Coupled size and boundary-condition effects in viscoelastic heterogeneous and composite bodies

摘要: Abstract Previous results of the author on influence size and boundary-conditions apparent properties elastic heterogeneous materials are recalled extended to viscoelastic case. Materials with random microstructures, possibly anisotropy, defects or damage, considered. In place classical concept effective properties, which holds for representative volume only, is recalled. It makes use special kinds appropriate stochastic averages required Hill condition still valid while ergodic assumption – legitimating equivalent homogeneous medium relaxed. Statistical defined various partitions a given initial specimen D 0 into set coarse specimens one hand, smaller other hand. The boundary-condition size-effects hierarchies derived in Huet (1990. Journal Mechanical Physics Solids 38, 813; 1997. Engineering Fracture Mechanics, (special issue) 58 (5–6) 459) Examples numerical verification by micromechanical simulations shown using 3D finite element models granular composites. Some salient features behavior non-metallic construction used civil engineering also shown, exhibiting trends similar case theoretical justification generalisation seeked paper. Use made Continuum Thermodynamics approach through first discussed constituents having dissipative constitutive equations any kind from natural definitions potential complementary energies derived. Dissipative extensions so-called obtained. Then, new minimum theorems viscoelasticity slight modification pseudo-convolutive procedure (1992. European A/Solids 5 (11) 653; In: Bazant, Z.P., Carol, I. (Eds.), Creep Shrinkage Concrete. Spon, London, pp. 189–200). From this, bounds size-effect statistical stiffness compliance function tensors their rates obtained time domain. found that bodies than exhibit, two classes uniform boundary-conditions, same as ones. Possible time-dependent physical quoted.