A scaled boundary polygon formulation for elasto-plastic analyses

• Polygon-based SBFEM for elasto-plasticity broadens its application to nonlinear problems.
• Displacement interpolation by scaled boundary shape functions similar to the FEM.
• Standard FE procedures to model plasticity.
• Semi-analytical evaluation of the stiffness matrix and internal load vector.
• Superior accuracy particularly for elasto-plastic fracture problems.

This study presents a novel scaled boundary polygon formulation to model elasto-plastic material responses in structures. The polygons have flexible mesh generation capabilities and are more accurate than standard finite elements, especially for problems with cracks and notches. Shape functions of arbitrary n-sided polygons are constructed using the scaled boundary finite element method. These shape functions are conforming and linearly complete. When modeling a crack, strain singularities are analytically modeled without enrichment. Standard finite element procedures are used to formulate the stiffness matrix and residual load vector. The nonlinear material constitutive matrix and the internal stresses are approximated locally in each polygon by a polynomial function. The stiffness matrix and the residual load vector are matrix power integrals that can be evaluated analytically even when a strain singularity is present. Standard nonlinear equation solvers e.g. the modified Newton–Raphson algorithm are used to obtain the nonlinear response of the structure. The proposed formulation is validated using several numerical benchmarks.