An improved algorithm for implementing beam element constitutive model based on a classical damage plastic model

Abstract

To address the limitation that classical Concrete Plastic Damage (CDP) models cannot be applied to beam elements, this paper proposes an improved multi-axis concrete constitutive integration algorithm suitable for three-dimensional beam elements. This method abandons the commonly used plane stress assumption at the integration point level and introduces a transversely elastic constraint assumption that is more physically universal. An elastic constraint stiffness coefficient is introduced to uniformly describe any transverse constraint state of the beam cross-section, ranging from a free surface to a fully constrained state. Based on this, a semi-implicit single-step return-mapping coupled solver is developed. This algorithm eliminates the nested loops associated with plastic correction and missing strain determination in traditional nested iterative schemes, significantly reducing computational cost while maintaining numerical accuracy. Numerical examples verify the convergence and accuracy of the algorithm. The results indicate that this method can obtain multiaxial mechanical responses highly consistent with the CDP model of solid elements within the beam element framework, providing a solution that combines accuracy and efficiency for high-precision nonlinear analysis of concrete beam and column members.