“…15 shows the evolution of the numerically obtained axial strains at different positions on the reinforcement bars as a function of the global force. Results are found to be comparable to the experimental data [55,56]. The model is able to capture positive and negative strains and thus to distinguish the parts of beam in traction or in compression.…”
Section: Numerical Resultssupporting
confidence: 73%
“…3 point bending test: position of the strain gauges[55,56]. 3 point bending test: finite element meshes and boundary conditions.…”
“…15 shows the evolution of the numerically obtained axial strains at different positions on the reinforcement bars as a function of the global force. Results are found to be comparable to the experimental data [55,56]. The model is able to capture positive and negative strains and thus to distinguish the parts of beam in traction or in compression.…”
Section: Numerical Resultssupporting
confidence: 73%
“…3 point bending test: position of the strain gauges[55,56]. 3 point bending test: finite element meshes and boundary conditions.…”
It is well known that it is necessary to introduce a length scale parameter in a continuum damage mechanics model to correctly simulate strain localization. The second gradient model, a special case of kinematically enriched continua, considers an internal length parameter by taking into account the second order derivatives of the displacements in the virtual power principle. In this paper, we show that the original second gradient finite element of Chambon and co-workers can present spurious oscillations, especially for mode I crack propagation problems. After providing the plane stress second gradient constitutive law, we propose to add a penalty term in the original formulation in order to improve numerical convergence and to avoid spurious oscillations in the local variables distributions. Two numerical examples using classical damage mechanics laws, a three points reinforced concrete beam and a trapezoidal notched specimen are used to test the performance of the formulation. Parametrical studies are also shown on the influence of the penalty parameter. The problem of unrealistic damage spreading for damage values close to one, occurring often in mode I crack propagation problems, is finally discussed.
“…The 1D approach (Figure 1a) is by far the most widely used in literature to represent these steel members [10,[15][16][17]. It is simple to apply on large and complex structures as it does not require any mesh constraints.…”
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
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
