3D analysis of reinforced concrete structural components using a multi-surface elasto-plastic-anisotropic-damage material model

Elastic-Plastic-Damage material models are widely adopted for the numerical modelling of concrete because of their capability of representing pressure sensitive 3D material behaviour considering permanent inelastic deformations as well as degradation of material moduli beyond the elastic range. In this paper, we develop a non-associative multi-surface plastic-damage material model for the 3D solid element based finite element analysis of reinforced concrete structural components. For the non-associative plastic flow, a linear potential function is adopted, while Menetrey–Willam and Rankine surfaces are adopted as the yield surfaces in compression and tension regimes, respectively. The degradation in the material stiffness under cyclic loading is incorporated by the damage component of the material model, which is generally anisotropic and assumed to be directly dependent on the evolution of the plastic strains. This assumption leads to a computationally efficient algorithm in terms of circumventing iterations to equate the stresses between the coupled damage and plasticity components of the material model. The rigorous details of the developed return-mapping methodology considering both the Cutting-Plane as well as the Closest-Point-Projection algorithms are provided. The material model is employed for the structural level analysis, in which case the concrete bulk is modelled by using an Eight-Node, Six-Degrees-Of-Freedom per-node solid element, and the reinforcement bars and stirrups are modelled by using the conventional Two-Node, Six-Degrees-Of-Freedom per-node Euler–Bernoulli beam-bar element. The inelastic behaviour of the reinforcements is determined by using a simpler elasto-plastic-damage based material model under the assumption of uni-axial stress-strain relations. An in-house fortran software is developed for the computer implementation. Comparisons with results from literature are shown for validation purposes. The validation cases include static analyses of a beam and a column under monotonic loading as well as a shear-wall under cyclic loading.