Efficient stress integration algorithm of memory surface model with shrinking rule under plane stress field

Abstract

Reliable nonlinear finite element analysis (FEA) of steel structures requires a constitutive model capable of predicting the cyclic plasticity of structural steels. Steel structure members are typically composed of multiple thin steel plates. The FEA of such structures has frequently used shell elements to capture the bending deformation and reduce the computational complexity, where its stress state can be regarded as the plane stress field. This study provides a constitutive model with a memory surface under a plane stress field for the cyclic plasticity of structural steels. A noble computationally efficient algorithm for stress integration and consistent tangent operator was proposed, where the constitutive equations were linearized after solving some unknown variables. The proposed model was implemented in the Abaqus FEA code. The residual-force convergence rate of the consistent tangent operator is investigated using a single-shell element under simple boundary conditions, where the consistent tangent operator achieves more than a quadratic convergence. The proposed model was validated by comparing the experimental results and FEA results with the proposed model for thin-walled steel members under cyclic loading. The average difference in peak forces between FEA and experimental results was 11.5 % for the local buckling tests and 8.4 % for the shear buckling tests at most. These results suggest that the proposed model provides an accurate prediction for other thin-walled steel structures under cyclic loading.