Plastic collapse of lattice structures under a general stress state

• We propose a numerical procedure to predict plastic collapse in periodic structures.
• The presented method is based on minimizing plastic dissipation inside a unit cell.
• The periodic structure is considered under a general state of macroscopic stress.
• Plastic collapse surfaces for regular and hierarchical honeycombs are obtained.
• Closed-form formulas for plastic collapse strength are derived accordingly.

We present a numerical minimization procedure to determine the macroscopic ‘plastic collapse strength’ of a tessellated cellular structure under a general stress state. The method is illustrated with sample cellular structures of regular and hierarchical honeycombs. Based on the deformation modes found by minimization of plastic dissipation, closed-form expressions for strength are derived. The current work generalizes previous studies on plastic collapse analysis of lattice structures, which are limited to very simple loading conditions.