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0.00 0.20 0 40 0 60 0 60 1.00 1.20 1.40 1 «0 1.00 2.DO

0.00 0.20 0 40 0 60 0 60 1.00 1.20 1.40 1 «0 1.00 2.DO

Figure 10. X displacement of node 10: elastic shear response.

no plastic sliding should occur. The elastic sliding is neglectable due to the high shear stiffness considered in the model.

The elastic response is clearly depicted in Figure 10.

3.4 Contact updating

A cubic block A with side equal to 0.7 m lies onto a 45° inclined face (1.0m • 4.2 m) of a hexahedron B. B has its base constrained. The gravitational force is the only force acting.

The geometrical configuration, forces and constraints and node numbering are summarize in Figure 11.

The static frictional coefficient is set equal to 1.1. Contact and mass damping have been considered in the analysis. The initial tilting couple, due to friction, equals the righting one, due to Wa, leading to an instable configuration. A small perturbation, like the one induced by the deformability of blocks or by the penalty approach, can start the motion.

A should roll over the inclined face of B. The face of A impacting with B is changing at each overturn

This configuration is therefore useful to check the contact updating routine.

Figure 11. Rolling: (a) geometrical model; (b) forces and constraints; (c) node numbering of block A.

Figure 11. Rolling: (a) geometrical model; (b) forces and constraints; (c) node numbering of block A.

Figure 12. Rolling: visual output of the numerical code at instant t = 40.

3.5 Rocking and damping

A slender block A with base equal to 0.2 m • 0.7 m and height equal to 1.0 m lies with one of the longer edges of its base onto a parallelepiped B.

B has its base constrained. The shorter edge of A base forms a 30° angle with the horizontal plane. The gravitational force is the only force acting.

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