A homogenized formulation to account for sliding of non-meshed reinforcements during the cracking of brittle matrix composites: Application to reinforced concrete

Abstract

Non-linear finite element modelling of complex structures made of composites, such as reinforced concrete, remains a challenge because, until now, the only way to consider the important phenomenon of sliding between the reinforcements and the brittle matrix of the composite has been to mesh the reinforcements and their interfaces explicitly. This method is accurate but so expensive in terms of computational resources that only critical small elements of composites structures are modelled using it. To get around this limit, a method avoiding the meshing of composite reinforcements is proposed. It consists in treating the sliding between reinforcements and matrix with a differential formulation that provides the deformation of reinforcements directly as a continuous field superimposed to the displacement field of the matrix. The method needs a minor modification of the finite element code, which can take advantage of its analogy with the anisotropic thermal formulation. After the analytical presentation of the method, two theoretical cases of study are given to confront the results obtained with this method without meshing of reinforcements, with reference results obtained using a complete mesh of the matrix, reinforcements and interfaces.

Modelling of the long-term evolution and performance of engineered barrier system

“…Furthermore, during the chemical damage processes (leaching, carbonation, or chloride ingress in the hydrated cement paste), the model also considers the amount and nature of aggregates on the macroscopic residual mechanical properties. In the case of reinforced concrete, which is the material considered in this structural component, until now, the phenomenon of reinforcement corrosion was decoupled from the chemical state of the concrete [38]; hence the lock to be lifted in this chemo-mechanical model consists in predicting the steel corrosion progress as a function of the concrete chemical state at the interface and in localized cracks; and deducing its effect in term of steel anchorage and their contribution on reinforced concrete mechanical performances [39].…”

Numerical prediction of cracking risk of reinforced concrete structures at early age

“…For mechanical damage, this can be modelled using Equation 11, which leads to a decrease in mechanical damage under the effect of hydration (which then acts as a selfhealing process of the cement paste). When the localized tensile damage, , decreases under the effect of hydration, the crack opening , is recalculated by inverting Equation 10 (some details can be found in [38]). (11) Finally, in the case of finite element applications, it should be noted that the local damage pattern is energy-regularized.…”

“…It is obvious that, when the aim is to predict the risk of cracking in the Vercors mock-up, explicit modelling of the reinforcement and steel-concrete interfaces, as carried out on the structures of the CEOS project, is unrealistic given the size of the structure and the high rate of reinforcement (in the 3 directions). The choice was therfore made to use homogenized modelling of the reinforced concrete by considering the reinforcements as inclusions in the REV with the method developed in [38]. It is based on a non-local formulation that considers, in the homogenized element, the effect of steel-concrete sliding within the REV on the reinforcement strain.…”

Non-Local Anisotropic Damage Coupled To Plasticity

“…In this work, it is proposed to extend the nonlocal method from the classical framework of isotropic state variables to second-order tensorial variables. For this purpose, the multivariable Helmholtz formulation, as clarified in [20], is adapted to consider several phase-fields. Two numerical implementation methods are possible: (1) each term of the plastic strain tensor is treated separately, resulting in six scalar differential equations of the Helmholtz form, to which the non-local method is applied directionally using anisotropic diffusion matrices expressed in the fixed coordinate system; (2) only three diffusion matrices need to be computed, each one associated with one principal direction of the plastic strain tensor.…”