Abstract

The computational efficiency of CAE tools for analysing failure progression in large layered composites is key. In particular, efficient approximation and solution methods for delamination modelling are crucial to meet today’s requirements on virtual development lead times. For that purpose, we present here an adaptive continuum shell element based on the isogeometric analysis framework, suitable for the modelling of arbitrary delamination growth. To achieve an efficient procedure, we utilise that, in isogeometric analysis, the continuity of the approximation field easily can be adapted via so-called knot insertion. As a result, the current continuum shell provides a basis for an accurate but also computationally efficient prediction of delamination growth in laminated composites. Results show that the adaptive modelling framework works well and that, in comparison to a fully resolved model, the adaptive approach gives significant time savings even for simple analyses where major parts of the domain exhibit delamination growth.

Highlights

  • To accurately predict damage growth in large, thin-walled laminated composite structures, it is required to have models that are able to capture relevant deformation mechanisms in a computationally efficient manner

  • In the current paper we demonstrate that the higher order in-plane continuity obtained with an isogeometric analysis (IGA) approach allows for an element-local recovery procedure for accurate prediction of out-of-plane stresses, similar to [17,18]

  • Upon a significantly large out-of-plane normal traction, a delamination crack initiates at the interface and the curves adapt towards the linear elastic fracture mechanics (LEFM) solution

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Summary

Introduction

To accurately predict damage growth in large, thin-walled laminated composite structures, it is required to have models that are able to capture relevant deformation mechanisms in a computationally efficient manner. Common challenges associated with many of these methods are to correctly predict the onset of delamination growth since transverse stress predictions in general are of low accuracy in traditional (inexpensive) shell elements, and how to enable the kinematic enrichment in an efficient manner. In this respect, continuum shell elements based on the concept of isogeometric analysis (IGA) provide an interesting option. The paper is closed with some conclusions and an outlook to future developments

Kinematics and equilibrium equations
Discretisation
Fundamentals of B-splines
Bézier extraction
Introducing discontinuities in the displacement field
Stress enhancement scheme for lumped elements
Element performance assessment
In-plane stress comparison
Out-of-plane stress comparison
Reconstructed stress comparison
Adaptive discretisation
Initialisation of new degrees of freedom
Updating Dirichlet boundary conditions
Extended crack tip and mixed elements
Numerical examples
Double cantilever beam simulation
Results
Efficiency gain
End notch flexure simulation
Simply supported thick beam simulation
Conclusions

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