A stereological ubiquitiformal softening model for concrete

Abstract

A stereological ubiquitiformal softening model for describing the softening behavior of concrete under quasi-static uniaxial tensile loadings is presented in this paper. In the model, both the damage evaluation process of fracture cross-sections and their distribution along the specimens axis are taken into account. The numerical results of a certain kind of full grade concrete made of crushed coarse aggregate are found to be in good agreement with the experimental data. Moreover, an experiental relation between the lower bound to the scale invariance of concrete and its tensile strength is also obtained by data fitting of the experimental data, which provides an effective approach to determine the lower bound to scale invariance of concrete.

A one dimensional ubiquitiform damage model for quasi-brittle materials

“…In order to couple the ubiquitiform characteristic of pore network with the strain softening model of quasi-brittle materials, the energy balance principle is employed again. According to references (Carpinteri et al, 2002(Carpinteri et al, , 2003(Carpinteri et al, , 2009Ou et al, 2019), in the damage band, the required energy to generate new pore surface is equal to the area under the stress-elongation curve in an interval with length of Dw j . Therefore, in the j-th softening subprocess, the energy balance equation is written as…”

“…In order to couple the ubiquitiform characteristic of pore network with the strain softening model of quasi-brittle materials, the energy balance principle is employed again. According to references (Carpinteri et al., 2002, 2003, 2009; Ou et al., 2019), in the damage band, the required energy to generate new pore surface is equal to the area under the stress-elongation curve in an interval with length of Δ w j . Therefore, in the j -th softening subprocess, the energy balance equation is written as where A is the cross-sectional area of the PUM, i.e., A = δitalicmax2; trueσ¯j is the stress of the material in the j -th softening subprocess; Δ w j is the increment of elongation in the j -th softening subprocess at the stress trueσ¯j; γf is the fracture surface energy equal to half of the material fracture energy G f; Δ S pj is the incremental pore surface area in the j -th subprocess, i.e., Δ S pj = S pj − S pj -1 .…”

“…Shi et al (2020) introduced the ubiquitiform parameters into the theoretical derivation of Mode I crack propagation, and the expression of ubiquitiform critical stress is verified by the experimental data. Meanwhile, based on the ubiquitiform characteristic of fracture cross-sections, Ou et al (2019) also presented a stereological ubiquitiformal softening model for describing the softening behavior of concrete. In addition, the ubiquitiformal theory has also been adopted to describe the equivalent material properties of composite materials (Ju et al, 2019;Li et al, 2016).…”

Research on one-dimensional ubiquitiformal constitutive relations for a bimaterial bar

“…In particular, a ubiquitiform has the same Hausdorff dimension as that of the initial element, which is always integral in practice, and a physical object in nature is a ubiquitiform. Recently, ubiquitiform has been applied successfully in the softening constitutive model of concrete (Ou et al, 2019), heat transfer in a bimaterial bar (Li et al, 2016), crack extension in concrete , and fracture energy of concrete .…”

“…(2.4), respectively.For a one kind of practical concrete materials(Stock et al, 1979), there are E m = 11.6 GPa, E a = 74.5 GPa, and r a = 60%. According toOu et al (2019), for concrete, the lower bound to scale invariance δ min can be expressed as a function of the tensile strength, asδ min = 221.38f −3.24 t (3.2)where f t is the tensile strength of the concrete, and the unit of δ min and f t are µm and MPa, respectively. For the concrete presented inStock et al (1979), f t = 2.38 MPa, and then δ min = 13.33 µm.…”