Determination of intergranular and transgranular failure of mesoscale model concrete under mode-I fracture

An extended universal morphological model for concrete mode‐I fracture: Parametric and case studies

“…The present study establishes a systematic meso-level theoretical modeling approach for the concrete mode-I fracture in accordance with the extensions of several fundamental works. [35][36][37][38] The current material model takes multiple mix variables into consideration. Thus, effects of properties and scales of meso structures on the performance of concrete can be explicitly revealed.…”

“…The current work mainly extends several fundamental works in Refs. [35][36][37][38] to establish the XUMM that is in the two-dimensional way. Since the meso-fracture criterion has been developed to the three-dimensional space in Ref.…”

“…In Equation ( 17), ω i ω m ¼ cos πη ð Þ: [34][35][36] According to the adopted constitutive laws for meso structures and the self-consistent finite stress model (SFSM), 37 one may obtain:…”

“…in which, f t,a and ε u,a are the tensile strength and the ultimate strain of aggregate, respectively; f tip t,m is the finite stress at the mortar crack tip; AF is the aggregate fracture index. 37 Furthermore, the critical state of the meso-level crack path criterion 37 is specifically considered in the present study, so that AF = MF c = πηcot(πη), where MF c is the critical mesoscopic fracture index, 37 therefore f t,a ¼ f tip t,m , which results in ω a ω m ¼ πηcot πη ð Þ, and thus Equation ( 17) is finally expressed as…”

“…34 The model is named of eXtended Universal Morphological Model (XUMM), and it is established based on the extensions of several fundamental works. [35][36][37][38] It is a meso-fracture model for the predictions of mechanical and fracture parameters of concrete, using both meso-fracture criteria and possibility parameters. This study develops a normalized analysis method based on the XUMM to evaluates the effects of properties and scales of meso structures on the performance of concrete, and based on which, investigates the aggregate strength effect, the aggregate volume effect, the maximum aggregate size (MAS) effect, the tortuosity of mesoscopic crack, the roughness of fracture surface and the characteristic length.…”