Benchmark solution
=====================


Calculation method used for the reference solution
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To establish the reference solution, software SIDOLO is used, which allows the simulation and identification of laws of behavior.

The equations of the model are written by the user in Fortran in the form of a system of first-order differential equations, solved by a Runge Kutta method of order 4 with adaptive steps.


Benchmark results
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:math:`{\sigma }_{\text{xx}},{\sigma }_{\text{xy}},{\varepsilon }_{\text{xx}},{\varepsilon }_{\text{xy}},{\mathrm{X1}}_{\text{xx}},{\mathrm{X2}}_{\text{xx}},p,R,q,{\xi }_{\text{xx}}` at the time :math:`P(t\mathrm{=}10s)` where :math:`\mathrm{X1}` and :math:`\mathrm{X2}` are the kinematic work hardening variables, :math:`p` the cumulative plastic deformation, :math:`R(p,q)` the isotropic work hardening variable and :math:`\xi` the internal variable allowing the work-hardening memory to be taken into account.


Uncertainty about the solution
----------------------------

Uncertainty of SIDOLO.


Bibliographical references
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1. SIDOLO, version 2.3, User manual, Ecole Nationale Supérieure des Mines de Paris, Materials Center, September 1995.