Multiscale thermoelastic modelling of composite strands using the “fundamental solutions” method. (English) Zbl 1497.74010
Summary: A novel computationally effective approach to multiscale thermoelastic modelling of composite structures and its application to a thermomechanical analysis of two ITER superconducting strands is presented. Homogenisation and recovering problems are solved by means of the “fundamental solutions” method, which was expanded to the case of thermoelastic analysis. We describe a general procedure of multiscale analysis on the basis of this method and apply it to recover stresses at the microscopic scale of a composite strands using a two-level procedure. The recovered micro-stresses are found to be in good correlation with the stresses obtained in the reference problem where the entire composite structure was modelled with a fine mesh.
MSC:
| 74F05 | Thermal effects in solid mechanics |
| 74E30 | Composite and mixture properties |
| 74Q05 | Homogenization in equilibrium problems of solid mechanics |
| 82D55 | Statistical mechanics of superconductors |
Keywords:
composite structure; stress recovery; superconducting strand; homogenisation; multiscale analysisReferences:
| [1] | Engquist, B.; Li, X.; Ren, W.; Vanden-Eijnden, E., Heterogeneous multiscale methods: a review, Commun Comput Phys, 2, 3, 367-450 (2007) · Zbl 1164.65496 |
| [2] | Kanouté, P.; Boso, DP; Chaboche, JL; Schrefler, BA, Multiscale methods for composites: a review, Archiv Comput Methods Eng, 16, 1, 31-75 (2009) · Zbl 1170.74304 · doi:10.1007/s11831-008-9028-8 |
| [3] | Voigt, W., Theoretische Studien über die Elasticitätsverhältnisse der Krystalle, Abh Kgl Ges Wiss Göttingen Math Kl, 34, 3-51 (1887) |
| [4] | Reuss, A., Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle, J Appl Math Mech, 9, 49-58 (1929) · JFM 55.1110.02 |
| [5] | Bensoussan, A.; Lions, JL; Papanicolaou, G., Asymptotic analysis for periodic structures (1978), Amsterdam: North-Holland Publ. Comp, Amsterdam · Zbl 0404.35001 |
| [6] | Bakhvalov, N.; Panasenko, G., Homogenization: averaging processes in periodic media (1989), Dordrecht: Kluwer, Dordrecht · Zbl 0692.73012 · doi:10.1007/978-94-009-2247-1 |
| [7] | Aboudi, J., Micromechanical analysis of composites by the method of cells-update, Appl Mech Rev, 49, 10, S83-S91 (1996) · doi:10.1115/1.3101981 |
| [8] | Hassani, B.; Hinton, E., A review of homogenization and topology optimization. II: analytical and numerical solutions of homogenization equations, Comput Struct, 69, 719-738 (1998) · Zbl 0948.74048 · doi:10.1016/S0045-7949(98)00132-1 |
| [9] | Pellegrino, C.; Galvanetto, U.; Schrefler, BA, Numerical homogenization of periodic composite materials with non-linear material components, Int J Numer Methods Eng, 46, 1609-1637 (1999) · Zbl 0968.74054 · doi:10.1002/(SICI)1097-0207(19991210)46:10<1609::AID-NME716>3.0.CO;2-Q |
| [10] | Hain, XM; Wriggers, P., Numerical homogenization of hardened cement paste, Comput Mech, 42, 197-212 (2008) · Zbl 1304.74057 · doi:10.1007/s00466-007-0211-9 |
| [11] | Temizer, İ.; Wriggers, P., Homogenization in finite thermoelasticity, J Mech Phys Solids, 59, 344-372 (2011) · Zbl 1270.74059 · doi:10.1016/j.jmps.2010.10.004 |
| [12] | Temizer, İ.; Wu, T.; Wriggers, P., On the optimality of the window method in computational homogenization, Int J Eng Sci, 64, 66-73 (2013) · Zbl 1423.74795 · doi:10.1016/j.ijengsci.2012.12.007 |
| [13] | Kijanski, W.; Barthold, FJ, Two-scale shape optimisation based on numerical homogenisation techniques and variational sensitivity analysis, Comput Mech, 67, 1021-1040 (2021) · Zbl 1477.74090 · doi:10.1007/s00466-020-01955-6 |
| [14] | Holtkamp, N., For the ITER project team: an overview of the ITER project, Fusion Eng Des, 82, 427-434 (2007) · doi:10.1016/j.fusengdes.2007.03.029 |
| [15] | Ekin, JW, Effect of transverse compressive stress on the critical current and upper critical field of Nb3Sn, J Appl Phys, 62, 4829-4834 (1987) · doi:10.1063/1.338986 |
| [16] | Haken, B.; Kate, HHJ, The degradation of the critical current density in a Nb3Sn tape conductor due to parallel and transversal strain, Fusion Eng Des, 20, 265-270 (1993) · doi:10.1016/0920-3796(93)90052-J |
| [17] | Wessel, WAJ; Nijhuis, A.; Ilyin, Y.; Abbas, W.; Haken, B.; Kate, HHJ, A novel, “Test Arrangement for Strain Influence on Strands” (TARSIS): mechanical and electrical testing of ITER Nb3Sn strands, Adv Cryog Eng, 50, 466-473 (2004) · doi:10.1063/1.1774603 |
| [18] | Ciazynski, D., Review of Nb3Sn conductors for ITER, Fusion Eng Des, 82, 488-497 (2007) · doi:10.1016/j.fusengdes.2007.01.024 |
| [19] | Lefik, M.; Schrefler, BA, Application of the homogenization method to the analysis of superconducting coils, Fus Eng Des, 24, 231-255 (1994) · doi:10.1016/0920-3796(94)90024-8 |
| [20] | Boso, DP; Lefik, M.; Schrefler, BA, A multilevel homogenised model for superconducting strand thermomechanics, Cryogenics, 45, 259-271 (2005) · doi:10.1016/j.cryogenics.2004.09.005 |
| [21] | Boso, DP; Lefik, M.; Schrefler, BA, Homogenisation methods for the thermo-mechanical analysis of Nb_3Sn strand, Cryogenics, 46, 7-8, 569-580 (2006) · doi:10.1016/j.cryogenics.2006.01.005 |
| [22] | Boso, DP, A simple and effective approach for thermo-mechanical modelling of composite superconducting wires, Supercond Sci Technol, 26, 1045006 (2013) · doi:10.1088/0953-2048/26/4/045006 |
| [23] | Palmov, VA; Borovkov, AI, Six fundamental boundary value problems in the mechanics of periodic composites, Appl Mech Mater, 5-6, 551-558 (2006) · doi:10.4028/www.scientific.net/AMM.5-6.551 |
| [24] | Borovkov, AI; Palmov, VA, Fundamental solutions and regular expansions in mechanics of periodic composites: transactions of SPbSTU, Comput Math Mech, 498, 73-97 (2006) |
| [25] | https://www.iter.org/mag/6/45 |
| [26] | Nemov, AS; Boso, DP; Voynov, IB; Borovkov, AI; Schrefler, BA, Generalized stiffness coefficients for ITER superconducting cables, direct FE modeling and initial configuration, Cryogenics, 50, 5, 304-314 (2010) · doi:10.1016/j.cryogenics.2009.11.006 |
| [27] | Bordini, B.; Alknes, P.; Bottura, L., An exponential scaling law for the strain dependence of the Nb 3Sn critical current density, Supercond Sci Technol, 26, 075014 (2013) · doi:10.1088/0953-2048/26/7/075014 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
