# Peridynamic Analysis of Marine Composites under Shock Loads by Considering Thermomechanical Coupling Effects

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## Abstract

**:**

## 1. Introduction

## 2. Peridynamic (PD) Theory

#### 2.1. Basic Concepts in PD Theory

#### 2.2. PD Mechanical Laminate Model

#### 2.3. PD Thermal Laminate Model

#### 2.4. Failure Criteria

## 3. Numerical Implementation

#### 3.1. Problem Description

#### 3.2. Numerical Results

#### 3.2.1. Subjected to Uniform Pressure Loading

#### 3.2.2. Subjected to Uniform Non-Uniform Pressure Load

## 4. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Illustration of PD laminate model for $\delta =2\Delta x$ and fibre direction, $\mathsf{\Phi}=0$.

**Figure 3.**Geometry dimension illustration of the test laminate. (Blue colour represents 0° and yellow colour represents 90° plies).

**Figure 4.**Illustration of PD discretization for one ply (blue colour represents the fixed boundary region and orange colour represents the inner part).

**Figure 6.**(

**a**) Illustration of non-uniform pressure distribution over the top ply and (

**b**) pressure profile.

**Figure 7.**(

**a**) Variation of the displacement in z direction of the central point as a function of time; (

**b**) Vertical displacement distribution for the top ply at $0.28453\times {10}^{-3}\text{\hspace{0.17em}}\mathrm{s}$.

**Figure 8.**(

**a**) Matrix damage and (

**b**) temperature change distribution (K) of top ply at $0.1538\times {10}^{-3}\text{\hspace{0.17em}}\mathrm{s}$.

**Figure 9.**(

**a**) Matrix damage and (

**b**) temperature change distribution (K) of middle (7th) ply at $0.1538\times {10}^{-3}\text{\hspace{0.17em}}\mathrm{s}$.

**Figure 10.**(

**a**) Matrix damage and (

**b**) temperature change distribution (K) of bottom ply at $0.1538\times {10}^{-3}\text{\hspace{0.17em}}\mathrm{s}$.

**Figure 11.**(

**a**) Matrix damage and (

**b**) temperature change distribution (K) of the laminate at $0.3461\times {10}^{-3}\text{}\mathrm{s}$.

**Figure 12.**Matrix damage comparison of top ply for (

**a**) coupled case and (

**b**) uncoupled case at $0.28453\times {10}^{-3}\text{\hspace{0.17em}}\mathrm{s}$.

**Figure 13.**Matrix damage comparison of middle (7th) ply for (

**a**) coupled case and (

**b**) uncoupled case at $0.28453\times {10}^{-3}\text{\hspace{0.17em}}\mathrm{s}$.

**Figure 14.**Matrix damage comparison of bottom ply for (

**a**) coupled case and (

**b**) uncoupled case at $0.28453\times {10}^{-3}\text{\hspace{0.17em}}\mathrm{s}$.

**Figure 15.**Matrix damage comparison of top ply for (

**a**) coupled case and (

**b**) uncoupled case at $0.3461\times {10}^{-3}\text{}\mathrm{s}$.

**Figure 16.**Matrix damage comparison of middle (7th) ply for (

**a**) coupled case and (

**b**) uncoupled case at $0.3461\times {10}^{-3}\text{}\mathrm{s}$.

**Figure 17.**Matrix damage comparison of bottom ply for (

**a**) coupled case and (

**b**) uncoupled case at $0.3461\times {10}^{-3}\text{}\mathrm{s}$.

**Figure 18.**Material damage during test [13].

**Figure 19.**Interlayer shear damage comparison for (

**a**) coupled case and (

**b**) uncoupled case at $0.3461\times {10}^{-3}\text{}\mathrm{s}$.

**Figure 20.**Interlayer shear damage of middle ply in coupled case at $0.3461\times {10}^{-3}\text{}\mathrm{s}$.

**Figure 21.**(

**a**) Distribution of temperature change (K) of top ply at $0.28453\times {10}^{-3}\text{\hspace{0.17em}}\mathrm{s}$; (

**b**) Distribution of temperature change (K) of top ply at $0.3461\times {10}^{-3}\text{}\mathrm{s}$; (

**c**) Maximum stretch distribution of top ply at $0.3461\times {10}^{-3}\text{}\mathrm{s}$.

**Figure 22.**(

**a**) Distribution of temperature change (K) of middle ply at $0.28453\times {10}^{-3}\text{\hspace{0.17em}}\mathrm{s}$; (

**b**) Distribution of temperature change (K) of middle ply at $0.3461\times {10}^{-3}\text{}\mathrm{s}$; (

**c**) Maximum stretch distribution of middle ply at $0.3461\times {10}^{-3}\text{}\mathrm{s}$.

**Figure 23.**(

**a**) Distribution of temperature change (K) of bottom ply at $0.28453\times {10}^{-3}\text{\hspace{0.17em}}\mathrm{s}$; (

**b**) Distribution of temperature change (K) of bottom ply at $0.3461\times {10}^{-3}\text{}\mathrm{s}$; (

**c**) Maximum stretch distribution of bottom ply at $0.3461\times {10}^{-3}\text{}\mathrm{s}$.

**Table 1.**Material properties of composite [8].

Mechanical Properties | Thermal Properties | ||
---|---|---|---|

${E}_{1}\text{\hspace{0.17em}}\left(\mathrm{GPa}\right)$ | 39.3 | ${\alpha}_{1}\text{\hspace{0.17em}}\left(\mathsf{\mu}\mathrm{m}/\mathrm{m}/\mathrm{K}\right)$ | 8.6 |

${E}_{2}\text{\hspace{0.17em}}\left(\mathrm{GPa}\right)$ | 9.7 | ${\alpha}_{2}\text{\hspace{0.17em}}\left(\mathsf{\mu}\mathrm{m}/\mathrm{m}/\mathrm{K}\right)$ | 22.1 |

${G}_{12}\text{\hspace{0.17em}}\left(\mathrm{GPa}\right)$ | 3.32 | ${k}_{1}\text{\hspace{0.17em}}\left(\mathrm{W}/\mathrm{mK}\right)$ | 10.4 |

Poisson’s ratio ${\nu}_{12}$ | 0.33 | ${k}_{2}\text{\hspace{0.17em}}\left(\mathrm{W}/\mathrm{mK}\right)$ | 0.89 |

$\rho \text{\hspace{0.17em}}\left({\mathrm{kg}/\mathrm{m}}^{3}\right)$ | 1850 | ${c}_{v}\text{\hspace{0.17em}}\left(\mathrm{J}/\left(\mathrm{kg}\cdot \mathrm{K}\right)\right)$ | 879 |

${E}_{m}\text{\hspace{0.17em}}\left(\mathrm{GPa}\right)$ | 3.792 | ${\alpha}_{m}\text{\hspace{0.17em}}\left(\mathsf{\mu}\mathrm{m}/\mathrm{m}/\mathrm{K}\right)$ | 63 |

${G}_{m}\text{\hspace{0.17em}}\left(\mathrm{GPa}\right)$ | 1.422 | ${k}_{m}\text{\hspace{0.17em}}\left(\mathrm{W}/\mathrm{mK}\right)$ | 0.34 |

Poisson’s ratio ${\nu}_{m}$ | 0.33 | ${\Theta}_{0}\left(\mathrm{K}\right)$ | 285 |

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**MDPI and ACS Style**

Gao, Y.; Oterkus, S.
Peridynamic Analysis of Marine Composites under Shock Loads by Considering Thermomechanical Coupling Effects. *J. Mar. Sci. Eng.* **2018**, *6*, 38.
https://doi.org/10.3390/jmse6020038

**AMA Style**

Gao Y, Oterkus S.
Peridynamic Analysis of Marine Composites under Shock Loads by Considering Thermomechanical Coupling Effects. *Journal of Marine Science and Engineering*. 2018; 6(2):38.
https://doi.org/10.3390/jmse6020038

**Chicago/Turabian Style**

Gao, Yan, and Selda Oterkus.
2018. "Peridynamic Analysis of Marine Composites under Shock Loads by Considering Thermomechanical Coupling Effects" *Journal of Marine Science and Engineering* 6, no. 2: 38.
https://doi.org/10.3390/jmse6020038