# Prediction of Structural Performance of Vinyl Ester Polymer Concrete Using FEM Elasto-Plastic Model

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Polymer Concrete Composition

#### 2.1.1. Vinyl-Ester Resin

#### 2.1.2. Fine and Coarse Aggregates

#### 2.1.3. Microfiller

#### 2.1.4. Mix Design

- A/B [g/g]—aggregate to binder ratio by mass;
- B/M [g/g]—microfiller to binder ratio by mass;
- P/M [g/g]—waste powder to microfiller mass ratio.

#### 2.2. Material Characterization

_{F}. Three samples of 100 × 100 × 100 mm with an initial notch 30 mm wide and 20 mm thick were used. The test was undertaken with a controlled speed of notch opening of v

_{COD}= 0.1 mm/min. The obtained graphs of the vertical load versus the crack mouth opened deflection (CMOD) are shown in Figure 5.

#### 2.3. Development of the Finite Element Model

#### 2.3.1. Concrete Damaged Plasticity Constitutive Model

#### 2.3.2. Finite Element Model of the Manhole Cover

## 3. Results

#### 3.1. Mesh Convergence Test and Internal Energy Comparison

#### 3.2. Stress–Strain Analysis

## 4. Discussion

## 5. Conclusions

- The concrete damage plasticity (CDP) material model can be successfully adopted to simulate the nonlinear mechanical behavior of polymer concrete.
- The CDP model takes many parameters and finding these parameters based on standard laboratory test data is not straightforward. The authors showed a clear procedure of finding CDP model input data based on standard laboratory tests.
- The CDP model was originally developed for the description of cement concrete. For polymer concrete, the authors proposed how to make necessary assumptions regarding the post-failure behavior.
- The authors showed that PC can be considered for the design of manhole covers. In this study, manhole cover made of plain PC showed too little structural capacity. However, in the authors’ opinion, the numerical approach presented here can still be considered as a valuable design tool (e.g., for manhole covers made of reinforced PC). The numerical solution can be used to choose the type and geometry of the reinforcement, which will be the subject of future studies. Evaluating the application of a certain material model and formulating necessarily steps for finding material parameters is an important milestone before proceeding to the reinforcement design, as it can significantly limit the number of laboratory tests.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Compressive (

**a**) and tensile (

**b**) strength of concrete mix vs. the material variables x1 = A/B (aggregate to polymer binder mass ratio), x2 = P/M (waste powder to microfiller mass ratio), B/M = 0.5.

**Figure 4.**(

**a**) Compressive strength test on Controls MCC8 hydraulic press, (

**b**) wedge splitting test (WST) test on the Instron 5567 machine, (

**c**) modulus of elasticity testing.

**Figure 7.**Compressive behavior assumed for the concrete damaged plasticity (CDP) model, (

**a**) uniaxial compressive behavior outside the elastic range defined as a tabular function of inelastic (or crushing) strain ${\epsilon}_{c}^{in}$ (

**b**) uniaxial compression damage variable ${d}_{c}$ as a tabular function of inelastic strain.

**Figure 8.**Tension behavior assumed for the CDP model, (

**a**) post-failure stress as a function of cracking strain ${\epsilon}_{t}^{ck}$, (

**b**) uniaxial tension damage variable ${d}_{t}$ as a tabular function of cracking strain.

**Figure 9.**Laboratory test setup of a vinyl ester polymer concrete manhole cover [27], (

**a**) before loading, (

**b**) after failure.

**Figure 10.**Geometry and boundary conditions (SI units) of the finite element model: (

**a**) axisymmetric model, (

**b**) 3D model view.

**Figure 11.**Finite element mesh of the 3D model with highlighted (yellow) elements with an aspect ratio greater than 1.5.

**Figure 12.**Load versus deflection curve comparison for different mesh densities of the axisymmetric model: (

**a**) full structure response, (

**b**) zoomed-in view of the failure region.

**Figure 14.**Contour plot of the tension damage parameter (${d}_{t}$) after failure (axisymmetric model, global mesh size: 0.5 mm); deformed configuration; displacements scaled 10 times.

**Figure 15.**Contour plot of the maximum principal logarithmic measure of strain (axisymmetric model, global mesh size: 0.5 mm); deformed configuration; displacements scaled 10 times.

**Figure 16.**Contour plot of maximum principal stress after failure (axisymmetric model, global mesh size: 0.5 mm); deformed configuration; displacements scaled 10 times.

**Figure 18.**Contour plot of the tension damage parameter (${d}_{t}$) after failure (3D model, global mesh size: 3 mm).

**Figure 19.**Contour plot of the maximum principal logarithmic measure of strain (3D model, global mesh size: 3 mm).

**Figure 20.**Locations of strain gauges used in the laboratory test presented in the axisymmetric model.

**Figure 21.**Comparison of radial strain between the experiment and finite element methodmodel (see also Figure 20).

**Table 1.**The properties of vinyl ester resin used as the binder of tested mixes (www.ciechresins.com).

Property | Test Method | Value |
---|---|---|

Viscosity (25 °C) | DIN 53015 | 350 ± 50 mPa·s |

Gelling time (25 °C) | ISO 2535 | 30 ± 5 min |

Flexural strength | ISO 178 | 110 MPa |

Tensile strength | ISO 527 | 75 MPa |

Elasticity modulus | ISO 527 | 3500 MPa |

Extension | ISO 527 | 2.8% |

Heat deflection temperature | ISO 75 | 95 °C |

Barcol hardness | ASTM D 2583 | 35 °B |

**Table 2.**Three-component curing system for vinyl ester resin used in tested mix (www.ciechresins.com).

Component | Function | Content (% of Resin Mass) |
---|---|---|

Cobalt naphthenate 1% | Accelerant | 0.6 |

Dimethylaniline 10% | Accelerant | 1.21 |

Benzoyl peroxide | Hardener | 1.97 |

Sand and Gravel | Resin | Fly Ash | Quartz Powder |
---|---|---|---|

1314 kg | 329 kg | 328.5 kg | 328.5 kg |

Test | Unit | Result | Standard Deviation |
---|---|---|---|

Compression (beam) | N/mm^{2} | 109.40 | 4.00 |

Compression (cube) | N/mm^{2} | 93.10 | 1.19 |

Compression (cylinder) | N/mm^{2} | 70.35 | 7.59 |

Bending | N/mm^{2} | 24.33 | 1.31 |

Tension | N/mm^{2} | 13.76 | 0.68 |

WST | N/m | 17.68 | 0.39 |

Young’s modulus | kN/mm^{2} | 21.80 | 1.090 |

ρ [kg/m^{3}] | E [GPa] | ν [–] | K [–] | χ [–] | ψ [°] | f_{b}_{0}/f_{c}_{0} [–] | μ [s] |
---|---|---|---|---|---|---|---|

2400 | 21.802 | 0.2 | 0.667 | 0.2 | 36 | 1.05 | 0.005 |

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**MDPI and ACS Style**

Józefiak, K.; Michalczyk, R. Prediction of Structural Performance of Vinyl Ester Polymer Concrete Using FEM Elasto-Plastic Model. *Materials* **2020**, *13*, 4034.
https://doi.org/10.3390/ma13184034

**AMA Style**

Józefiak K, Michalczyk R. Prediction of Structural Performance of Vinyl Ester Polymer Concrete Using FEM Elasto-Plastic Model. *Materials*. 2020; 13(18):4034.
https://doi.org/10.3390/ma13184034

**Chicago/Turabian Style**

Józefiak, Kazimierz, and Rafał Michalczyk. 2020. "Prediction of Structural Performance of Vinyl Ester Polymer Concrete Using FEM Elasto-Plastic Model" *Materials* 13, no. 18: 4034.
https://doi.org/10.3390/ma13184034