The most important feature of peridynamic modeling is the use of summation of
force interactions between material points for a continuum description of material
behavior. Contrary to the local theory of elasticity, the peridynamic equation of
motion proposed by Silling (J. Mech. Phys. Solids 2000; 48:175–209) is free of
spatial derivatives of the displacement field. A linearization theory of the
peridynamic properties of thermoelastic composites (CMs) with ordinary state-based
peridynamic properties of phases of arbitrary geometry is analyzed for either
periodic or random structure CMs under volumetric homogeneous remote
boundary conditions. The effective properties are represented by the introduced
micropolarization tensor averaged over the external interaction interface of the
inclusion, rather than over the entire space. The basic hypotheses of peridynamic
micromechanics are proposed by a generalization of the local micromechanics
concepts. The solution method for the general integral equations (GIE) is obtained
without any auxiliary assumptions, such as the effective field hypothesis (EFH)
implicitly used in popular micromechanical methods of local elasticity. In particular,
in the proposed generalized effective field method (EFM), the effective field is
estimated from self-consistent estimates by the closure of the corresponding general
integral equations for random structure CMs. In doing so, the hypothesis of the
ellipsoidal symmetry (describing the random structure of CMs) is not used and the
classical EFH is relaxed.
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