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  • 1.
    Ostoja-Starzewski, Martin
    et al.
    University of Illinois at Urbana-Champaign, USA.
    Shen, Lihua
    Capital Normal University, Beijing, China.
    Malyarenko, Anatoliy
    Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
    Tensor random fields in conductivity and classical or microcontinuum theories2015In: Mathematics and mechanics of solids, ISSN 1081-2865, E-ISSN 1741-3028, Vol. 20, no 4, p. 418-432Article in journal (Refereed)
    Abstract [en]

    We study the basic properties of tensor random fields (TRFs) of the wide-sense homogeneous and isotropic kind with generally anisotropic realizations. Working within the constraints of small strains, attention is given to antiplane elasticity, thermal conductivity, classical elasticity and micropolar elasticity, all in quasi-static settings albeit without making any specific statements about the Fourier and Hooke laws. The field equations (such as linear and angular momentum balances and strain–displacement relations) lead to consequences for the respective dependent fields involved. In effect, these consequences are restrictions on the admissible forms of the correlation functions describing the TRFs.

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