundamentals of the mechanics of continua” by E. Hellinger. ZAMM J. Appl. Math. Mech. (Z. Angew. Math. Mech.) 98(1), 31–68 (2018)\nEugster, S.R., et al.: Exegesis of sect. III. B from “Fundamentals of the mechanics of continua” by E. Hellinger. ZAMM J. Appl. Math. Mech. (Z. Angew. Math. Mech.) 98(1), 69–105 (2018)\nFish, J., Chen, W.: Higher-order homogenization of initial\u002Fboundary-value problem. J. Eng. Mech. 127(12), 1223–1230 (2001)\nFish, J., Kuznetsov, S.: From homogenization to generalized continua. Int. J. Comput. Methods Eng. Sci. Mech. 13(2), 77–87 (2012)\nForest, S., Sab, K.: Cosserat overall modeling of heterogeneous materials. Mech. Res. Commun. 25(4), 449–454 (1998)\nGeers, M.G., Kouznetsova, V.G., Brekelmans, W.: Multi-scale computational homogenization: trends and challenges. J. Comput. Appl. 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Phys. 57(1), 79–90 (1970)\nPorfiri, M., dell’Isola, F., Santini, E.: Modeling and design of passive electric networks interconnecting piezoelectric transducers for distributed vibration control. Int. J. Appl. Electromagn. Mech. 21(2), 69–87 (2005)\nTurco, E., dell’Isola, F., Cazzani, A., Rizzi, N.L.: Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models. Z. Angew. Math. Phys. 67(4), 85 (2016)\nTurco, E., Giorgio, I., Misra, A., dell’Isola, F.: King post truss as a motif for internal structure of (meta) material with controlled elastic properties. R. Soc. Open Sci. 4(10), 171,153 (2017)\nVán, P., Berezovski, A., Engelbrecht, J.: Internal variables and dynamic degrees of freedom. J. Non-equilib. Thermodyn. 33(3), 235–254 (2008)\nVinogradov, A.M., Kupershmidt, B.A.: The structures of Hamiltonian mechanics. Russ. Math. 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