# Response and Energy Absorption of Concrete Honeycombs Subjected to Dynamic In-Plane Compression: A Numerical Approach

^{*}

## Abstract

**:**

## 1. Introduction

^{3}with different mixing ratios, and revealed that specific energy absorption of foam concrete reaches its maximum with density 1000 kg/m

^{3}and water–cement ratio of 0.6–0.7, in a range of 5 to 14 MJ/m

^{3}. Nevertheless, the energy absorption capacity of foam concrete in different literature cannot be compared as the mixing ratios, additives, and densities are different.

## 2. Smoothed Particle Hydrodynamics

**x**) can be approximately represented by the integral of interpolation of a group of disordered points in the neighborhood:

**x**)> is the approximation of f(

**x**),

**x**is displacement vector, Ω is an object containing

**x**, W(

**x**− x′,h) is the smoothing function depending on the displacement between two points and smoothing length h, usually chosen as third order spline kernel function [12]:

_{i}and ρ

_{i}are mass and density of particle i. N is the total particle number.

## 3. Numerical Model

## 4. Results and Discussions

#### 4.1. Dynamic Response and Critical Velocity

#### 4.2. Energy Absorption

#### 4.3. Shock Front Velocity

_{s}is the velocity of the shock front propagating in the cellular solid. V is the impacting plate speed and ε

_{D}is the densification strain. Figure 8 shows the relationship between the shock front speed and impacting velocity, which is a constant. It is seen that the gradient of the line is almost a constant, suggesting that the relationship is linear within the range of impacting velocity 1–15 m/s, which implies that the relationship is valid in cellular solid, no matter the foam is made of ductile or brittle material.

#### 4.4. Limitations

## 5. Conclusions

- (a)
- With increasing crushing velocity, the deformation mode of concrete honeycomb gradually changes from uniform global response with local shear K or V mode to progressive collapse I mode.
- (b)
- The critical velocity of concrete honeycomb of porosity 0.864, cell size 0.5 mm, and 35 MPa concrete is in the range between 25–40 m/s.
- (c)
- The energy absorption capacity of concrete honeycombs increases with loading velocity and honeycomb density.
- (d)
- The relationship between shock front and plate impacting velocity during concrete honeycomb crushing is linear.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Micro-structure and cell size distribution of a foam concrete sample: (

**a**) Micro-structure; (

**b**) statistics of cell size distribution.

**Figure 2.**Illustration of the concrete honeycomb models: (

**a**) for response mode; (

**b**) for energy absorption.

**Figure 3.**Response of concrete honeycomb subjected to 1 m/s constant speed crushing: (

**a**) t = 0.876 ms; (

**b**) t = 1.753 ms; (

**c**) t = 5.259 ms; (

**d**) t = 8.765 ms.

**Figure 4.**Response of concrete honeycomb subjected to 18 m/s constant speed crushing: (

**a**) t = 0.0487 ms; (

**b**) t = 0.0974 ms; (

**c**) t = 0.292 ms; (

**d**) t = 0.457 ms.

**Figure 5.**Response of concrete honeycomb subjected to 40 m/s constant speed crushing: (

**a**) t = 0.022 ms; (

**b**) t = 0.0438 ms; (

**c**) t = 0.131 ms; (

**d**) t = 0.219 ms.

**Table 1.**Properties of steel and concrete [13].

Steel | Concrete | ||
---|---|---|---|

Density (g/cm^{3}) | 7.83 | Density (g/cm^{3}) | 2.31 |

Yield stress (MPa) | 792 | Compressive strength (MPa) | 35 |

Young’s modulus (GPa) | 210 | Shear modulus (GPa) | 6.3 |

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**MDPI and ACS Style**

Shen, W.; Zhou, H.; Zhang, X.; Wang, X.
Response and Energy Absorption of Concrete Honeycombs Subjected to Dynamic In-Plane Compression: A Numerical Approach. *Symmetry* **2019**, *11*, 175.
https://doi.org/10.3390/sym11020175

**AMA Style**

Shen W, Zhou H, Zhang X, Wang X.
Response and Energy Absorption of Concrete Honeycombs Subjected to Dynamic In-Plane Compression: A Numerical Approach. *Symmetry*. 2019; 11(2):175.
https://doi.org/10.3390/sym11020175

**Chicago/Turabian Style**

Shen, Wenjing, Hongyuan Zhou, Xuejian Zhang, and Xiaojuan Wang.
2019. "Response and Energy Absorption of Concrete Honeycombs Subjected to Dynamic In-Plane Compression: A Numerical Approach" *Symmetry* 11, no. 2: 175.
https://doi.org/10.3390/sym11020175