### Abstract

The mechanical behavior of 2-D periodic cellular materials is investigated using a continuum-based modeling approach. Two micromechanical models are developed on the basis of representative unit cell concept in which skeleton of cellular material is modeled as elastic beams. The ANSYS finite element code is used to solve the beam model of skeleton. Elastic moduli of square and triangular networks comprising the microstructure of the cellular material are calculated based on an equivalent continuum model. This is achieved by equating the stored energy in skeleton of a unit cell to the strain energy of the equivalent continuum under a set of prescribed boundary conditions. A proper displacement-controlled (essential) boundary condition generates a uniform strain field in both models which corresponds to calculation of one elastic modulus at a time. Then, effective Young's modulus and Poisson's ratio of continuum are extracted from the calculated elastic moduli. The dependence of effective elastic constants on relative density and thickness to length ratio of the microstructure is investigated. Furthermore, the in-plane behavior of cellular solids in compression is explored with the help of current modeling. The proposed models may contribute to optimal designs of a new class of materials with tailored geometry and material properties which could be useful in a broad range of structural applications.

Original language | English |
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Title of host publication | ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE) |

Publisher | American Society of Mechanical Engineers (ASME) |

Volume | 9 |

ISBN (Print) | 9780791856383 |

DOIs | |

Publication status | Published - 2013 |

Event | ASME 2013 International Mechanical Engineering Congress and Exposition, IMECE 2013 - San Diego, CA, United States Duration: Nov 15 2013 → Nov 21 2013 |

### Other

Other | ASME 2013 International Mechanical Engineering Congress and Exposition, IMECE 2013 |
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Country | United States |

City | San Diego, CA |

Period | 11/15/13 → 11/21/13 |

### Fingerprint

### Keywords

- Cellular material
- Continuum model
- Effective elastic moduli
- Finite element analysis
- Unit cell

### ASJC Scopus subject areas

- Mechanical Engineering

### Cite this

*ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE)*(Vol. 9). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/IMECE2013-64190

**Micromechanical modeling of two-dimensional periodic cellular materials.** / Alzebdeh, K.; Al-Shabibi, A.; Pervez, T.

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

*ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE).*vol. 9, American Society of Mechanical Engineers (ASME), ASME 2013 International Mechanical Engineering Congress and Exposition, IMECE 2013, San Diego, CA, United States, 11/15/13. https://doi.org/10.1115/IMECE2013-64190

}

TY - GEN

T1 - Micromechanical modeling of two-dimensional periodic cellular materials

AU - Alzebdeh, K.

AU - Al-Shabibi, A.

AU - Pervez, T.

PY - 2013

Y1 - 2013

N2 - The mechanical behavior of 2-D periodic cellular materials is investigated using a continuum-based modeling approach. Two micromechanical models are developed on the basis of representative unit cell concept in which skeleton of cellular material is modeled as elastic beams. The ANSYS finite element code is used to solve the beam model of skeleton. Elastic moduli of square and triangular networks comprising the microstructure of the cellular material are calculated based on an equivalent continuum model. This is achieved by equating the stored energy in skeleton of a unit cell to the strain energy of the equivalent continuum under a set of prescribed boundary conditions. A proper displacement-controlled (essential) boundary condition generates a uniform strain field in both models which corresponds to calculation of one elastic modulus at a time. Then, effective Young's modulus and Poisson's ratio of continuum are extracted from the calculated elastic moduli. The dependence of effective elastic constants on relative density and thickness to length ratio of the microstructure is investigated. Furthermore, the in-plane behavior of cellular solids in compression is explored with the help of current modeling. The proposed models may contribute to optimal designs of a new class of materials with tailored geometry and material properties which could be useful in a broad range of structural applications.

AB - The mechanical behavior of 2-D periodic cellular materials is investigated using a continuum-based modeling approach. Two micromechanical models are developed on the basis of representative unit cell concept in which skeleton of cellular material is modeled as elastic beams. The ANSYS finite element code is used to solve the beam model of skeleton. Elastic moduli of square and triangular networks comprising the microstructure of the cellular material are calculated based on an equivalent continuum model. This is achieved by equating the stored energy in skeleton of a unit cell to the strain energy of the equivalent continuum under a set of prescribed boundary conditions. A proper displacement-controlled (essential) boundary condition generates a uniform strain field in both models which corresponds to calculation of one elastic modulus at a time. Then, effective Young's modulus and Poisson's ratio of continuum are extracted from the calculated elastic moduli. The dependence of effective elastic constants on relative density and thickness to length ratio of the microstructure is investigated. Furthermore, the in-plane behavior of cellular solids in compression is explored with the help of current modeling. The proposed models may contribute to optimal designs of a new class of materials with tailored geometry and material properties which could be useful in a broad range of structural applications.

KW - Cellular material

KW - Continuum model

KW - Effective elastic moduli

KW - Finite element analysis

KW - Unit cell

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U2 - 10.1115/IMECE2013-64190

DO - 10.1115/IMECE2013-64190

M3 - Conference contribution

AN - SCOPUS:84903450631

SN - 9780791856383

VL - 9

BT - ASME International Mechanical Engineering Congress and Exposition, Proceedings (IMECE)

PB - American Society of Mechanical Engineers (ASME)

ER -