Isogeometric analysis of continuum damage in rotation-free composite shells
X. Deng, A. Korobenko, J. Yan, Y. Bazilevs
Department of Structural Engineering, University of California, San Diego, La Jolla, USA
• A large-deformation, isogeometric rotation-free shell formulation is equipped with a damage model to simulate progressive
failure in composites.
• Four intralaminar modes of failure are considered: Longitudinal and transverse tension, and longitudinal and transverse
• The proposed methodology is valid in the regime of thin shell structures where damage occurs without significant evidence of
• The damage model is extensively validated against experimental data and its use is also illustrated in the context of multiscale
composite damage analysis.
A large-deformation, isogeometric rotation-free Kirchhoff–Love shell formulation is equipped with a damage model to
efficiently and accurately simulate progressive failure in laminated composite structures. The damage model consists of Hashin’s
theory of damage initiation, a bilinear material model for damage evolution, and an appropriately chosen Gibbs free-energy
density. Four intralaminar modes of failure are considered: Longitudinal and transverse tension, and longitudinal and transverse
compression. The choice of shell formulation and modes of failure modeled make the proposed methodology valid in the regime of
relatively thin shell structures where damage occurs without significant evidence of delamination. The damage model is extensively
validated against experimental data and its use is also illustrated in the context of multiscale composite damage analysis.
5. Conclusions and future work
In this paper a recently proposed large-deformation isogeometric Kirchhoff–Love shell formulation is enhanced
with a damage model, which enables the simulation of progressive damage in laminated composite structures. The
damage model consists of Hashin’s theory for damage initiation, and a bilinear material model for damage evolution.
Four intralaminar modes of failure – longitudinal and transverse tension, and longitudinal and transverse compression
– are considered. The model is valid in the regime of relatively thin shell structures where through-thickness transverse
shear may be ignored and where damage occurs without significant evidence of delamination.370 X. Deng et al. / Comput. Methods Appl. Mech. Engrg. 284 (2015) 349–372
Special attention is paid to model validation and behavior under mesh refinement. The computation of damage
in an unnotched carbon-fiber–reinforced laminate (AS4/3501-6) revealed that the present model is among the best
in predicting failure strength of composite laminates. However, the results of the present study as well as those
reported by the participants of the ‘World-Wide Failure Exercise’ (WWFE) indicate that the initial failure stress
is significantly underpredicted by all the models, while some of the models, including the present one, are able to
predict the final failure stress quite well. The large spread in the data reported by the WWFE participants indicates the
lack of consensus regarding failure modeling in laminated composites, and suggests that further research is necessary
to improve the predictive power of failure models.
The computation of damage in a carbon-fiber–reinforced laminate (IM7/8552) with a circular notch showed very
good agreement with the experimental data. Good convergence of the failure stress and displacement under mesh
refinement were also observed. This good accuracy of the simulations and a consistent convergence pattern is attributable to the exact specimen geometry representation, and to the use of an IGA discretization of higher order
and continuity. Besides exhibiting good numerical properties the model produced valuable data on how the stress
redistributes in the complex-geometry specimen as the damage inside it initiates and evolves.
In this paper the damage model is also illustrated in the context of multiscale composite damage analysis. An
appropriate micromechanical model based on an RVE representing a given fiber packing configuration is used to
compute the lamina material properties employed in a macroscale computation of a composite plate damage. The
ability to use the model in the context of multiscale composite damage analysis opens way for its use in full-scale
composite structures, such as modern aircraft fuselage and wings, and wind-turbine blades. Although the main
objectives of this paper were to develop and present an IGA-based composite damage modeling framework, and
to perform its careful validation using actual experimental data at the coupon level, current efforts are underway to
integrate the framework with realistic large-scale structural designs. In particular, of great interest is the integration
of the current framework with Dynamic Data-Driven Application Systems (DDDAS)  for large-scale composite
Other future directions for IGA-based damage modeling in composites is to incorporate more complex throughthickness behavior to enable modeling of delamination, which to this day presents a significant challenge. One pathway to delamination modeling is the recently proposed continuum or solid-like shell formulations [60,61]. High-cycle
fatigue damage presents another important research direction. Finally, although strain localization and the associated
mesh sensitivity was not observed in the examples computed in this paper, such phenomena may occur even in the
context of smooth IGA discretizations, and would require appropriate modeling and numerical treatment, such as, for
example, using a nonlocal, gradient-enhanced damage model [8–11].
The corresponding author and the second author were supported through AFOSR Award FA9550-12-1-0005. The
first author was supported through AFOSR Award FA9550-12-1-0046. This support is gratefully acknowledged. The
authors would also like to express their gratitude to Prof. Hyonny Kim, Structural Engineering, UC, San Diego,
for fruitful discussions about failure in composite laminates and for pointing us to the World-Wide Failure Exercise
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