Periodic homogenization and damage evolution in RVE composite material with inclusion

Amel Hamri,Karim Benyahi,Mohand Said Kachi,Sarah Benakli,Youcef Bouafia

doi:10.3221/igf-esis.58.24

Abstract

This work deals with the coupling between a periodic homogenization procedure and a damage process occurring in a RVE of inclusion composite materials. We mainly seek on the one hand to determine the effective mechanical properties according to the different volume fractions and forms of inclusions for a composite with inclusions at the macroscopic level, and on the other hand to explore the rupture mechanisms that can take place at the microstructure level. To do this; the first step is to propose a periodic homogenization procedure to predict the homogenized mechanical characteristics of an inclusion composite. This homogenization procedure is applied to the theory based on finite element analysis by the Abaqus calculation code. The inclusions are modeled by a random object modeler, and the periodic homogenization method is implemented by python scripts. It is then a matter of introducing the damage into the problem of homogenization, that is to say; once the homogenized characteristics are assessed in the absence of the damage initiated by microcracks and micro cavitations, it is then possible to introduce damage models by a subroutine (Umat) in the Abaqus calculation code. The verifications carried out focused on RVE of composite materials with inclusions.

Highlights

The term "homogenization" is a process of calculating effective mechanical properties, and the term "localization" is used to determine stress and local strain (Suquet [1])
Xia et al [7] proposed a method of micromechanical Finite Element Method (FEM) analysis applied to unidirectional, and right-angle laminates subjected to multiaxial loading conditions
On the basis of the general conditions of periodicity stated by Suquet [1]. They presented an explicit form of boundary conditions suitable for Finite Element Method (FEM) analyzes, of parallelepipedic Representative Volume Element (RVE) models subjected to multiaxial loads

Summary

INTRODUCTION

The term "homogenization" is a process of calculating effective mechanical properties, and the term "localization" is used to determine stress and local strain (Suquet [1]). The periodic homogenization model (Numerical Model) gives good results, which approach the experiment allowing a better prediction of the elastic characteristics, and that for different volume fractions Once the effective mechanical characteristics are assessed in the absence of damage, we introduce damage models for the RVE in composite materials, by a subroutine (Umat) on the Abaqus calculation code In this example the heterogeneous material consists of a matrix and inclusions. This for different volume fractions of inclusions (spheroidal, ellipsoidal, cylindrical) This involves comparing the numerical results obtained by the periodic homogenization method (finite element model with periodic boundary conditions), with the results obtained by the Mori-Tanaka model [35]. We notice, the more we increase the percentage of fibers, the shape of the local stress-strain behavior curve decreases, which corresponds to a less ductile behavior

CONCLUSION

Findings

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