2. Benchmark solution

2.1. Calculation method used for the reference solution

In the general case, the complex form of the law does not allow a reference solution to be calculated.

To validate the law, we use the case of linear kinematic work hardening (the power and the kinematic limit force are not given). The forces as well as the energy dissipated can be calculated analytically.

	The data is: , ,,, etc., and the amplitude of displacement: Which gives:

Figure 2.1.a: loading cycle.

For a stabilized cycle (displacement ranging from 0 to

unto

unto

) the energy dissipated is

.

In the general case of power law, an external program made it possible to validate the responses in efforts.

2.2. Benchmark results

The tests are carried out on:

1. the effort at each load reversal;

2. the energy dissipated at the end of charging.

For both models, a table shows the parameters of the law as well as the values of the forces and the energy dissipated at the end of the cycle.

2.3. Uncertainty about the solution

For the case of linear kinematic work hardening there is no uncertainty, the solution is analytical, both in terms of effort and energy.

For the case of non-linear work hardening, the reference solution is given by an external program.