# NUMERICAL STUDY ON HONEYCOMB BEHAVIORS UNDER COMBINED SHEAR-COMPRESSION

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## Folding events in successive crushing

Zhao and Abddenadher found that the folding cycles are composed of two stages. At the start, crush is obtained by bending in the middle of the flat plates (the two trapezoids around nodes B or B′ in Figure 2.12) and there exist small areas around the four corner lines (the two adjacent triangles around node A in Figure 2.12) which remain vertical and can support more external load. The second stage begins with the buckling of the corner line areas as shown on the right of Figure 2.12. The buckling of these edge zones corresponds to a decrease of the global crushing load.

### Mechanism of dynamic enhancement

#### Details on square tube crushing process

In this subsection, we are going to investigate the deformation details of the square tube in order to check the adaptability of inertia effect model to the dynamic enhancement. The complete deformation process is examined carefully and the relation between tube deforming configurations and the overall carrying capacity is determined.
Figure 2.18 presents the force/crush of square tube made of Material 1 under impact velocity of V2＝30m/s. The whole deforming process is from zero crush to compressive displacement of δ=6mm. In Figure 2.18, segment a represents the elastic deformation period, b, d and c, e are respectively the two ascending and descending segments of in successive crush. Points A, C, B and D denote respectively the two peaks and two troughs of the curve.

Dynamic enhancement of the first peak

The stress distributing along the central line is also checked for the three loading cases. As shown in Figure 2.22, the increase of loading velocity elevates not only the maximum stress but also the whole stress distribution on the tube walls, which results in finally the initial peak enhancement of the tube.

CHAPTER 1 INTRODUCTION
1.1 RESEARCH BACKGROUND
1.2 RESEARCH PROGRESSES
1.2.1 Dynamic enhancement of cellular materials
1.2.3 Multi-axial behavior of honeycombs
1.3 OUTLINE OF DISSERTATION
PART I DYNAMIC ENHANCEMENT OF HONEYCOMBS
CHAPTER 2 DYNAMIC ENHANCEMENT MECHANISM OF THIN-WALLED
STRUCTURES
2.1 LATERAL INERTIA EFFECT AND THE SIMPLIFIED MODEL
2.1.1 Lateral inertia effect
2.1.2 Simplified inertia effect model
2.2 MICRO-SIZE DOUBLE-PLATE MODEL FOR VALIDATION
2.2.1 Model installation
2.2.2 Implicit and explicit
2.2.3 Lateral inertial effect
2.3 LATERAL INERTIA EFFECT IN THE CRUSHING PROCESS OF TUBE
2.3.1 Works of Zhao and Abdennadhe
2.3.2 Micro-size tube model
2.3.3 Details on square tube crushing process
2.3.4 Dynamic enhancement of the first peak
2.3.5 Dynamic enhancement of the successive peak
2.3.6 Influence of base material on the dynamic enhancement of square tube
2.4 LATERAL INERTIA EFFECT IN THE OUT-OF-PLANE CRUSHING OF HONEYCOMBS
2.4.1 Simplified cell-model of honeycomb
2.4.2 Deformation details of cell-model and the dynamic strength enhancement
2.4.3 Definitions
2.4.4 Calculating results with different cell-size
2.4.5 Calculating results with different cell-wall thickness
2.4.6 Calculating results with different base material
2.5 SUMMARY
CHAPTER 3 EXPERIMENTAL STUDIES ON DYNAMIC ENHANCEMENT OF ALUMINIUM HONEYCOMBS
3.1 LARGER DIAMETER SOFT HOPKINSON BAR TECHNIQUE
3.1.1 Introduction of classical Hopkinson bar
3.1.2 Specific problems in cellular materials testing
3.1.3 Large diameter, viscoelastic Hopkinson bar technique
3.1.4 Wave dispersion correction of larger diameter viscoelastic Hopkinson bars
3.1.5 Data processing of SHPB for cellular materials
3.2 QUASI-STATIC EXPERIMENTS FOR CELLULAR MATERIALS
3.3 MATERIALS AND SPECIMENS
3.4 QUASI-STAIC AND DYNAMIC EXPERIMENTAL RESULTS
3.4.1 Reproducibility
3.4.2 Dynamic enhancement of honeycombs
3.4.3 Influence of cell-size
3.4.4 Influence of cell-wall thickness
3.4.5 Influence of base material
3.5 SUMMARY
PARTⅡ MULTI-AXIAL BEHAVIOR OF HONEYCOMBS UNDER COMBINED SHEAR-COMPRESSION
4.1.1 Combined shear-compression set-up
4.1.2 Effects of beveled bars on data process method
4.2 VALIDATION OF THE COMBINED SHEAR-COMPRESSION METHOD BY FEM
4.2.1 FEM model installation
4.2.2 Comparison between three basic waves
4.2.3 Estimation of friction between beveled bars and Teflon sleeve
4.2.4 Estimation of beveled bar deformation
4.3 QUAIS-STATIC COMBINED SHEAR-COMPRESSIVE EXPERIMENTS
4.4 SUMMARY
CHAPTER 5 EXPERIMENTAL RESULTS OF HONEYCOMBS UNDER COMBINED SHEAR-COMPRESSION
5.1 MATERIAL AND SPECIMEN
5.2 EXPERIMENTAL RESULTS OF HONEYCOMBS
5.2.1 Reproducibility
5.2.2 Dynamic experimental results under combined shear-compression
5.2.3 Quasi-static experimental results under combined shear-compression
5.2.4 Comparison between dynamic and quasi-static results
5.3 DEFORMATION PATTERN OBSERVATIONS OF HONEYCOMBS
5.4 LIMITATION OF THE COMBINED SHEAR-COMPRESSION DEVICE
5.5 SUMMARY
CHAPTER 6 NUMERICAL STUDY ON HONEYCOMB BEHAVIORS UNDER COMBINED SHEAR-COMPRESSION
6.1 INSTALLATION OF FE MODELS
6.1.1 Complete model
6.1.2 Simplified models
6.2 COMPARISON BETWEEN NUMERICAL AND EXPERIMENTAL RESULTS
6.2.1 Comparison on pressure/crush curves
6.2.2 Comparison on deformation patterns
6.3 BIAXIAL BEHAVIOR OF HONEYCOMBS UNDER COMBINED SHEAR-COMPRESSION
6.3.1 Normal and shear behaviors
6.3.2 Dynamic enhancement of normal and shear behaviors of honeycombs
6.3.3 Macroscopic yield envelop estimation
6.4 SUMMARY
REFERENCES

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