The present paper generalizes the results obtained by R. Reiss for classical elastic bodies to composites modeled as mixtures of dipolar elastic materials.
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References
A. C. Eringen, Microcontinuum Field Theories I: Foundations and Solids, New York-Berlin-Heidelber, Springer-Verlag (1999).
A. E. Green and R. S. Rivlin, “Multipolar continuum mechanics,” Arch. Rational Mech. Anal., 17, 113-147(1964).
M. E. Gurtin, The Linear Theory of Elasticity, Handbuch der Physik, C. Truesdell (ed.), Vol. VIa/2, Berlin, Springer (1972).
R. D. Mindlin, “Microstrucure in linear elasticity,” Arch. Rational Mech. Anal., 16, 51-77 (1964).
M. Marin, “On weak solutions in elasticity of dipolar bodies with voids,” J. Comp. Appl. Math., 82, No. 1-2, 291-297 (1997).
M. Marin, “An approach of a heat-flux dependent theory for micropolar porous media,” Meccanica, 51, No.5, 1127-1133 (2016).
M. Marin, “Some estimates on vibrations in thermoelasticity of dipolar bodies,” J. Vibr. Control, 16, No. 1, 33-47 (2010).
R. J. Twiss, “Theory of mixtures for micromorphic materials-II. Elastic constitutive equations,” Int. J. Eng. Sci., 10, No. 5, 437-465 (1972).
N. T. Dunwoody, “Balance laws for liquid crystal mixtures,” ZAMP, 26, No. 1, 105-117 (1975).
A. C. Eringen, “Micropolar mixture theory of porous media,” J. Appl. Phys., 94, No. 6, 4184-4190 (2003).
S. De Cicco and L. Nappa, “Uniqueness theorem for mixtures with memory,” Appl. Math. Infor., 13, No. 1, 13-23 (2008).
D. Iesan, “Method of potentials in elastostatics of solids with double porosity,” Int. J. Eng. Sci., 88, 118-127 (2015).
E. Fried and M. E. Gurtin, “Thermomechanics of the interface between a body and its environment,” Continuum Mech. Therm., 19, No. 5, 253-271 (2007).
R. Picard, S. Trostorff, and M. Waurick, “On some models for elastic solids with micro-structure,” ZAMM, J. Appl. Math. Mech., 95, No. 7, 664-689 (2015).
M. Marin and D. Baleanu, “On vibrations in thermoelasticity without energy dissipation for micropolar bodies,” BoundValueProbl., No. 111, 1-19 (2016)
H. Altenbach and V. A. Eremeyev, “Vibration analysis of non-linear 6-parameter prestressed shells,” Meccanica, 49, No. 8, 1751-1761 (2014).
M. Weps, K. Naumenkoand, and H. Altenbach, “Unsymmetric three-layer laminate with soft core for photovoltaic modules,” Compos. Struct., 105, 322-339 (2013).
H. Altenbach, K. Naumenko, G. Lvov, V. Sukiasov and A. Podgorny, “Prediction of accumulation of technological stresses in a pipeline upon its repair by a composite band,” Mech. Compos. Mater., 51, No. 2, 139-156 (2015).
H. J. Li, A. Öchsner, et al., “Crystal plasticity finite element modelling of the effect of friction on surface asperity flattening in cold uniaxial planar compression,” Appl. Surf. Sci., 359, 236-244 (2015).
M. Marin and E. M. Craciun, “Uniqueness results for a boundary value problem in dipolar thermoelasticity to model composite materials,” Composites: Part B, 126, 27-37 (2017).
M. Marin and A. Öchsner, “The effect of a dipolar structure on the H¨older stability in Green–Naghdi thermoelasticity,” Continuum Mech. Therm., 29, No. 6, 1365-1374 (2017).
R. Reiss, “Minimum principles for linear elastodynamics,” J. Elast., 8, No. 1, 35-46 (1978).
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Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 54, No. 4, pp. 761-780, July-August, 2018.
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Marin, M., Öchsner, A. & Vlase, S. Minimum Principle for a Composite Modeled as Two Interacting Dipolar Continua. Mech Compos Mater 54, 523–536 (2018). https://doi.org/10.1007/s11029-018-9761-5
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DOI: https://doi.org/10.1007/s11029-018-9761-5