Parametric study of the Lattice Discrete Particle Model (LDPM) constitutive law for fiber reinforced concretes (FRCs)

The growing adoption of fiber reinforced concrete (FRC) as a structural material is motivating plenty of research in this field, especially those regarding the experimental aspects and the development of numerical models. The composite nature of the material suggests that the final mechanical performance is due to the contribution of both components and to their interaction. In this respect, the experimental research has a fundamental importance for the identification of the mechanical response scatter, as the natural heterogeneity of concrete is further incremented by the randomness of fiber distribution. When the mechanical behavior of FRCs is simulated numerically, this aspect needs to be properly reproduced to get a reliable response of the fiber reinforced concretes. In this framework, the present paper illustrates a numerical model describing the behavior of a FRC concrete reinforced with polymeric fibers, developed with the Lattice Discrete Particle Model (LDPM). This theory is able to reproduce the behavior of only concrete (LDPM), by describing the mechanical interaction between the aggregates, and also the interaction with fibers (LDPM-F). The model has been already validated for the plain concrete short- and long-term behavior (M-LPDM); in the recent years, the fiber-bridging action due to the reinforcement has been introduced. Many numerical parameters concerning the fiber geometry and its mechanics determine the whole response: the discretization of each fiber, the definition of its shape, its elastic modulus and also the orientation of the fibrous reinforcement in the concrete matrix. Furthermore, polymeric fibers may be characterized by a crimped profile to improve the matrix-to-fiber bond and, so, it is fundamental to consider their actual shape also numer-ically. Their geometry is defined by the number of segments in which each fiber is divided and its tortuosity. This paper performs a parametric analysis of these specific aspects showing how they affect the flexural behav-ior of macro-synthetic fiber reinforced concrete beams. The fiber elastic modulus handles the force transferring when concrete is cracked so defines the post-peak strength in the flexural behavior: a value between the tangent and secant elastic modulus has to be considered in the calibration. The orientation of the reinforcement, espe-cially in the crack surroundings, drives the crack development: the randomness is what influences more the scatter in the response that, in turn, depends on the number of fibers connecting the crack. In this numerical approach the counting of fibers has been also performed and, at a given fibers dosage, the orientation is a parameter calibrated to make the numerical count close to the experimental. Finally, regarding the concrete composition, the aggregates are here generated according to the minimum and maximum size: the minimum value given is shown to influence the post peak behavior especially in terms of cracking evolution under flexural load.