Two New Methods of Fictitious‐Crack Model and Their Applications

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Abstract
This paper presents several new results in the studies of the fictitious‐crack model. First, an engineering version of the stability theory of the fictitious‐crack model is presented in the framework of the finite element method. Then, the rupture condition of the fictitious‐crack model is extended to the case of multiple loads for the linear softening materials, which leads to a new formula to predict tensile strength. In addition, a new semianalytic model is proposed to study beams without notch, from which a very simple size‐effect formula is derived. This new formula currently has been adopted in a German code to predict the concrete response under multiple loads. Extensive experimental results are collected and compared with our theoretical predictions. In view of the comparison, it appears that, for normal concrete, a linear softening relation is sufficient for the purpose of describing its modulus of rupture.

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