Finite element modelling of 1D steel components in reinforced and prestressed concrete structures

Abstract

International audienceThis paper introduces a new approach for FE modelling of 1D steel inclusions within a 3D concrete domain. Reinforcements modelled with 1D meshes, when included in 3D domains, are indeed responsible for pathological effects like stress concentration at the local scale. The alternative solution of an explicit 3D mesh of the steel elements requires a large amount of work, and a relatively fine conform mesh (and therefore, additional computation cost). It is thus hardly applicable to large-scale structures. The approach proposed in this contribution, called “1D-3D”, generates an equivalent volume from a 1D mesh of the reinforcements. Associated stresses and stiffnesses, which can be condensed on the boundaries of the newly created volume, are then applied to concrete 3D elements using kinematic relations. This approach is validated on two representative cases of civil engineering applications, including active and passive steel reinforcements. It provides results similar to an explicit 3D approach, without its meshing complexity. It thus combines the advantages of 1D and 3D approaches in a single modelling

Yield design‐based numerical analysis of three‐dimensional reinforced concrete structures

“…An alternative approach for the finite element modeling of 1D steel inclusions in 3D concrete volumes has been recently proposed by Llau et al Likewise, in a more explicit reference to the homogenization procedure, three‐dimensional fem elastoplastic analyses on reinforced concrete structural elements have been performed by Figueiredo et al Their approach, which will be adopted in this contribution, may be described as follows.…”

“…The generalization to the more realistic situation of linear reinforcing inclusions placed into three‐dimensional concrete bodies is posing a somewhat serious challenge as regards the possibility of treating such a case in a 1D‐3D mixed modeling approach. Some attempts to circumvent this problem have already been proposed either in the context of the finite element formulation or making use of an implicit homogenization method or multiphase model …”

Numerical upper bounds to the ultimate load bearing capacity of three‐dimensional reinforced concrete structures

“…6 for more details). Some attempts to circumvent this problem have already been proposed either in the context of the finite element formulation 7 or making use of an implicit homogenization method 8 or multiphase model 9 . The problem has been quite recently addressed in a previous contribution 6 by resorting to an extended homogenization technique according to which each reinforcing inclusion with its surrounding concrete material is replaced by a homogenized reinforced concrete material.…”

Enhanced finite element formulation incorporating stress jumps and interface behavior in structures with embedded linear inclusions

“…Mixed-modeling may however lead to large errors in the solution close to the inclusion zone when perfect bonding and refined meshes are adopted in the analysis. In such circumstances, being the physical cross-sectional dimension of the reinforcement not taken into account by the 1D representation of the inclusion, the resulting geometrical singularity can lead to spurious stress concentrations in the matrix as pointed out by Llau et al 48 and Vincent et al. 49 This drawback can therefore represent a serious limitation when material nonlinearities are included in the model since nonphysical material degradations can take place.…”