PSI - Issue 78

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

2103

climatic performance in buildings and infrastructure, as noted by Song et al. (2017). Cementitious materials in partic ular, due to their wide use in all construction typologies, comprise an excellent vehicle for creating embedded struc tural health monitoring systems and multi-functional solutions, as explained in Ubertini and D’Alessandro (2018); Drougkas et al. (2023a). Therefore, understanding the physical mechanisms behind their piezoresistive performance and acquiring the capability of modelling and predicting their behaviour is of crucial importance for preventive main tenance and structural control. Micromechanics are an attractive approach for the modelling of cementitious materials subjected to various phys ical e ff ects. Through simple and intuitive homogenisation schemes, micromechanics can account for the impact of di ff erent material phases and inhomogeneities on the mechanical and electrical properties of composite materials. Mean-field approaches in particular are especially e ffi cient in that regard, being characterised by reduced compu tational e ff ort and accurate results under certain conditions, as described by Bruggeman (1935); Mori and Tanaka (1973). E ff orts in numerically predicting the piezoresistive gauge factor of cementitious materials have been proposed in the literature, such as by Garc´ıa-Mac´ıas et al. (2017). These e ff orts have mostly focused on capturing the e ff ect of dispersed conductive inclusions on the gauge factor at varying concentration levels and appear to account for increases in the gauge factor mostly through the increase of the e ff ective volume fraction of conductive fillers in the deformed composite. However, they have not been able to accurately capture the gauge factor of unmodified materials, producing values well below experimental observations. The present paper aims to quantitatively interpret the e ff ect of various micro-scale material features on the piezore sistive performance of cementitious materials. These features include the presence of micro- and macro- crack net works, generated by shrinkage or mechanical loading, whose closure under compression can lead to drastic changes in electrical conductivity, and the shift in aspect ratio and apparent volumetric fraction of the various phases of the deformed cementitious composite. The influence of these features is implemented in a micromechanics context, sub sequently employed for exploring their influence on piezoresistive sensitivity.

2. Homogenisation schemes

2.1. General considerations

Mean-field homogenisation schemes in three dimensions proposed for composite materials were employed for deriving the properties of the composite material. In this context, the hardened paste is treated as the matrix ( m ). In this context, all inclusions are treated as ellipsoidal inhomogeneities embedded in the matrix and characterised by three half-lengths: a 1 , a 2 and a 3 . Fig. 1a illustrates an ellipsoidal inclusion with the half-lengths indicated.

y

y

a 2

Crack

x

a 3

x

Pore Aggregate

z

z

a 1

b)

a)

Fig. 1. a) Ellipsoidal inclusion; b) Composite material consisting of ellipsoidal inclusion families dispersed in matrix.

The aggregate particles ( a ) and the pores ( p ) are treated as spherical inclusions ( a 1 = a 2 = a 3 ). The cracks are treated as penny-shaped inclusions, with two equal half-lengths substantially greater than the third ( a 1 = a 2 ≫ a 3 ).