PSI - Issue 78

Anastasios Drougkas et al. / Procedia Structural Integrity 78 (2026) 2102–2109

2107

Table 1. Reference values of material and geometrical properties for numerical analysis. Phase Parameter Symbol

Value

Units

2

Paste

Young’s modulus Poisson’s ratio Electrical resistivity

E m ν m ρ m ω m E a ν a ρ a ω a E p ν p ρ p ω p

15000

N / mm

0.20

− − − − − − − − − − − 2 2 2

3e + 05

Ω · cm

Volume fraction

0.27

Aggregate

Young’s modulus Poisson’s ratio Electrical resistivity

30000

N / mm

0.20

1e + 06

Ω · cm

Volume fraction

0.30

a a 1 : a a 2 : a a 3

1 . 0 : 1 . 0 : 1 . 0

Half-lengths

Pores

Young’s modulus Poisson’s ratio Electrical resistivity

0

N / mm

0.00

1e + 08

Ω · cm

0.30

Volume fraction

Half-lengths

a p 1 : a p 2 : a p 3

1 . 0 : 1 . 0 : 1 . 0

Crack

Young’s modulus Poisson’s ratio Electrical resistivity

E c ν c ρ c ω c

0

N / mm

0.00

1e + 08

Ω · cm

Volume fraction

0.03

a c 1 : a c 2 : a c 3

20 . 0 : 20 . 0 : 1 . 0

Half-lengths

applied in the x -direction, leading to a shortening and widening of the composite along this axis. The shift in geometry would lead in a decrease in the observed resistivity according to Ohm’s second law for electrical resistance:

L A

R = ρ

(15)

where R is the electrical resistance of an element with cross-section A , measured along a distance L .

Table 2. Reference values of mechanical and loading parameters for cementitious composite. Compressive strength f c

2 2 2 2

− 20 f c / 20 f c / 10 − 3 σ cc

N / mm N / mm N / mm N / mm

Applied compressive stress Crack closure stress mean

σ c

σ cc

Crack closure stress standard deviation

s

Skewness

a

− 5

−

The analysis results for di ff erent combinations of contributing mechanisms are summarised in Table 3. For the above prescribed properties and loading, the resulting gauge factor for the composite ignoring the changes in shape and volume of the phases, as well as disregarding crack closure, is λ = 1 . 31, which is precisely equal to 1 + 2 · ν ,with ν being the resulting Poisson’s ratio of the composite. Conversely, considering all three mechanisms prescribed in the model (AR, VF and CC), the resulting gauge factor is λ = 49 . 04. This value is well within the range of experimentally observed values for unmodified cementitious materials found by, for example, Birgin et al. (2021); Drougkas et al. (2023a), which are in the order of 10 − 100. The main mechanism driving the remarkable increase in λ is CC, with 30% of the x -oriented cracks being closed after loading. When considering only the AR and VF mechanisms, the resulting gauge factor is slightly increased to λ = 1 . 56. The AR mechanism tends to decrease the gauge factor when the composite is subjected to compression. This is due to the strain in the aggregates, which are an electrically insulating phase, deforming less than the surrounding material due to their higher sti ff ness. Considering only the VF mechanism, the resulting gauge factor is equal to λ = 8 . 06, which, while substantially higher than the value obtained when discounting all three mechanisms, is still much lower than typical experimentally-observed values.