### Abstract

This study presents an investigation of thermal fluctuations of a graphene layer by using peridynamics (PD). The stored energy in the graphene layer due to the fluctuations is expressed in a quadratic form in terms of the stiffness matrix under von Karman assumptions. The Gibbs free energy of the graphene layer related to the partition function is calculated using the Gaussian integrals. However, the partition function requires the evaluation of the determinant of stiffness matrix appearing in the energy expression. Although conceptually very attractive, computing the determinant of an extremely large stiffness matrix whose size is dictated by the characteristic length scale poses computational challenges. Therefore, the PD form of the stiffness matrix is constructed by using two levels of discretization in order to evaluate its determinant accurately without any computational challenges. The derivatives of the partition function permit the determination of several thermodynamic quantities such as the thermal expansion coefficient and its dependence on temperature. This approach enables the exploration of the effect of different geometries, boundary conditions and the nature of loading conditions as well as heterogeneous material properties on the fluctuations.

Original language | English (US) |
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Title of host publication | Proceedings - IEEE 69th Electronic Components and Technology Conference, ECTC 2019 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 825-833 |

Number of pages | 9 |

ISBN (Electronic) | 9781728114989 |

DOIs | |

State | Published - May 1 2019 |

Event | 69th IEEE Electronic Components and Technology Conference, ECTC 2019 - Las Vegas, United States Duration: May 28 2019 → May 31 2019 |

### Publication series

Name | Proceedings - Electronic Components and Technology Conference |
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Volume | 2019-May |

ISSN (Print) | 0569-5503 |

### Conference

Conference | 69th IEEE Electronic Components and Technology Conference, ECTC 2019 |
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Country | United States |

City | Las Vegas |

Period | 5/28/19 → 5/31/19 |

### Fingerprint

### Keywords

- Graphene
- Partition function
- Peridynamics
- Thermal expansion coefficient

### ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Electrical and Electronic Engineering

### Cite this

*Proceedings - IEEE 69th Electronic Components and Technology Conference, ECTC 2019*(pp. 825-833). [8811213] (Proceedings - Electronic Components and Technology Conference; Vol. 2019-May). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ECTC.2019.00130

**Peridynamics for predicting thermal expansion coefficient of graphene.** / Madenci, Erdogan; Barut, Atila; Dorduncu, Mehmet.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - IEEE 69th Electronic Components and Technology Conference, ECTC 2019.*, 8811213, Proceedings - Electronic Components and Technology Conference, vol. 2019-May, Institute of Electrical and Electronics Engineers Inc., pp. 825-833, 69th IEEE Electronic Components and Technology Conference, ECTC 2019, Las Vegas, United States, 5/28/19. https://doi.org/10.1109/ECTC.2019.00130

}

TY - GEN

T1 - Peridynamics for predicting thermal expansion coefficient of graphene

AU - Madenci, Erdogan

AU - Barut, Atila

AU - Dorduncu, Mehmet

PY - 2019/5/1

Y1 - 2019/5/1

N2 - This study presents an investigation of thermal fluctuations of a graphene layer by using peridynamics (PD). The stored energy in the graphene layer due to the fluctuations is expressed in a quadratic form in terms of the stiffness matrix under von Karman assumptions. The Gibbs free energy of the graphene layer related to the partition function is calculated using the Gaussian integrals. However, the partition function requires the evaluation of the determinant of stiffness matrix appearing in the energy expression. Although conceptually very attractive, computing the determinant of an extremely large stiffness matrix whose size is dictated by the characteristic length scale poses computational challenges. Therefore, the PD form of the stiffness matrix is constructed by using two levels of discretization in order to evaluate its determinant accurately without any computational challenges. The derivatives of the partition function permit the determination of several thermodynamic quantities such as the thermal expansion coefficient and its dependence on temperature. This approach enables the exploration of the effect of different geometries, boundary conditions and the nature of loading conditions as well as heterogeneous material properties on the fluctuations.

AB - This study presents an investigation of thermal fluctuations of a graphene layer by using peridynamics (PD). The stored energy in the graphene layer due to the fluctuations is expressed in a quadratic form in terms of the stiffness matrix under von Karman assumptions. The Gibbs free energy of the graphene layer related to the partition function is calculated using the Gaussian integrals. However, the partition function requires the evaluation of the determinant of stiffness matrix appearing in the energy expression. Although conceptually very attractive, computing the determinant of an extremely large stiffness matrix whose size is dictated by the characteristic length scale poses computational challenges. Therefore, the PD form of the stiffness matrix is constructed by using two levels of discretization in order to evaluate its determinant accurately without any computational challenges. The derivatives of the partition function permit the determination of several thermodynamic quantities such as the thermal expansion coefficient and its dependence on temperature. This approach enables the exploration of the effect of different geometries, boundary conditions and the nature of loading conditions as well as heterogeneous material properties on the fluctuations.

KW - Graphene

KW - Partition function

KW - Peridynamics

KW - Thermal expansion coefficient

UR - http://www.scopus.com/inward/record.url?scp=85072277822&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072277822&partnerID=8YFLogxK

U2 - 10.1109/ECTC.2019.00130

DO - 10.1109/ECTC.2019.00130

M3 - Conference contribution

AN - SCOPUS:85072277822

T3 - Proceedings - Electronic Components and Technology Conference

SP - 825

EP - 833

BT - Proceedings - IEEE 69th Electronic Components and Technology Conference, ECTC 2019

PB - Institute of Electrical and Electronics Engineers Inc.

ER -