Intrinsically anomalous roughness of admissible crack traces in concrete

Abstract

We study the roughness of postmortem cracks in concrete plates of different size. We find that the set of admissible crack paths exhibits an intrinsically anomalous roughness; nevertheless, any individual crack trace in concrete is essentially self-affine. We also find that both the local and the global amplitudes of crack traces are distributed according to a log-logistic distribution characterized by the same scaling exponent, whereas the mean-square width distribution is best fitted by the Pearson distribution, while the log-normal distribution also provides quite good adjustments and cannot be clearly rejected.

Entropic rigidity of a crumpling network in a randomly folded thin sheet

“…0 21 . 0 3 ± = δ [36]. Further, it was found that under the uniaxial and radial compressions randomly folded thin sheets exhibit Poisson's expansion obeying a power-law behavior with the 7 universal Poisson's index 01 .…”

“…Accordingly, the folding phenomena are associated with a rich class of crumpling phenomena [3], which belong to a wider class of interfacial deformation phenomena [5]. Because of their biological and technological importance, the properties of randomly folded thin materials are now the subject of increasingly growing attention [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45].…”

“…The properties of ridges have been studied thoroughly. Scaling laws governing the energy and size of the ridge have been obtained analytically [5,49] and tested numerically [9,32,48,50] and experimentally [36,37,43].…”

“…However, numerical simulations [32] and experiments [17,36] suggest that the mechanical behavior of randomly folded sheets in a thee-dimensional stress state ( 3 = k ) is dominated by the volume dependence of crumpling network enthalpy, U , leading to the power-law force-compression relation:…”

“…Furthermore, it was suggested that crumpling network governs the mechanical behavior of randomly folded materials [9,32,48], which exhibit anomalously low compressibility under hydrostatic pressure [17,32,36,37].…”