Multi-scale computational model for failure analysis of metal frames that includes softening and local buckling

In this work we present a new modelling paradigm for computing the complete failure of metal frames by combining the stress-resultant beam model and the shell model. The shell model is used to compute the material parameters that are needed by an inelastic stress-resultant beam model; therefore, we consider the shell model as the meso-scale model and the beam model as the macro-scale model. The shell model takes into account elastoplasticity with strain-hardening and strain-softening, as well as geometrical nonlinearity (including local buckling of a part of a beam). By using results of the shell model, the stress-resultant inelastic beam model is derived that takes into account elastoplasticity with hardening, as well as softening effects (of material and geometric type). The beam softening effects are numerically modelled in a localized failure point by using beam finite element with embedded discontinuity. The original feature of the proposed multi-scale (i.e. shell-beam) computational model is its ability to incorporate both material and geometrical instability contributions into the stress-resultant beam model softening response. Several representative numerical simulations are presented to illustrate a very satisfying performance of the proposed approach.