### Abstract

Periodic homogenization models are often used to compute the elastic properties of periodic composite materials based on the shape/periodicity of a given material unit-cell. Conversely, in material design, the unit-cell is not known a priori, and the goal is to design it to attain specific properties values – inverse homogenization problem. This problem is often solved by formulating it as an optimization problem. In this approach, the unit-cell is assumed infinitely small and with periodic boundary conditions. However, in practice, the composite material comprises a finite number of measurable unit-cells and the stress/strain fields are not periodic near the structure boundary. It is thus critical to investigate whether the obtained topologies are affected when applied in the context of real composites. This is done here by scaling the unit-cell an increasing number of times and accessing the apparent properties of the resulting composite by means of standard numerical experiments.

Original language | English |
---|---|

Pages (from-to) | 21-32 |

Number of pages | 12 |

Journal | Computers and Structures |

Volume | 174 |

DOIs | |

Publication status | Published - 1 Oct 2016 |

### Fingerprint

### Keywords

- Cellular
- Homogenization
- Microstructures
- Optimization
- Scale
- Topology

### Cite this

*Computers and Structures*,

*174*, 21-32. https://doi.org/10.1016/j.compstruc.2015.10.001

}

*Computers and Structures*, vol. 174, pp. 21-32. https://doi.org/10.1016/j.compstruc.2015.10.001

**Scale-size effects analysis of optimal periodic material microstructures designed by the inverse homogenization method.** / Coelho, P. G.; Amiano, L. D.; Guedes, J. M.; Rodrigues, H. C.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Scale-size effects analysis of optimal periodic material microstructures designed by the inverse homogenization method

AU - Coelho, P. G.

AU - Amiano, L. D.

AU - Guedes, J. M.

AU - Rodrigues, H. C.

N1 - Sem PDF. FCT, through IDMEC (UID/EMS/50022/2013FCT-Portugal) FCT, under LAETA (UID/EMS/50022/2013FCT-Portugal)

PY - 2016/10/1

Y1 - 2016/10/1

N2 - Periodic homogenization models are often used to compute the elastic properties of periodic composite materials based on the shape/periodicity of a given material unit-cell. Conversely, in material design, the unit-cell is not known a priori, and the goal is to design it to attain specific properties values – inverse homogenization problem. This problem is often solved by formulating it as an optimization problem. In this approach, the unit-cell is assumed infinitely small and with periodic boundary conditions. However, in practice, the composite material comprises a finite number of measurable unit-cells and the stress/strain fields are not periodic near the structure boundary. It is thus critical to investigate whether the obtained topologies are affected when applied in the context of real composites. This is done here by scaling the unit-cell an increasing number of times and accessing the apparent properties of the resulting composite by means of standard numerical experiments.

AB - Periodic homogenization models are often used to compute the elastic properties of periodic composite materials based on the shape/periodicity of a given material unit-cell. Conversely, in material design, the unit-cell is not known a priori, and the goal is to design it to attain specific properties values – inverse homogenization problem. This problem is often solved by formulating it as an optimization problem. In this approach, the unit-cell is assumed infinitely small and with periodic boundary conditions. However, in practice, the composite material comprises a finite number of measurable unit-cells and the stress/strain fields are not periodic near the structure boundary. It is thus critical to investigate whether the obtained topologies are affected when applied in the context of real composites. This is done here by scaling the unit-cell an increasing number of times and accessing the apparent properties of the resulting composite by means of standard numerical experiments.

KW - Cellular

KW - Homogenization

KW - Microstructures

KW - Optimization

KW - Scale

KW - Topology

UR - http://www.scopus.com/inward/record.url?scp=84989861972&partnerID=8YFLogxK

U2 - 10.1016/j.compstruc.2015.10.001

DO - 10.1016/j.compstruc.2015.10.001

M3 - Article

VL - 174

SP - 21

EP - 32

JO - Computers and Structures

JF - Computers and Structures

SN - 0045-7949

ER -