# Non-Linear Numerical Modelling of Sustainable Advanced Composite Columns Made from Bamboo Culms

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## Abstract

**:**

## 1. Introduction

#### 1.1. Why Bamboo?

#### Environmental Benefits and Sustainability of Bamboo

#### 1.2. Aim and Objectives

- Formulate constitutive models that describe the behaviours of the constituent parts of the composite bamboo columns, to be given as input to ABAQUS.
- Create numerical models that realistically represent the physical specimen produced, tested, and reported by Mofidi et al. [3].
- Use FEA to carry out a buckling analysis on the specimens under axial compressive loads considering the FEA method of analysis, Element types, and Imperfections as the parameters of the study.
- Extract the outputs from the FEA to determine the load-displacement behaviour, load at rupture, and stress distribution, and compare the results gained from the FEA with the experimental results in literature.

## 2. Literature Review

#### 2.1. Research on Bamboo as a Construction Material

#### 2.1.1. Research on Bamboo for Surface Applications

#### 2.1.2. Research on Bamboo used as Load-Bearing Structural Members

#### 2.2. Background to FEA of Advanced Composites

#### 2.2.1. Static Riks Method

#### 2.2.2. Linear Buckling/Eigenvalue Analysis

#### 2.2.3. Imperfection Size

## 3. Numerical Modelling Methodology

#### 3.1. Material Properties Used as Input

#### 3.1.1. Moso Bamboo

#### 3.1.2. Epoxy

#### 3.1.3. PVC

#### 3.2. Eigenvalue Buckling Analysis

#### 3.3. Contact/Interaction

#### 3.4. Mesh Refinement and Element Types

#### 3.5. Non-Linear Buckling Analysis Using Static Riks Method

## 4. Results and Discussion

#### 4.1. Load-Displacement Behaviour

#### 4.2. Effect of Using Different Imperfection Sizes

#### 4.3. Effect of Using Different Element Types

#### 4.4. Stress Distributions

## 5. Conclusions

- The experimental results published by this group were supported by the FEA carried out in the present paper. The impressive load at rupture of the physical specimens (601.1kN) was either equalled or slightly exceeded by the results given by the numerical models. This confirmed the large increase in the compressive resistance of the composite member as compared to raw bamboo.
- When comparing the imperfections used for the composite bamboo models, those designed for raw bamboo work optimally as opposed to the steel imperfections based on Eurocode 3 that were also evaluated. In particular, the imperfection designed for raw Mao Jue bamboo gave results that were exceptionally close to the experimental values of load and axial deflections at rupture.
- Solid elements with reduced integration were shown to give results marginally closer to the experimental results as compared with identical elements without reduced integration.
- Shell elements were found to be sufficient when modelling the full culm Moso bamboo fibres in the model, producing outputs that were in line with the values given using solid elements. Shell elements produced the most precise prediction of axial displacement at failure.
- The stress distributions obtained by the software showed large stresses particularly in the fibres, with the matrix subject to high stress concentrations only at certain locations, and the confinement experiencing relatively moderate stresses throughout the part. This suggests that fibres that can withstand large axial compressive loads are essential to prevent failure of the composite as a whole. Bamboo performs considerably well in this role, creating advanced composites that perform exceptionally well under compressive loads, whilst being sustainable and having a low environmental impact.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Physical composite constructed of full culm Moso bamboo fibres, epoxy matrix, and PVC confinement that the model in the present paper is based on Mofidi et al. [3].

**Figure 6.**Composite modelled in ABAQUS with full culm Moso bamboo fibres, epoxy matrix, and PVC confinement.

**Figure 7.**First five collapse mode shapes from eigenvalue buckling analysis using imperfection for Kao Jue and C3D8 elements.

**Figure 8.**The experimental failure mode of the sample modelled in this paper with associated experimental load-displacement behaviour labelled as FCB-EPX-I: (

**a**) Physical failed specimen; (

**b**) Load-displacement behaviour of the physical model among other tested specimens.

**Figure 9.**Load vs displacement behaviour of the modelled specimens, using C3D8R elements, for a 6.4 mm Kao Jue imperfection, a 3.4 mm Mao Jue imperfection, and a 2.67 mm steel imperfection.

**Figure 10.**Engineering stress vs strain behaviour of the modelled specimens, using C3D8R elements, for a 6.4 mm Kao Jue imperfection, a 3.4 mm Mao Jue imperfection, and a 2.67 mm steel imperfection.

**Figure 11.**Engineering stress vs strain behaviour for specimens with C3D8R elements, C3D8 elements, and S4R elements for the fibres and C3D8R elements for the confinement and matrix with a constant 3.4 mm Mao Jue imperfection.

**Table 1.**Experimental results of Mofidi et al. [3].

Specimen | Load at Rupture (kN) | Area of Cross-Section (mm ^{2}) | End Shortening at Peak (mm) | Density of Specimen (kg/m ^{3}) | Axial Stress (MPa) | Gain (%) | Capacity Over Weight (kN/kN) |
---|---|---|---|---|---|---|---|

Control | 152.4 | 2764.6 | 5.75 | 1147.3 | 55.1 | − | 12,323 |

FCB-EPX-I | 601.1 | 8332.3 | 13.82 | 1174.5 | 72.1 | 294.4 | 15,681 |

**Table 2.**Outputs given by the FEA for varying imperfection sizes and element types caused minor changes in the ultimate load behaviour.

Element Used | Imperfection (mm) | Load at Rupture (kN) | Axial Displacement at Rupture (mm) | Axial Stress at Rupture (MPa) |
---|---|---|---|---|

C3D8R | 2.67 | 652.4 | 16.31 | 73.93 |

C3D8R | 3.40 | 631.2 | 16.26 | 71.52 |

C3D8R | 6.40 | 606.0 | 15.11 | 68.67 |

C3D8 | 2.67 | 655.3 | 15.49 | 73.55 |

C3D8 | 3.40 | 645.4 | 15.41 | 73.13 |

C3D8 | 6.40 | 607.2 | 15.26 | 68.80 |

C3D8R + S4R | 3.40 | 650.8 | 14.01 | 73.74 |

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**MDPI and ACS Style**

Richardson, C.; Mofidi, A.
Non-Linear Numerical Modelling of Sustainable Advanced Composite Columns Made from Bamboo Culms. *Constr. Mater.* **2021**, *1*, 169-187.
https://doi.org/10.3390/constrmater1030011

**AMA Style**

Richardson C, Mofidi A.
Non-Linear Numerical Modelling of Sustainable Advanced Composite Columns Made from Bamboo Culms. *Construction Materials*. 2021; 1(3):169-187.
https://doi.org/10.3390/constrmater1030011

**Chicago/Turabian Style**

Richardson, Cameron, and Amir Mofidi.
2021. "Non-Linear Numerical Modelling of Sustainable Advanced Composite Columns Made from Bamboo Culms" *Construction Materials* 1, no. 3: 169-187.
https://doi.org/10.3390/constrmater1030011