# Modelling of Mechanical Behavior of Biopolymer Alginate Aerogels Using the Bonded-Particle Model

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## Abstract

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## 1. Introduction

## 2. Results

#### 2.1. Experimental Characterisation

#### 2.1.1. Mechanical Behavior

#### 2.1.2. Deformation and Densification

#### 2.2. Simulation Results

#### 2.2.1. Uni-Axial Compression

#### 2.2.2. Three-Point Bending

## 3. Discussion

## 4. Materials and Methods

#### 4.1. Materials

#### 4.2. Modelling Approach

#### 4.2.1. Bonded-Particle Model

- structural model: spatial material distribution, positions and radii of primary particles, connection between primary particles, bonds radii, etc.;
- functional model: functional dependencies to describe forces and moments acting in the bonds and between primary particles;
- model parameters: model parameters to describe plasticity, softening, and so forth.

#### 4.2.2. Elasto-Plastic Bond Model

#### 4.2.3. Adjustment of Model Parameters

#### 4.2.4. Model Setup

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

BPM | Bonded Particle Model |

DEM | Discrete Element Method |

$\mu $CT | Micro Computed Tomography |

## References

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**Figure 1.**Averaged stress-strain characteristics for alginate aerogel samples synthesised with different CaCl${}_{2}$ concentrations.

**Figure 3.**Deformation behavior of aerogel samples: (

**a**) Initial and compressed sample with local buckling (wrinkling) effects, (

**b**) Global buckling effects.

(a) | (b) |

**Figure 4.**Reconstructions obtained from $\mu $CT analysis for alginate aerogel crosslinked with a CaCl${}_{2}$ concentration 5 g/L. (

**a**) 3D volume reconstruction, (

**b**) horizontal cross-cut and (

**c**) vertical-cross cut of material.

(a) | (b) | (c) |

**Figure 8.**Force-displacement characteristics for three-point bending tests (calcium chloride concentration 5 g/L).

**Figure 9.**Preparation of cylindrical alginate gel (

**a**); alginate gel removed from the dialysis tube (

**b**) and cut into cylinders (

**c**).

(a) | (b) | (c) |

**Figure 11.**Bonded particle model (BPM) representation of cylindrical aerogel sample (

**a**) and its cross-cut (

**b**).

(a) | (b) |

Structural Model | |
---|---|

Radius of particles [$\mathsf{\mu}$m] | 152.5 |

Radius of bonds [$\mathsf{\mu}$m] | 122.5 |

Particles number | ≈99,000 |

Number of solid bonds | ≈380,000 |

Average bond length [$\mathsf{\mu}$m] | ≈370 |

Functional model for bonds | |

Compressive yield strain ${\u03f5}_{y}$ [%] | 3.52 |

Plastic failure $\beta $ [-] | −0.3 |

Interlocking stiffness factor $\alpha $ [-] | 30 |

Poisson ratio | 0.2 |

Functional model for primary particles | |

Poisson ratio | 0.2 |

Friction coefficient | 0.1 |

Rolling friction | 0.05 |

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**MDPI and ACS Style**

Dosta, M.; Jarolin, K.; Gurikov, P. Modelling of Mechanical Behavior of Biopolymer Alginate Aerogels Using the Bonded-Particle Model. *Molecules* **2019**, *24*, 2543.
https://doi.org/10.3390/molecules24142543

**AMA Style**

Dosta M, Jarolin K, Gurikov P. Modelling of Mechanical Behavior of Biopolymer Alginate Aerogels Using the Bonded-Particle Model. *Molecules*. 2019; 24(14):2543.
https://doi.org/10.3390/molecules24142543

**Chicago/Turabian Style**

Dosta, Maksym, Kolja Jarolin, and Pavel Gurikov. 2019. "Modelling of Mechanical Behavior of Biopolymer Alginate Aerogels Using the Bonded-Particle Model" *Molecules* 24, no. 14: 2543.
https://doi.org/10.3390/molecules24142543