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Linearized ordinary state-based peridynamic micromechanics of composites

Valeriy A. Buryachenko

Vol. 18 (2023), No. 4, 445–477
Abstract

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.

Keywords
microstructures, inhomogeneous material, peridynamics, nonlocal methods, multiscale modeling
Milestones
Received: 7 September 2022
Revised: 21 February 2023
Accepted: 8 March 2023
Published: 30 May 2023
Authors
Valeriy A. Buryachenko
Micromechanics and Composites LLC
Cincinnati, OH
United States