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Internal stresses and relations between effective thermoelastic properties of stochastic solids - Some exact solutions. (English) Zbl 0647.73003
We consider composites made of two phases and polycrystalline aggregates composed of hexagonal, tetragonal, or trigonal crystals. Within linear elasticity exact relations between effective elastic constants, effective thermal expansion, stored elastic energy, and internal stresses are derived. Two sources of internal stresses are taken into account: external loading and differential or anisotropic thermal expansion. If the fluctuation of elastic constants can be neglected, we obtain solutions for internal stresses and stored energy which are valid for any phase topology.

MSC:
74F05 Thermal effects in solid mechanics
74A40 Random materials and composite materials
74E05 Inhomogeneity in solid mechanics
74E10 Anisotropy in solid mechanics
82D25 Statistical mechanics of crystals
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
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