# Numerical Investigation of Different Core Topologies in Sandwich-Structured Composites Subjected to Air-Blast Impact

^{*}

## Abstract

**:**

## 1. Introduction

## 2. State of the Art

## 3. Classification of Core Topologies

- Polymeric, ceramic, and metal foams with stochastic void distribution (open-cell foams or closed-cell foams);
- Periodic prismatic core geometries (open or closed);
- Periodic lattice-type core geometries (lattice cores).

#### 3.1. Core Topologies and Their Parameterisation

**Figure 7.**Sections of conventional one-layer 3D lattice core variants with their associated unit cells. From top to bottom: pyramidal core, tetrahedral core, and 3D Kagomé core [57].

#### 3.2. Considered Core Topologies for Numerical Studies

_{c}of the prismatic cores is performed automatically and—in order to maintain the weight—depends exclusively on the total cell wall area available in the interstitial space. The parameters of the conventional core geometries are based on common values for sandwich structures of this size.

_{c}of the lattice bars replaces the wall thickness t

_{c}of the prismatic cores. The design of the cell structure is carried out here exclusively by means of circular solid cross-sections.

## 4. Modeling of the Blast Loading

## 5. Description of the Numerical Model

- Failure due to the growth, coalescence, and regeneration of micro-voids.
- Shear/slip failure due to local shear bands.
- Necking instabilities (local necking).

## 6. Simulation Results

_{3}) and the plastically dissipated energy (ALLPD) in the time interval under consideration. In addition, a comparative compilation of the respective maximum values–which are normalized by individually dividing them by the corresponding reference values for the monolithic reference plate of the same area and mass–enables a clear qualitative classification of the different design strategies. The aforementioned values represent typical mechanical parameters useful for assessing structural performance and estimating possible physical injury in dynamic stress situations.

_{top}and RP

_{bot}).

## 7. Discussion

_{3}). Thus, the reference configuration has a coefficient of performance of 1.0. Lower values indicate an improvement in the overall structural behavior.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**Deformation states of the top and bottom sides for honeycomb cores No. 01–03 subjected to air-blast loading (t = 0.6 ms).

**Figure A2.**Deformation states of the top and bottom sides for honeycomb cores No. 04–07 subjected to air-blast loading (t = 0.6 ms).

**Figure A3.**Deformation states of the top and bottom sides for prismatic, one-layered, non-auxetic cores No. 08–10 subjected to air-blast loading (t = 0.6 ms).

**Figure A4.**Deformation states of the top and bottom sides for prismatic, one-layered, non-auxetic cores No. 11, 12, and 17 subjected to air-blast loading (t = 0.6 ms).

**Figure A5.**Deformation states of the top and bottom sides for prismatic, multi-layered, non-auxetic cores No. 13–16 subjected to air-blast loading (t = 0.6 ms).

**Figure A6.**Deformation states of the top and bottom sides for prismatic, multi-layered, auxetic cores No. 18–21 subjected to air-blast loading (t = 0.6 ms).

**Figure A7.**Deformation states of the top and bottom sides for 3D lattice, one- and multi-layered, non-auxetic cores with cell angle α = 0° subjected to air-blast loading (t = 0.6 ms).

**Figure A8.**Deformation states of the top and bottom sides for 3D lattice, one- and multi-layered, non-auxetic cores with cell angle α > 0° subjected to air-blast loading (t = 0.6 ms).

**Figure A9.**Deformation states of the top and bottom sides for 3D lattice, one- and multi-layered, auxetic cores with cell angle α < 0° subjected to air-blast loading (t = 0.6 ms).

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**Figure 1.**Examples of prismatic core structures based on the standard auxetic topology. (

**Left**) open-cell core. (

**Right**) closed-cell core.

**Figure 4.**Sections of conventional prismatic open-cell cores with their respective unit cells (one layer, 1L). From top to bottom: I, Y, triangle, diamond, and container truss core.

**Figure 5.**Sections of non-auxetic prismatic and one-side-open core structures with their associated unit cells (two-layer, 2L). From top to bottom: honeycomb, isogrid, and quadratic core.

**Figure 6.**Sections of auxetic prismatic and one-side-open core structures with their associated unit cells (two-layer, 2L). From top to bottom: standard auxetic core (90° rotated), standard auxetic core, and dart core (concave deltoid).

**Figure 8.**Three-dimensional lattice core variants with associated unit cells and geometry parameters (one-layer, 1L). From top to bottom: non-auxetic honeycomb cell, auxetic honeycomb cell, and auxetic arrow geometry.

**Figure 9.**Three-dimensional lattice cores in single- and multi-layer configurations (side view in parallel projection).

**Figure 10.**Cell shape changes of 3D lattice cores with variations in the grid cell angle α (side view in parallel projection).

**Figure 11.**Temporal pressure curve (stationary) for detonation wave propagation in the free field according to the modified Friedlander equation.

**Figure 12.**Plot of the momentum ratio I

_{t}/I

_{0}as a function of the time scale ratio q for assessing fluid–structure interaction according to the Taylor relationship.

**Figure 13.**Configuration of the numerical model, including the support structure and the load source (air blast).

**Figure 15.**Position of the discrete evaluation points in the center of the panel on the upper and lower cover surfaces.

**Figure 19.**Honeycomb cores: normalized maximum values for displacement u

_{3,bot}and reaction force RF

_{3}.

**Figure 20.**Honeycomb cores: normalized maximum values for displacement u

_{3,top}and displacement ratio u

_{3,top}/u

_{3,bot}.

**Figure 22.**Prismatic cores: normalized maximum values for displacement u

_{3,bot}and reaction force RF

_{3}.

**Figure 23.**Prismatic cores: normalized maximum values for displacement u

_{3,top}and displacement ratio u

_{3,top}/u

_{3,bot}.

**Figure 25.**Three-dimensional lattice cores: normalized maximum values for displacement u

_{3,top}and displacement ratio u

_{3,top}/u

_{3,bot}.

**Figure 26.**Three-dimensional lattice cores: normalized maximum values for displacement u

_{3,bot}and reaction force RF

_{3}.

**Figure 27.**Three-dimensional lattice cores: normalized maximum values for plastic dissipation energy.

**Table 1.**Topology and parameters: closed prismatic honeycomb cores. See Figure 3.

No. | Designation | h_{uc} in mm | b_{uc} in mm | l_{1} in mm | α in ° | t_{c} in mm |
---|---|---|---|---|---|---|

01 | honeycomb | 15.00 | 17.32 | 8.66 | 120 | 0.2500 |

02 | square-honeycomb | 2000 | 20.00 | - | - | 0.3305 |

03 | closed isogrid core | 3000 | 34.64 | 17.32 | 60 | 0.1645 |

04 | auxetic honeycomb (h-15) | 15.00 | 17.32 | - | 120 | 0.1895 |

05 | auxetic honeycomb (h-20) | 20.00 | 23.09 | - | 120 | 0.2498 |

06 | auxetic honeycomb (h-25) | 25.00 | 28.87 | - | 120 | 0.3200 |

07 | auxetic honeycomb (h-30) | 30.00 | 34.64 | - | 120 | 0.3609 |

No. | Designation | h_{uc} in mm | b_{uc} in mm | l_{1} in mm | α in ° | t_{c} in mm |
---|---|---|---|---|---|---|

08 | I-core (g = 20 mm) | 20.00 | - | - | - | 0.6610 |

09 | Y-core (b_{1} = 4 mm) | 20.00 | 20.00 | 8.00 | 45 | 0.3602 |

10 | container truss core | 20.00 | 60.00 | 20.00 | 45 | 0.5476 |

11 | triangle-core | 20.00 | 40.00 | - | 45 | 0.4674 |

12 | diamond-core | 20.00 | 20.00 | - | 90 | 0.2337 |

13 | square-honeycomb (2L) | 10.00 | 10.00 | - | - | 0.2203 |

14 | square-honeycomb (4L) | 5.00 | 5.00 | - | - | 0.0944 |

15 | honeycomb (2L) | 10.00 | 11.55 | 5.77 | 120 | 0.1808 |

16 | honeycomb (4L) | 5.00 | 5.77 | 2.89 | 120 | 0.0864 |

17 | open isogrid core | 10.00 | 11.55 | 5.77 | 60 | 0.0603 |

**Table 3.**Topology and parameters: one-side-open auxetic prismatic cell cores. See Figure 6.

No. | Designation | h_{uc} in mm | b_{uc} in mm | l_{1} in mm | α in ° | t_{c} in mm |
---|---|---|---|---|---|---|

18 | auxetic (2L) | 10.00 | 11.55 | - | 120 | 0.1421 |

19 | auxetic (4L) | 5.00 | 5.77 | - | 120 | 0.0663 |

20 | auxetic rotated-90° (4L) | 6.86 | 5.94 | - | 120 | 0.0722 |

21 | dart (2L, β = 120°) | 12.00 | 13.86 | 4.00 | 60 | 0.0753 |

**Table 4.**Topology and parameters: auxetic and non-auxetic 3D lattice cores. See Figure 8.

No. | Designation | Layers | Cell | h_{uc} in mm | α in ° | r_{c} in mm |
---|---|---|---|---|---|---|

22 | honeycomb_+45°_L1 | 1 | 15 × 15 | 20.00 | +45 | 1.2455 |

23 | honeycomb_+45°_L2 | 2 | 30 × 30 | 10.00 | +45 | 0.5897 |

24 | honeycomb_+45°_L4 | 4 | 60 × 60 | 5.00 | +45 | 0.2881 |

25 | honeycomb_+30°_L1 | 1 | 15 × 15 | 20.00 | +30 | 1.2058 |

26 | honeycomb_+30°_L2 | 2 | 30 × 30 | 10.00 | +30 | 0.5736 |

27 | honeycomb_+30°_L4 | 4 | 60 × 60 | 5.00 | +30 | 0.2754 |

28 | honeycomb_+15°_L1 | 1 | 15 × 15 | 20.00 | +15 | 1.2108 |

29 | honeycomb_+15°_L2 | 2 | 30 × 30 | 10.00 | +15 | 0.5507 |

30 | honeycomb_+15°_L4 | 4 | 60 × 60 | 5.00 | +15 | 0.2619 |

31 | cube_+0°_L1 | 1 | 15 × 15 | 20.00 | 0 | 1.1231 |

32 | cube_+0°_L2 | 2 | 30 × 30 | 10.00 | 0 | 0.5131 |

33 | cube_+0°_L4 | 4 | 60 × 60 | 5.00 | 0 | 0.2474 |

34 | auxetic_−15°_L1 | 1 | 15 × 15 | 20.00 | −15 | 1.0732 |

35 | auxetic_−15°_L2 | 2 | 30 × 30 | 10.00 | −15 | 0.4776 |

36 | auxetic_−15°_L4 | 4 | 60 × 60 | 5.00 | −15 | 0.2308 |

37 | auxetic_−30°_L1 | 1 | 15 × 15 | 20.00 | −30 | 0.9624 |

38 | auxetic_−30°_L2 | 2 | 30 × 30 | 10.00 | −30 | 0.4353 |

39 | auxetic_−30°_L4 | 4 | 60 × 60 | 5.00 | −30 | 0.2070 |

40 | auxetic_−45°_L1 | 1 | 15 × 15 | 20.00 | −45 | 0.8251 |

41 | auxetic_−45°_L2 | 2 | 30 × 30 | 10.00 | −45 | 0.3676 |

42 | auxetic_−45°_L4 | 4 | 60 × 60 | 5.00 | −45 | 0.1775 |

Young’s Modulus | Poisson’s Ratio | Density |
---|---|---|

70.000 N/mm² | 0.33 | 2.700 kg/m³ |

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**MDPI and ACS Style**

Walkowiak, M.; Reinicke, U.; Anders, D.
Numerical Investigation of Different Core Topologies in Sandwich-Structured Composites Subjected to Air-Blast Impact. *Appl. Sci.* **2022**, *12*, 9012.
https://doi.org/10.3390/app12189012

**AMA Style**

Walkowiak M, Reinicke U, Anders D.
Numerical Investigation of Different Core Topologies in Sandwich-Structured Composites Subjected to Air-Blast Impact. *Applied Sciences*. 2022; 12(18):9012.
https://doi.org/10.3390/app12189012

**Chicago/Turabian Style**

Walkowiak, Marcel, Ulf Reinicke, and Denis Anders.
2022. "Numerical Investigation of Different Core Topologies in Sandwich-Structured Composites Subjected to Air-Blast Impact" *Applied Sciences* 12, no. 18: 9012.
https://doi.org/10.3390/app12189012