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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2018022670
pages 1-18

EFFECTIVE ELASTIC MODULUS OF PERISTATIC BAR WITH PERIODICALLY DISTRIBUTED DAMAGE

Valeriy A. Buryachenko
Civil Engineering Department, University of Akron, Akron, Ohio 44325-3901, USA and Micromechanics and Composites LLC, 2520 Hingham Lane, Dayton, Ohio 45459, USA

ABSTRACT

A basic concept in engineering design is a damage theory which is obtained as a physically natural justification in the framework of peridynamics. The basic feature of the peridynamic model considered is a continuum description of a material behavior as the integrated nonlocal force interactions between infinitesimal material points. In contrast to the classical theories, the peridynamic equation of motion introduced by Silling is free of any spatial derivatives of displacements. The material points interact with each other directly across finite distances through central forces known as "bonds". The damage concept is introduced by permitting these bonds to break irreversibly. A peristatic bar with periodically distributed damage is analyzed by a generalization of the classical locally elastic computational homogenization to its peristatic counterpart. One introduces the new volumetric periodic boundary conditions at the interaction boundary of a representative unit cell whose local limit implies the known locally elastic periodic boundary conditions. The applicability of local elasticity theory is demonstrated for description of effective elastic behavior of this bar. Estimation of the effective moduli of a damaged medium (initially homogeneous) as the functions of the local damage, damage functions, and micromodulus profiles are obtained. One analyzes either the translation invariant damage functions or non-translation-invariant ones (which can be considered as a model of damage localization).