Finite strain modeling of hyperelastoplastic structures with application to beam-like members

This paper presents a comprehensive framework for the finite strain modeling of hyperelastoplastic structures, with a specific focus on beam-like members. The study introduces three fundamental contributions to bridge the gap between advanced constitutive theory and robust, efficient implementation for industrial-scale simulations. First, a novel computational technique for finite strain kinematic hardening is developed, ensuring dynamic consistency and numerical stability without resorting to accuracy-compromising approximations. Second, an exact, closed-form solution for updating plastic strains is formulated, providing a non-iterative methodology that guarantees unconditional stability and enhances computational efficiency, overcoming the convergence difficulties of classical return-mapping algorithms. Third, a novel, fully three-dimensional exact displacement field is introduced for beam elements undergoing planar motion, enabling high-fidelity capture of complex cross-sectional deformations at finite strains. The resulting beam element formulation is rigorously validated against experimental data and high-fidelity 3D finite element models in various scenarios, including buckling and bending. The results demonstrate that the proposed beam model achieves accuracy comparable to 3D solid elements while reducing computational cost by orders of magnitude. Finally, the model’s efficacy is demonstrated by accurately predicting the nonlinear response of complex lattice structures, establishing it as a powerful tool for the efficient simulation of large-scale, elastoplastic frameworks.