Homogenization coarse graining (HCG) of the lattice discrete particle model (LDPM) for the analysis of reinforced concrete structures

Abstract

In this study, a coarse-graining framework for discrete models is formulated on the basis of multiscale homogenization. The discrete model considered in this paper is the Lattice Discrete Particle Model (LDPM), which simulates concrete at the level of coarse aggregate pieces. In LDPM, the size of the aggregate particles follows the actual particle size distribution that is used in experiment to produce concrete specimens. Consequently, modeling large structural systems entirely with LDPM leads to a tremendous number of degrees of freedom and is not feasible with the currently available computational resources. To overcome this limitation, this paper proposes the formulation of a coarse-grained model obtained by (1) increasing the actual size of the particles in the fine-scale model by a specific coarsening factor and (2) calibrating the parameters of the coarse grained model by best fitting the macroscopic, average response of the coarse grained model to the corresponding fine scale one for different loading conditions. A Representative Volume Element (RVE) of LDPM is employed to obtain the macroscopic response of the fine scale and coarse grained models through a homogenization procedure.Accuracy and efficiency of the developed coarse graining method is verified by comparing the response of fine scale and coarse grained simulations of several reinforced concrete structural systems in terms of both accuracy of the results and computational cost.

New perspective of fracture mechanics inspired by gap test with crack-parallel compression

“…Another example is the gross overestimation of the forces exerted by sea ice on the legs of oil platforms. Neither LEFM nor CCM could ever fit the data, but the CBM (with M7) (8,(10)(11)(12)(13) and the LDPM (14,15) could. This experience is what partly inspired this study.…”

Analytical random field-based model for fracture in concrete

“…The autocorrelation length of H 1,1,1 (x) along x 1 can be calculated using T = T 1 in Eq. (12). One might be interested in analyzing the derivative of the averaged random process H 1,1,1 (x) along the first axis, x 1 , denoted aṡ H T (x).…”

“…The characteristic length emerges from contribution of two sources, the constitutive relationship between discrete units and geometrical properties of them. We utilize here a simplified version of the lattice discrete particle model developed in [4][5][6]12]. The numerical model used here is the same as the one presented in [9].…”

Symmetric high order microplane model for damage localization and size effect in quasi‐brittle materials

“…One particularly successful meso‐scale, discrete model is the so‐called lattice discrete particle model (LDPM) formulated by Cusatis and his collaborators. Originally developed for concrete, this model was successfully used to simulate the behavior of plain concrete, 15,56–60 reinforced concrete, 61,62 fiber reinforced concrete, 63–67 and to reproduce multi‐physics phenomena such as aging, ASR, 68–72 as well as hygro‐thermal and chemical processes 73–76 . LDPM has also been used to simulate rocks 77,78 and masonry 79,80 …”