Abstract
In this study, a 3-dimensional (3D) implementation of representative volume element homogenization using bond-based peridynamic formulation is presented. Periodic boundary condition is established by coupling the displacements of periodic point pairs. Homogenized (effective) material properties are obtained based on peridynamic displacement gradient tensor. The current approach is validated by considering a composite material without defects and comparing homogenized properties with results obtained from another homogenization approach. Next, the capability of the current approach is demonstrated by considering randomly generated cracks with arbitrary orientation and location. It can be concluded that the current approach can be an alternative approach to obtain 3-dimensional homogenized material properties for heterogeneous materials with defects.
Highlights
To perform structural analysis at macroscopic scale, homogenized properties are utilized to approximately represent the material behavior
To treat each individual microstructural effect as part of the analysis is usually intractable and homogenization approach is necessary which can consider the effect of voids and microcracks
Newly developed peridynamic formulation [5] can be more suitable since equations of motion of peridynamics are in the form of integro-differential equations and do not contain any spatial derivatives
Summary
To perform structural analysis at macroscopic scale, homogenized properties are utilized to approximately represent the material behavior. This approach usually gives reasonably accurate results, microstructural effects due to voids and microcracks can have significant influence on the macroscopic material behavior, especially fracture characteristics. Spatial derivatives used as part of these homogenization approaches are not defined along crack surfaces In such cases, finite element analysis can be a suitable option. To validate the current approach, peridynamic homogenization is performed by considering a composite material and effected properties are calculated. To demonstrate the capability of the current approach, randomly oriented cracks are introduced in representative volume element to investigate their influence on effective material properties
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