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Mathematical and numerical multi-scale modelling of multiphysics problems

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EN
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EN
In this paper we discuss two multi-scale procedures, both of mathematical nature as opposed to purelynumerical ones. Examples are shown for the two cases. Attention is also devoted to thermodynamical aspects such as thermodynamic consistency and non-equilibrium thermodynamics. Advances for the firstaspect are obtained by adopting the thermodynamically constrained averaging theory TCAT as shown in the case of a stress tensor for multi-component media. The second aspect has allowed to solve numerically,with relative ease, the case of non-isothermal leaching. The absence of proofs of thermodynamic consistencyin case of asymptotic theory of homogenization with ?nite size of the unit cell is also pointed out.
Rocznik
Strony
91--113
Opis fizyczny
Bibliogr. 80 poz., rys., tab., wykr.
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autor
autor
autor
autor
  • Department of Structural and Transportation Engineering, University of Padova via F. Marzolo 9, 35131 Padova, Italy, bas@dic.unipd.it
Bibliografia
  • [1] P. Baggio, C. Bonacina, B.A. Schrefler. Some considerations on modeling heat and mass transfer in porous media. Transport in Porous Media, 28: 233–251, 1997.
  • [2] F. Bellina, D. Boso, B.A. Schrefler, G. Zavarise. Modeling a multistrand SC cable with an electrical DC lumped network. IEEE Trans. Appl. Supercond., 12(1): 1408–12, 2002.
  • [3] A. Bensoussan, J.L. Lions, G. Papanicolau. Asymptotic Analysis for Periodic Structures. North-Holland, Amsterdam, 1976.
  • [4] R.I. Borja. Cam-clay plasticity. Part V: a mathematical framework for three-phase deformation and strain localization analyses of partially saturated porous media. Comput. Methods Appl. Mech. Engrg, 193: 5301–5338, 2004.
  • [5] D.P. Boso, M. Lefik, B.A. Schrefler. A multilevel homogenised model for superconducting strand thermomechanics, Cryogenics, 45(4): 259–271, 2005.
  • [6] D.P. Boso, M. Lefik, B.A. Schrefler. Multiscale analysis of the influence of the triplet helicoidal geometry on the strain state of a Nb3Sn based strand for ITER coils. Cryogenics, 45(9): 589–605, 2005.
  • [7] D.P. Boso, M. Lefik, B.A. Schrefler. Homogenisation methods for the thermo-mechanical analysis of Nb3Sn strand. Cryogenics, 46(7–8): 569–80, 2006.
  • [8] D.P. Boso, M. Lefik, B.A. Schrefler. Thermo-mechanics of the hierarchical structure of ITER superconducting cables. IEEE Trans. Appl. Supercond., 17(2): 1362–5, 2007.
  • [9] D.P. Boso, M. Lefik, B.A. Schrefler. Generalized self-consistent like method for mechanical degradation of fibrous composites. ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 91(12): 967–78, 2011.
  • [10] D.P. Boso, M. Lefik, B.A. Schrefler. Recent developments in numerical homogenization. Comput. Assis. Mech. Eng. Sci., 16(3–4): 161–83, 2009.
  • [11] D.P. Boso, M. Lefik, B.A. Schrefler. Generalised self consistent homogenisation as an inverse problem. ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 90(10–11): 847–60, 2010.
  • [12] D.P. Boso, M. Lefik. A thermo-mechanical model for Nb3Sn filaments and wires: Strain field for different strand layouts. Superconductor Science and Technology, 22(12), article number 125012, 2009.
  • [13] D.P. Boso, M. Lefik. Numerical phenomenology: Virtual testing of the hierarchical structure of a bundle of strands. CMES – Computer Modeling in Engineering and Sciences, 55(3): 319–37, 2010.
  • [14] D.P. Boso, M. Lefik, B.A. Schrefler. Thermal and bending strain on Nb3Sn strands. IEEE Trans. Appl. Supercond., 16(2): 1823–7, 2006.
  • [15] D.P. Boso, G. Zavarise, B.A. Schrefler. A formulation for electrostatic-mechanical contact and its numerical solution. Int. J. Numer. Methods Eng., 64(3): 382–400, 2005.
  • [16] D.P. Boso, P. Litewka, B.A. Schrefler, P. Wriggers. A 3D beam-to-beam contact finite element for coupled electric-mechanical fields. Int. J. Numer. Methods Eng., 64(13): 1800–15, 2005.
  • [17] D. Boso, C. Pellegrino, U. Galvanetto, B.A. Schrefler. Macroscopic damage in periodic composite materials. Communications in Numerical Methods in Engineering, 16(9): 615–23, 2000.
  • [18] W. Chen, J. Fish. A dispersive model for wave propagation in periodic heterogeneous media based on homogenization with multiple spatial and temporal scales. Journal of Applied Mechanics, 68: 153–161, 2001.
  • [19] O. Coussy. Mechanics of Porous Continua. Wiley, Chichester, 1995.
  • [20] O. Coussy. PoroMechanics, Wiley, Chichester, 2004.
  • [21] R. de Boer,W. Ehlers, S. Kowalski, J. Plischka. Porous media, a survey of different approaches. Forschungsbericht aus dem Fachbereich Bauwesen, 54, Universit¨at-Gesamthochschule Essen, 1991.
  • [22] J.D. Eshelby. The determination of the elastic field of an ellipsoidal inclusion and related problems. Proc. Roy. Soc., A241: 376–396, 1957.
  • [23] J. Fish, Q. Yu. Multiscale Damage Modeling for Composite Materials: Theory and Computational Framework. Int. J. Num. Meth. Engn., 52(1–2): 161–192, 2001.
  • [24] D. Gawin, P. Baggio, B.A. Schrefler. Coupled heat, water and gas flow in deformable porous media. Int. J. Num. Meth. in Fluids, 20: 969–987, 1995.
  • [25] D. Gawin, M. Lefik, B.A. Schrefler. ANN approach to sorption hysteresis within a coupled hygro-thermomechanical FE analysis. Int. J. Num. Meth. Engrg, 50: 299–323, 2001.
  • [26] D. Gawin, C.E. Majorana, B.A. Schrefler. Numerical Analysis of Hygro-Thermic Behaviour and Damage of Concrete at High Temperature. Mech. Cohes.-Frict. Mater., 4: 37–74, 1999.
  • [27] D. Gawin, F. Pesavento, B.A. Schrefler. Modelling of Hygro-Thermal Behaviour and Damage of Concrete at Temperature Above the Critical Point of Water. Int. J. Numer. Anal. Meth. Geomech. 26: 537–562, 2002.
  • [28] D. Gawin, F. Pesavento, B.A. Schrefler. Modelling of hygro-thermal behaviour of concrete at high temperature with thermo-chemical and mechanical material degradation. Comput. Methods Appl. Mech. Engrg., 192: 1731–1771, 2003.
  • [29] D. Gawin, F. Pesavento, B.A. Schrefler. Modelling of deformations of high strength concrete at elevated temperatures. Mat. Struct., 37(268): 218–236, 2004.
  • [30] D. Gawin, F. Pesavento, B.A. Schrefler. Hygro-thermo-chemo-mechanical modelling of concrete at early ages and beyond. Part I: Hydration and hygro-thermal phenomena. Int. J. Num. Meth. Engrg., 67(3): 299–331, 2006.
  • [31] D. Gawin, F. Pesavento, B.A. Schrefler. Hygro-thermo-chemo-mechanical modelling of concrete at early ages and beyond. Part II: Shrinkage and creep of concrete. Int. J. Num. Meth. Engrg., 67(3): 332–363, 2006.
  • [32] D. Gawin, F. Pesavento, B.A. Schrefler. Towards prediction of the thermal spalling risk through a multi-phase porous media model of concrete. Comput. Methods Appl. Mech. Engrg., 195(41–43): 5707–5729, 2006.
  • [33] D. Gawin, F. Pesavento, B.A. Schrefler. Modelling creep and shrinkage of concrete by means of effective stresses. Mater. Struct., 40(6): 579–591, 2007.
  • [34] D. Gawin, F. Pesavento, B.A. Schrefler. Modeling of cementitious materials exposed to isothermal calcium leaching, with considering process kinetics and advective water flow. Part 1: Theoretical model. Int. J. Solids Struct., 45(25–26): 6221–6240, 2008.
  • [35] D. Gawin, F. Pesavento, B.A. Schrefler. Modeling of cementitious materials exposed to isothermal calcium leaching, with considering process kinetics and advective water flow. Part 2: Numerical solution. Int. J. Solids Struct., 45(25–26): 6241–6268, 2008.
  • [36] D. Gawin, F. Pesavento, B.A. Schrefler. Modeling deterioration of cementitious materials exposed to calcium leaching in non-isothermal conditions. Comput. Methods Appl. Mech. Engrg., 198: 3051–3083, 2009.
  • [37] D. Gawin, L. Sanavia. A unified approach to numerical modeling of fully and partially saturated porous materials by considering air dissolved in water. CMES – Computer Modeling in Engineering & Sciences, 53(3): 255–302, 2009.
  • [38] W.G. Gray, S.M. Hassanizadeh. Unsaturated flow theory including interfacial phenomena, Water Resour. Res., 27: 1855–1863, 1991.
  • [39] W.G. Gray, C.T. Miller. Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 1. Motivation and overview. Advances in Water Resources, 28: 161–180, 2005.
  • [40] W.G. Gray, B.A. Schrefler, F. Pesavento. The solid stress tensor in porous media mechanics and the Hill-Mandel condition. J. of the Mechanics and Physics of Solids, 57: 539–544, 2009.
  • [41] W.G. Gray, B.A. Schrefler. Analysis of the solid phase stress tensor in multiphase porous media. Int. J. Numer. Anal. Meth. Geomech., 31(4): 541–581, 2007.
  • [42] J.L. Guermond, webpage: http://www.math.tamu.edu/?guermond.
  • [43] Z. Hashin, S. Shtrikman, A. Variational. Approach to the theory of the Elastic Behaviour ofMultiphase Materials. J. Mech. Phys. Sol., 11(2): 127–141, 1964.
  • [44] S.M. Hassanizadeh, W.G. Gray. Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries. Advances in Water Resources, 13(4): 169–186, 1990.
  • [45] S.M. Hassanizadeh, W.G. Gray. General Conservation Equations for Multi-Phase Systems: 1. Averaging Procedure. Advances in Water Resources, 2: 131–144, 1979.
  • [46] S.M. Hassanizadeh, W.G. Gray. General Conservation Equations for Multi-Phase Systems: 2. Mass, Momenta, Energy and Entropy Equations. Advances in Water Resources, 2: 191–203, 1979.
  • [47] S.M. Hassanizadeh, W.G. Gray. General Conservation Equations for Multi-Phase Systems: 3. Constitutive Theory for Porous Media Flow. Advances in Water Resources, 3: 25–40, 1980.
  • [48] T.J.R. Hughes, M. Mallet, L.P. Franca. Entropy-stable finite element methods for compressible fluids: application to high order Mach number flows with shocks, In: P.G. Bergan, K.J. Bathe, W. Wunderlich, eds., Finite Element Methods for Nonlinear Problems, 761–773. Springer, Berlin, 1986.
  • [49] T.J.R. Hughes, L.P. Franca, M. Mallet. A new finite element formulation for computational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier–Stokes equations and the second law of thermodynamics. Comput. Methods Appl. Mech. Engrg., 54: 223–234, 1986.
  • [50] K. Hutter, L. Laloui, L. Vulliet. Thermodynamically based mixture models of saturated and unsaturated soils. Mech. Cohesive-Frict. Mater., 4: 295–338, 1999.
  • [51] C. Johnson, A. Szepessy. On the convergence of a finite element Method for a nonlinear hyperbolic conservation law. Math. Comp., 49: 427–444, 1987.
  • [52] P. Kanout´e, D.P. Boso, J.L. Chaboche, B.A. Schrefler. Multiscale Methods for Composites: a Review. Archives of Computational Methods in Engineering. 16(1): 31–75, 2009.
  • [53] M. Koniorczyk, D. Gawin. Heat and moisture transport in porous building materials containing salt. Journal of Building Physics, 31(4): 279–300, 2008.
  • [54] M. Koniorczyk, D. Gawin. Numerical modeling of salt transport and precipitation in non-isothermal partially saturated porous media considering kinetics of salt phase changes. Transport in Porous Media, 87(1): 57–76, 2011.
  • [55] E. Kröner. Bounds for Effective Elastic Moduli of Disordered Materials. J. Mech. Phys. Sol., 25(2): 137–155, 1977.
  • [56] E. Kröner. Self-consistent scheme and graded disorder in polycristal elasticity. J. Phys. F., 8: 2261–2267, 1978.
  • [57] M. Lefik, D.P. Boso, B.A. Schrefler. Generalized self-consistent homogenization using the finite element method.ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 89(4): 306–19, 2009.
  • [58] M. Lefik, D.P. Boso, B.A. Schrefler. Artificial neural networks in numerical modelling of composites. Comput. Methods Appl. Mech. Engng., 198(21–26): 1785–1804, 2009.
  • [59] M. Lefik, B.A. Schrefler. 3D Finite Element Analysis of Composite Beams with Parallel Fibres Based on the Homogenisation Theory. Computational Mechanics, 14(1): 2–15, 1994.
  • [60] M. Lefik, B.A. Schrefler. Application of the Homogenisation Method to the Analysis of Superconducting Coils. Fusion Engineering and Design, 24: 231–255, 1994.
  • [61] W.K. Liu, D. Qian, S. Gonella, S.F. Li, W. Chen, S. Chirputkar, Multiscale methods for mechanical science of complex materials: Bridging from quantum to stochastic multiresolution continuum. Int.J. Numer. Meth. Engng., 83(8–9): 1039-1080, 2010.
  • [62] T. Mori, K. Tanaka. Average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions. Acta Metallurgica, 21: 571–574, 1973.
  • [63] A.S. Nemov, D.P. Boso, I.B. Voynov, A.I. Borovkov, B.A. Schrefler. Generalized stiffness coefficients for ITER superconducting cables, direct FE modeling and initial configuration. Cryogenics, 50(5): 304–13, 2010.
  • [64] C. Pellegrino, U. Galvanetto, B.A. Schrefler, Numerical homogenisation of periodic composite materials with non-linear material components. Int. J. Num. Meth. Engng., 46, 1609–1637, 1999.
  • [65] F. Pesavento, D. Gawin, B.A. Schrefler. Modeling cementitious materials as multiphase porous media: theoretical framework and applications. Acta Mechanica, 201(1–4): 313–339, 2008.
  • [66] R.C. Picu. Foreword to Special Issue on Linking Discrete and Continuum Models. Int. J. Multiscale Computational Engng., 1(1): VII–VIII, 2003.
  • [67] A. Reuss. Berechnung der Fliessgrenze von Mischkristallen auf grund der Plastizitatsdingung fur Einkristalle. Z. Angew. Math. Mech., 9: 49, 1926.
  • [68] P.L. Ribani, D.P. Boso, M. Lefik, Y. Nunoya, L. Savoldi Richard, B.A. Schrefler, R. Zanino . THELMA code analysis of bronze route Nb3Sn strand bending effect on Ic. IEEE Trans. Appl. Supercond., 16(2): 860–863, 2006.
  • [69] L. Sanavia, F. Pesavento, B.A. Schrefler. Finite element analysis of non-isothermal multiphase geomaterials with application to strain localization simulation. Computational Mechanics, 37(4): 331–348, 2005.
  • [70] E. Sanchez-Palencia. Non-Homogeneous Media and Vibration Theory. Springer, Berlin, 1980
  • [71] B.A. Schrefler. Mechanics and thermodynamics of saturated-unsaturated porous materials and quantitative solutions. Appl. Mech. Rev., 55(4): 351–388, 2002.
  • [72] W. Specking, J.L Duchateau and P. Decool. Critical current vs. strain tests on EU strands and subsize Cable-in-Condiuts with stainless steel and incoloy jackets. GB5-M27 ITER taskN. NIITT45, Final report, October 1997.
  • [73] A. Szepessy. Convergence of the streamline diffusion finite element method for conservation laws, PhD. Thesis, Mathematics Department, Chalmers University of Technology, G¨oteborg, 1989.
  • [74] K. Terada, N. Kikuchi. A class of general algorithms for multi-scale analyses of heterogeneous media. Comput. Methods Appl. Mech. Engrg., 190: 5427–5464, 2001.
  • [75] W. Voigt. Lehrbuch der Kristallphysik. Teubner-Leipzig-Berlin, 1910.
  • [76] J.R. Willis. Bounds and self-consistent estimates for the overall properties of anisotropic composites. J. Mech. Phys. Sol., 25: 185–202, 1977.
  • [77] M. Xu, R. Gracie, T. Belytschko. A continuum-to-atomistic bridging domain method for composite lattices. Int. J. Numer. Meth. Engrg., 81(13): 1635–1658, 2010.
  • [78] R. Zanino, D.P. Boso, M. Lefik, P.L. Ribani, L. Savoldi Richard, B.A. Schrefler. Analysis of bending effects on performance degradation of ITER-relevant Nb3Sn strand using the THELMA code. IEEE Trans. Appl. Supercond., 18(2): 1067–1071, 2008.
  • [79] H.W. Zhang, D.P. Boso, B.A. Schrefler. Homogeneous Analysis of Periodic Assemblies of Elastoplastic Disks in Contact. International Journal for Multiscale Computational Engineering, 1(4): 349–370, 2003.
  • [80] H.W. Zhang, S. Zhang, J.Y. Bi, B.A. Schrefler. Thermo-mechanical analysis of periodic multiphase materials by a multiscale asymptotic homogenization approach. Int. J. Numer. Meth. Engrg., 69(1): 87–113, 2007.
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