ORALS

Non-Extensive Statistical Physics (NESP) is based on a generalization of the standard Boltzmann-Gibbs expression of the entropy. It was introduced a few decades ago by Tsallis [1] in an attempt to describe and enlighten phenomena with “anomalous” behaviour for which the statistical mechanical concepts of the Boltzmann-Gibbs approach have been proven inadequate. A typical class of such phenomena are the ones involving long-range interactions and memory effects. Given that fracture is characterized by both long-range interactions and memory effects [2], it is reasonable to examine whether the mechanical response of brittle building materials at load levels approaching these causing fractures could be described in terms of concepts based on NESP. The challenge is to detect proper and clear indicators that could be considered as early warning signals of the upcoming entrance of the system (loaded specimen or structure) into its “critical stage”, i.e., that of impending fracture. In this direction, advantage is taken of experimental data gathered from a long series of experimental protocols with specimens made of brittle building materials submitted to a variety of loading schemes (direct tension, uniaxial compression, three-point bending, shear) either monotonic or stepwise. The protocols include both elementary and structural tests. The study is carried out in terms of characteristic parameters of the Acoustic Emissions detected during loading. It is concluded that the time evolution of the entropic parameters of NESP provide reliable pre-failure indicators, in good agreement to the respective ones obtained from completely different analyses of the acoustic activity (as it is, for example, the F-function [3] or the Ib-value) or even from different monitoring tools (as it is, for example, the Pressure Stimulated Currents technique [4]).

References:
1. Tsallis C. (1988). Possible generalization of Boltzmann-Gibbs statistics. Journal of Statistical Physics, 52(1), 479-487.
2. Vallianatos F., Benson P., Meredith P., Sammonds P. (2012). Experimental evidence of a non-extensive statistical physics behaviour of fracture in triaxially deformed Etna basalt using acoustic emissions. EPL (Europhysics Letters), 97(5), 58002.
3. Triantis D., Kourkoulis S.K. (2018). An alternative approach for representing the data provided by the acoustic emission technique. Rock Mechanics and Rock Engineering, 51(8), 2433-2438.
4. Anastasiadis C., Triantis D., Stavrakas I., & Vallianatos F. (2004). Pressure Stimulated Currents (PSC) in marble samples. Annals of Geophysics, 47(1), 21-28.
5. Loukidis A., Triantis D., Stavrakas I. (2021). Non-extensive statistical analysis of Acoustic Emissions: The variability of entropic index q during loading of brittle materials until fracture. Entropy, 23(3), 276.