Constitutive Modelling for Anisotropic Damage in Woven E-Glass Reinforcements

Ping Yang*, Ying Tong
College of Mechanical and Electrical Engineering, Chongqing College of Electronic Engineering, Chongqing 401331, China

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© 2017 Yang and Tong.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: ( This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the College of Mechanical and Electrical Engineering, Chongqing College of Electronic Engineering, Chongqing 401331, China; Tel: 15922900904; E-mails:,


It is easy for composite laminates to be damaged by relative lower velocity impact which could give rise to internal delamination that will strongly weaken the compressive strength of laminates. In order to predict the occurrence of matrix failure, the elastic-brittle behaviors of fiber-reinforced composites were modeled constitutively by an anisotropic damage model. The dynamic tensile testing was performed at a constant velocity of 2 mm/min until the sample broke to achieve the mechanical parameters of E-glass reinforcements. The elastic constitutive equation and the constitutive damage model were obtained on basis of the fundamental theory of mechanics about the orthotropic constitutive of reinforcements. The methodology for this constitutive model which is developed by Hashin considered both the effect of fiber and matrix failure. Then, the developed constitutive equations were incorporated into the FE (finite element) codes, ABAQUS, through the user subroutine module to simulate the process of projectile impacting GFRP composite laminates. The results show that the material deformation reaches a maximum at 24 μs, then occurs rebound with the increase of the time. The stress of reinforcements traverse section linearly increases outward from 0 MPa to 509.8 MPa. Material damage area increases with the prolonging of time, and for a fixed time, material damage gradually increases from the edges to the center and reaches a constant value of 1, which means the rupture of the damage process.

Keywords: Fiber-reinforced Composites, Numerical simulation, Constitutive model, Damage, E-Glass Reinforcements.