Postgraduate Research Conference 2009
The Prize Winners
PRESENTATION: Modelling Transverse Matrix Cracking in Composite Structure
student: Fahad Almaskari
supervisor: Dr Shuguang Li
Abstract
This paper presents a modified approach to incorporate Li’s continuum damage model for
matrix cracking into finite element. The new approach simplified the analysis to a laminar level
by incorporating the laminar constitutive relations in ABAQUS via UMAT user subroutine. The
new approach was used to predict the development of matrix cracking in indented composite
tube.
Introduction
The full potential of composite materials has not been utilized yet due to the lack of understand
of their failure process. Failure of composite materials is a complex process because of their
heterogeneity and anisotropy characteristics. Damage stage is defined in the failure process as
the stage from the first sign of failure in the material which corresponding to a micro-structural
change in the material that leads to a drop in the stress-strain relation to the ultimate failure
where the material loses all its capability to withstand the applied loads. Matrix cracking is the
first and the most common damage mode in composite materials. Modelling matrix cracking in
composite is still a challenging task due to the difficulties to tracing and predicting its
propagation.
Continuum damage model have been successfully used to represent the damage state and
predicts its evolution. This paper presents a modified approach to Li’s continuum damage model
[1]. Matrix cracks are represented by damage parameter and the constitutive relations is defined
in terms of stresses, strains and damage parameter. The incremental form of the constitutive
relations is coded in user-defined subroutine (UMAT) and ABAQUS finite element package
was used to determine the structural response. As an example of the application of the new
model, the response of composite tube subject to indentation is presented.
Method
Li’s model takes into the account three sources of nonlinearity during the laminate analysis.
These sources are transverse matrix cracking, plastic shear stress-strain relation and fibre
reorientation. These sources where included in the constitutive equations and then incorporated
into ABAQUS via UGEN user-defined subroutine, where the nonlinear mechanical behaviour
of general shell section is defined. The new approach considered the same sources of
nonlinearity but simplified the analysis to the lamina level, by providing the laminar constitutive
relation at material integration points. The mechanical constitutive behaviour of laminar is
express in an incremental form then is coded in UMAT. By applying the model at the lamina
level, not only the application of the model becomes simpler, but it gains more generality and
reliability.
Results
The results of the indentation problem are presented below in global and local area. In the
global structure area, the overall response of the composite tube is determined from the load displacement
relation during the indentation. The intensity and extend of damage zone is present
in the local area, especially right under the indenter, where extensive damage where observed.
Figure 1. Comparison of modeling and experimental load versus indentation curves
Conclusions
The implementation of continuum damage model into finite element for structural response was
successfully applied in ABAQUS via the UMAT user subroutine. The results of the indentations
modelling of composite tube are in a good agreement with that from experiments. This work
presents an improvement on the modelling capability of damage in composite structure. Further
work is on progress to extend the modelling to dynamic analysis, where low speed impact can
be modelled.
References
[1]Li, S., et al., Modelling transverse cracking damage in thin, filament-wound tubes subjected
to lateral indentation followed by internal pressure. International Journal of Mechanical
Sciences, 2005. 47(4-5 SPEC. ISS.): p. 621-646.