Numerically Efficient Three-Dimensional Model for Non-Linear Finite Element Analysis of Reinforced Concrete Structures

The paper concerns the non-linear finite element analysis (NLFEA) of Reinforced Concrete (RC) structures for engineering applications. The required level of complexity of constitutive models for such analysis was discussed and non-linear elastic models combined with the smeared cracking approach proved to be efficient. A new constitutive hypoelastic-brittle model of concrete based on these assumptions was proposed. Moreover, a method including the tension stiffening effect (TS) was developed. This phenomenon is connected with the bond properties between concrete and steel and, in some situations, has significant influence on the deflections of RC structures. It is often neglected by or included in the constitutive model of concrete. In the paper, an alternative approach was presented, in which this phenomenon is taken into account by generalising the material model of reinforcing steel. This approach is consistent with modern design standards and has solid physical foundations. The proposed models were implemented in the Abaqus code via UMAT user’s procedure coded in FORTRAN. Model verification and validation were presented in four case studies, concerning: a Willam’s test (examination on material point level), a beam with bending failure, and two beams with shear failure (with and without stirrups). The obtained results were compared with experimental outcomes and numerical results obtained by other researchers. The presented approach enables the accurate prediction not only of load capacity but of structural deformability, due to the precise description of TS. Thus, it promises to be a useful engineering tool.