Chatzigeorgiou, George; Javili, Ali; Steinmann, Paul Unified magnetomechanical homogenization framework with application to magnetorheological elastomers. (English) Zbl 1355.74065 Math. Mech. Solids 19, No. 2, 193-211 (2014). Summary: The aim of this work is to present a general homogenization framework with application to magnetorheological elastomers under large deformation processes. The macroscale and microscale magnetomechanical responses of the composite in the material and spatial description are presented, and the conditions for a well-established homogenization problem in Lagrangian description are identified. The connection between the macroscopic magnetomechanical field variables and the volume averaging of the corresponding microscopic variables in the Eulerian description is examined for several types of boundary conditions. It is shown that the use of kinematic and magnetic field potentials instead of kinetic field and magnetic induction potentials provides a more appropriate homogenization process. Cited in 19 Documents MSC: 74Q05 Homogenization in equilibrium problems of solid mechanics 74F15 Electromagnetic effects in solid mechanics Keywords:Hill-Mandel condition; volume averaging PDFBibTeX XMLCite \textit{G. Chatzigeorgiou} et al., Math. Mech. Solids 19, No. 2, 193--211 (2014; Zbl 1355.74065) Full Text: DOI Link References: [1] Kordonsky W, Journal of Magnetism and Magnetic Materials 122 pp 395– (1993) [2] Jolly MR, Smart Mater Structures 5 pp 607– (1996) [3] DOI: 10.1016/S0957-4158(99)00064-1 [4] Ginder JM, Intl J Mod Phys B 16 pp 2412– (2002) [5] DOI: 10.1142/S0217979202012499 [6] Varga Z, Polymer 47 pp 227– (2006) [7] Pao YH, Mech Today 4 pp 209– (1978) [8] Eringen AC, Electrodynamics of Continua I: Foundations and Solid Media (1989) [9] Maugin GA, Material Inhomogeneities in Elasticity 3 (1993) [10] Kovetz A, Electromagnetic Theory (2000) [11] Vu DK, Intl J Solids Structures 44 pp 7891– (2007) · Zbl 1167.74410 [12] Bustamante R, Maths Mech Solids 13 pp 725– (2008) · Zbl 1175.74033 [13] Vu DK, Maths Mech Solids 15 pp 239– (2010) · Zbl 1257.74053 [14] Brigadnov IA, Intl J Solids Structures 40 pp 4659– (2003) · Zbl 1054.74677 [15] Dorfmann A, Acta Mechanica 167 pp 13– (2004) · Zbl 1064.74066 [16] Steigmann DJ, Intl J Non-Lin Mech 39 pp 1193– (2004) · Zbl 1348.74116 [17] DOI: 10.1016/j.jmps.2004.04.007 · Zbl 1115.74321 [18] Bustamante R, Acta Mechanica 210 pp 183– (2010) · Zbl 1397.74063 [19] Kanouté P, Arch Computat Meth Engng 16 pp 31– (2009) · Zbl 1170.74304 [20] Charalambakis N, Appl Mech Rev 63 (3) pp 030803– (2010) [21] DOI: 10.1016/0022-5096(63)90060-7 · Zbl 0108.36902 [22] DOI: 10.1016/0022-5096(63)90036-X · Zbl 0114.15804 [23] Bensoussan A, Asymptotic Methods for Periodic Structures (1978) [24] Sanchez-Palencia E, Non-homogeneous Media and Vibration Theory 127 (1978) [25] DOI: 10.1007/978-94-009-3489-4 [26] Miehe C, Arch Appl Mech 72 pp 300– (2002) · Zbl 1032.74010 [27] Suquet PM. Elements of Homogenization for Inelastic Solid Mechanics (Lecture Notes in Physics, vol. 272). Berlin: Springer-Verlag, 1987, pp. 193–278. [28] Hill R, Proceedings of the Royal Society of London A 326 pp 131– (1972) · Zbl 0229.73004 [29] DOI: 10.1016/S0167-6636(98)00073-8 [30] Miehe C, Comput Meth Appl Mech Engng 171 pp 387– (1999) · Zbl 0982.74068 [31] Miehe C, Comput Meth Appl Mech Engng 192 pp 559– (2003) · Zbl 1091.74530 [32] Hirschberger CB, Philos Mag 88 pp 3603– (2008) [33] Ricker S, Intl J Fracture 166 pp 203– (2010) · Zbl 1203.74149 [34] McBride A, J Mech Phys Solids 60 pp 1221– (2012) [35] Borcea L, J Mech Phys Solids 49 pp 2877– (2001) · Zbl 0999.74050 [36] Yin HM, Mech Mater 34 pp 505– (2002) [37] Wang D, Finite Elements Anal Des 39 pp 765– (2003) [38] Yin HM, J Mech Phys Solids 54 pp 975– (2006) · Zbl 1120.74471 [39] Ponte Castañeda P, J Mech Phys Solids 59 pp 194– (2011) · Zbl 1270.74075 [40] Truesdell C, The Non-Linear Field Theories of Mechanics, 3. ed. (2004) · Zbl 1068.74002 [41] Gurtin ME, The Mechanics and Thermodynamics of Continua (2009) [42] Marsden JE, Mathematical Foundations of Elasticity (1994) [43] Ogden RW, Non-Linear Elastic Deformations (1997) [44] Maugin GA, Configurational Forces: Thermomechanics, Physics, Mathematics, and Numerics (2010) · Zbl 1234.74002 [45] Costanzo F, Intl J Engng Sci 43 pp 533– (2005) · Zbl 1211.74181 [46] Hill R, Math Proc Cambridge Philos Soc 95 pp 481– (1984) · Zbl 0553.73025 [47] Bettaieb MB, J Multiscale Computat Engng 10 pp 281– (2012) 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.