Numerical method for analysis of concrete under multi-axial loads

A constitutive model for plain concrete under monotonic increasing multi-axial loads is presented. An equation for determining the incremental tangent modulus is adopted and modified for implementation in finite element analysis. The parameters required in this model are the stresses and strains at failure, and the Poisson ratio. The equivalent uniaxial strain, adopted by some earlier researchers, is replaced by the strain indicator, ε_si, proposed in the present study. A five-parameter failure surface is used to predict the stresses at failure, and a numerical method for obtaining a closed-form solution is developed. The constitutive model is then implemented in a well-established finite element software via a user subroutine and the analytical results are verified against established experimental values. The predicted ultimate stress of the concrete falls within a 20% deviation from the experimental value and the proposed model is able to approximate the stress–strain curve reasonably well.