Ostoja-Starzewski, Martin; Costa, Luis; Ranganathan, Shivakumar I. Scale-dependent homogenization of random hyperbolic thermoelastic solids. (English) Zbl 1341.60072 J. Elasticity 118, No. 2, 243-250 (2015). Summary: The scale-dependent homogenization is applied to a hyperbolic thermoelastic material with two relaxation times, where conductivity and stiffness are wide-sense stationary ergodic random fields. The previously established scaling functions for the Fourier-type conductivity and linear elastic responses are used to describe the trends to scale from the mesoscale statistical volume element level (SVE) to the (representative volume element) RVE level of a deterministic homogeneous continuum. In the case of white-noise type random fields, this finite-size scaling can be quantified via universally appearing stretched exponentials for conductivity and elasticity problems. MSC: 60H30 Applications of stochastic analysis (to PDEs, etc.) 60G60 Random fields 74A40 Random materials and composite materials 74A60 Micromechanical theories 74Q20 Bounds on effective properties in solid mechanics 74F05 Thermal effects in solid mechanics 80A17 Thermodynamics of continua Keywords:hyperbolic thermoelasticity; random fields; finite-size scaling; homogenization; relaxation times; representative volume element; statistical volume element; stretched exponentials PDFBibTeX XMLCite \textit{M. Ostoja-Starzewski} et al., J. Elasticity 118, No. 2, 243--250 (2015; Zbl 1341.60072) Full Text: DOI References: [1] Ostoja-Starzewski, M.: Microstructural Randomness and Scaling in Mechanics of Materials. CRC Press, Boca Raton (2007) · Zbl 1148.74002 [2] Blanco, P.J., Giusti, S.M.: Thermomechanical multiscale constitutive modeling: accounting for microstructural thermal effects. J. Elast. 115(1), 27-46 (2014). doi:10.1007/s10659-013-9445-2 · Zbl 1357.74005 [3] Green, A.E., Lindsay, K.A.: Thermoelasticity. J. Elast. 2(1), 1-7 (1972) · Zbl 0775.73063 [4] Ignaczak, J., Ostoja-Starzewski, M.: Thermoelasticity with Finite Wave Speeds. Oxford University Press, Oxford (2009) · Zbl 1183.80001 [5] Lord, H.W., Shulman, Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15, 299-309 (1967) · Zbl 0156.22702 [6] Ostoja-Starzewski, M.: Dissipation function in hyperbolic thermoelasticity. J. Therm. Stresses 34(1), 68-74 (2011). doi:10.1080/01495739.2010.511934 [7] Ziegler, H.: An Introduction to Thermomechanics. North Holland, Amsterdam (1983) · Zbl 0531.73080 [8] Ranganathan, S.I., Ostoja-Starzewski, M.: Mesoscale conductivity and scaling function in aggregates of cubic, trigonal, hexagonal, and tetragonal symmetries. Phys. Rev. B 77, 214308 (2008). doi:10.1103/PhysRevB.77.214308 [9] Dalaq, A.S., Ranganathan, S.I., Ostoja-Starzewski, M.: Scaling function in conductivity of planar random checkerboards. Compos. Mater. Sci. 79, 252-261 (2013). http://dx.doi.org/10.1016/j.commatsci.2013.05.006 [10] Ranganathan, S.I., Ostoja-Starzewski, M.: Scaling function, anisotropy and the size of RVE in elastic random polycrystals. J. Mech. Phys. Solids 56, 2773-2791 (2008). doi:10.1016/j.jmps.2008.05.001 · Zbl 1171.74410 [11] Raghavan, B.V., Ranganathan, S.I.: Bounds and scaling laws in planar elasticity. Acta Mech. (2014). doi:10.1007/s00707-014-1099-z · Zbl 1302.74010 [12] Ranganathan, S.I., Ostoja-Starzewski, M.: Universal elastic anisotropy index. Phys. Rev. Lett. 101, 055504 (2008). doi:10.1103/PhysRevLett.101.055504 [13] Khisaeva, Z.F., Ostoja-Starzewski, M.: Scale effects in infinitesimal and finite thermo elasticity of random composites. J. Therm. Stresses 30, 587-603 (2007). doi:10.1080/01495730701274195 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.