A bidirectional plasticity model was implemented that allows bidirectional interaction to be considered in the dynamic analysis of a pendulum system in two orthogonal directions. This is achieved by defining an interaction surface of the system capacity in both directions. The plasticity model returns elastic or plastic forces corresponding to a certain deformation. It is implemented using a backward-Euler procedure, which is the general form of the radial return plasticity method.

The general yield surface can have different strengths in different directions and the shape of the curve can be controlled. The yield surface is governed by the equation:

Where F1, F2 are the forces in directions 1 and 2, and Fy1, Fy2 are the yield capacities in each direction. Figure 25 shows the bidirectional yield surfaces with and without bidirectional interaction. The parameter n is the interaction sufrace power, and it controls the shape of the interaction surface. Figure 26 shows the effect of n on the shape of the interaction surface.

Figure 25: Bidirectional yield surface with and without interaction

Figure 26: Effect of n on the shape of the interaction surface