Analysis of Concrete Failure on the Descending Branch of the Load-Displacement Curve

Abstract

:

1. Introduction

2. Materials and Methods

2.1. Mechanical Model: A Brief Description

  • Concrete is viewed as a structure composed of interacting mesoscale elements.
  • The material of each element obeys Hooke’s law.
  • The modulus of elasticity, strength and other physical and mechanical properties of the material of each element do not depend on its size and do not change over time.
  • With an increase in the external load, and hence displacement, individual mesoscale elements are destroyed, as a result of which the effective area decreases, and the load is redistributed to the elements that remain intact. As a result, the average statistical value of the effective stresses in the material of the remaining intact mesoscale elements increases.
  • The destruction of mesoscale elements and their conglomerates leads to a decrease in the effective area and a decrease in the resistance of the macrostructure to external force, which corresponds to the descending branch of the “load – displacement” diagram. However, effective stresses (i.e., stresses in the material of mesoscale elements) increase. The growth of effective stresses is limited by the ultimate strength of the material of mesoscale elements.
  • Stresses determined without taking damage into account can be called apparent stresses [12].
  • The Poisson effect can cause some growth in the transverse dimensions and a corresponding change in the cross-sectional area of the sample under uniaxial compression. Thus, two trends should be analyzed: first, a decrease in cross-sectional area due to destruction of mesoscale elements and, second, an increase in area due to the Poisson effect.
  • The primary source of information for the mathematical description of the model and obtaining numerical results is the load-displacement diagram (Figure 1).

2.2. Mathematical Description of the Mechanical Model

2.2.1. Determination of

2.2.2. Determination of

2.2.3. Determination of

2.2.4. Effective Area, Damage Function and Effective Modulus of Elasticity

2.2.5. Curve Equation

3. Results and Discussion

3.1. Some Features of the Model

3.2. Effective Stress

3.3. Comparison with Experiments Known in the Literature

3.4. Relationship between Load and Displacement and Bending Stress-Strain

4. Conclusions

Funding

Conflicts of Interest

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Number of Samples: 1 2 3 4 5 6 7 8 9
Fiber volume, % 0.00 0.50 0.75 1.00 0.00 0.50 0.75 1.00 1.25
, MPa [22] 28.19 29.34 29.94 30.87 54.65 54.86 57.94 59.82 56.91
, mε; [22]

(1 mε = 0.001)

1.950 2.657 2.931 2.954 2.050 3.08 3.000 3.080 3.080
, MPa, (13)

(if = )

76.63 79.75 81.39 83.91 148.55 149.12 157.50 162.61 154.70
, MPa; (8) 39,297 30,017 27,767 28,407 72,465 48,417 52,499 52,795 50,226
, MPa; [22] 25,260 25,090 25,900 25,990 45,210 46,570 47,160 47,400 46,540
1, MPa; [18] 31,515 24,073 22,269 22,782 58,116 38,829 42,103 42,340 40,280

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Kolesnikov, G. Analysis of Concrete Failure on the Descending Branch of the Load-Displacement Curve. Crystals 2020, 10, 921. https://doi.org/10.3390/cryst10100921

Kolesnikov G. Analysis of Concrete Failure on the Descending Branch of the Load-Displacement Curve. Crystals. 2020; 10(10):921. https://doi.org/10.3390/cryst10100921

Chicago/Turabian Style

Kolesnikov, Gennadiy. 2020. “Analysis of Concrete Failure on the Descending Branch of the Load-Displacement Curve” Crystals 10, no. 10: 921. https://doi.org/10.3390/cryst10100921

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