# Numerical Modelling of the Constitutive Behaviour of FRCM Composites through the Use of Truss Elements

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## Abstract

**:**

## 1. Introduction

## 2. Simplified Modeling Approach

#### 2.1. Tensile 1D Model

- the fiber fabric is considered to be a bidirectional grid and only the fibers parallel to the load are considered to carry the load;
- geometrical imperfections are neglected (i.e., the FRCM strip has a straight axis);
- both phases behave only in pure tension;
- the first crack opens at the member’s ends;
- the fabric-to-matrix interface can transfer pure shear stress.

#### 2.2. Calibration of Interface Parameters

#### 2.3. Shear-Bond 1D Model

## 3. Reference Experimental Tests

^{2}and a yarn cross-sectional area of 0.83 mm

^{2}. embedded between two layers of cement and lime-based mortar, respectively. Whereas, specimens of the set FRCM4 are made of lime-based mortar and a coated-basalt-fiber grid, with a unit weight of 250 g/m

^{2}and a yarn cross-sectional area of 0.23 mm

^{2}.

## 4. Numerical Results

#### 4.1. Validation of the Tensile 1D Model

#### 4.2. Validation of the Shear-Bond 1D Model

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**Numerical-experimental comparison of tensile behavior for Basalt-FRCM: (

**a**) FRCM1 (unilyon); (

**b**) FRCM1 (cut); (

**c**) FRCM2 (cut); (

**d**) FRCM4 (unich); (

**e**) FRCM4 (unina); (

**f**) FRCM4 (unisannio).

**Figure 7.**Numerical-experimental comparison of shear-bond behavior for Basalt-FRCM: (

**a**) FRCM1 (unilyon); (

**b**) FRCM1 (cut); (

**c**) FRCM2 (cut); (

**d**) FRCM4 (unich); (

**e**) FRCM4 (unina); (

**f**) FRCM4 (unisannio).

FRCM System | Fabric | Matrix | |||||
---|---|---|---|---|---|---|---|

ID | Yarn Cross-Section[mm^{2]} | Unit Weight[g/m^{2}] | ${\mathit{E}}_{\mathit{f}}$[GPa] | ${\mathit{f}}_{\mathit{f}}$[MPa] | Type | ${\mathit{f}}_{\mathit{m},\mathit{f}}$[MPa] | ${\mathit{f}}_{\mathit{m},\mathit{c}}$[MPa] |

FRCM1 (unilyon) | 0.83 | 220 | 111.5 * | 1669 * | cement-based | 4.3 | 16.3 |

FRCM1 (cut) | 0.83 | 220 | 111.5 * | 1669 * | cement-based | 4.6 | 14.8 |

FRCM2 (cut) | 0.83 | 220 | 111.5 * | 1669 * | lime-based | 5.8 | 16.2 |

FRCM4 (unich) | 0.23 | 250 | 51 | 802 | lime-based | 6.2 | 15 ** |

FRCM4 (unina) | 0.23 | 250 | 45.3 | 940 | lime-based | 6.2 | 15 ** |

FRCM4 (unisannio) | 0.23 | 250 | 89 ** | 1542 ** | lime-based | 6.2 | 12.4 |

FRCM System | Length | Width | Thickness | Fiber Cross-Section |
---|---|---|---|---|

ID | [mm] | [mm] | [mm] | [mm^{2}] |

FRCM1 (unilyon) | 650 | 90 | 10 | 2.49 |

FRCM1 (cut) | 584/587 | 75/77 | 10/11.6 | 2.49 |

FRCM2 (cut) | 581/588 | 75/77 | 10/11.8 | 2.49 |

FRCM4 (unich) | 500 | 100 | 10 | 3.89 |

FRCM4 (unina) | 600 | 100 | 10 | 3.89 |

FRCM4 (unisannio) | 500 | 100 | 10 | 3.89 |

FRCM System | Bond Length | Bond Width | FRCM Thickness | Fibre Cross-Section |
---|---|---|---|---|

ID | [mm] | [mm] | [mm] | [mm^{2}] |

FRCM1 (unilyon) | 260 | 90 | 10 | 2.49 |

FRCM1 (cut) | 260 | 75 | 10/11.6 | 2.49 |

FRCM2 (cut) | 260 | 75 | 10/11.8 | 2.49 |

FRCM4 (unich) | 260 | 100 | 10 | 3.89 |

FRCM4 (unina) | 260 | 125 | 10 | 3.89 |

FRCM4 (unisannio) | 260 | 125 | 10 | 3.89 |

FABRIC-MATRIX | MATRIX-SUPPORT | |||||
---|---|---|---|---|---|---|

FRCM System | ${\mathit{k}}_{\mathit{C},\mathit{fm}}$ | ${\mathit{\tau}}_{\mathit{max}}$ | ${\mathit{\tau}}_{\mathit{res}}$ | ${\mathit{s}}_{\mathit{max}}$ | ${\mathit{k}}_{\mathit{C},\mathit{ms}}$ | ${\mathit{s}}_{\mathit{max},\mathit{ms}}$ |

ID | [N/mm^{3}] | [MPa] | [MPa] | [mm] | [N/mm^{3}] | [mm] |

FRCM1 (unilyon) | 3.27 | 0.60 | 0.01 | 7.55 | 0.12 | 2.08 |

FRCM1 (cut) | 2.82 | 0.60 | 0.20 | 2.56 | 0.80 | 0.75 |

FRCM2 (cut) | 3.02 | 0.80 | 0.01 | 2.72 | 1.50 | 0.73 |

FRCM4 (unich) | 2.37 | 0.40 | 0.10 | 3.71 | 0.15 | 2.33 |

FRCM4 (unina) | 2.14 | 0.45 | 0.10 | 4.44 | 0.20 | 1.25 |

FRCM4 (unisannio) | 2.85 | 0.70 | 0.10 | 3.55 | 0.15 | 1.30 |

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**MDPI and ACS Style**

Oddo, M.C.; Minafó, G.; Di Leto, M.; La Mendola, L.
Numerical Modelling of the Constitutive Behaviour of FRCM Composites through the Use of Truss Elements. *Materials* **2023**, *16*, 1011.
https://doi.org/10.3390/ma16031011

**AMA Style**

Oddo MC, Minafó G, Di Leto M, La Mendola L.
Numerical Modelling of the Constitutive Behaviour of FRCM Composites through the Use of Truss Elements. *Materials*. 2023; 16(3):1011.
https://doi.org/10.3390/ma16031011

**Chicago/Turabian Style**

Oddo, Maria Concetta, Giovanni Minafó, Marielisa Di Leto, and Lidia La Mendola.
2023. "Numerical Modelling of the Constitutive Behaviour of FRCM Composites through the Use of Truss Elements" *Materials* 16, no. 3: 1011.
https://doi.org/10.3390/ma16031011