Thermo-mechanical computations taking into account the mechanical dissipation

26 March 2012

by S. Fayolle, EDF R&D / AMA

The test hsna105 V7.20.105 (automatic translation) illustrates the creation of a thermomechanical calculation taking into account the mechanical dissipation as a heat source in the heat equation.

To achieve this type of calculation, we opted for a classical approach in the literature knows as isothermal staggered procedure. This approach allows to solve separately the thermal and mechanical equations and ensures accurate results. The command sequence is generic enough to work for all static and dynamic studies.

To use this approach, it is necessary that the constitutive equation calculates and stores the mechanical dissipation rate as an internal variable. The only law in Code_Aster that performs this calculation is the VMIS_JOHN_COOK law. It is defined by a von Mises yield criterion and an isotropic hardening of Johnson-Cook. This constitutive law is flexible enough in his writing to model a linear elastic law, an elastoplastic law with linear isotropic hardening or an elastoplastic law with isotropic hardening following a power function.

To illustrate the interest of such an approach, we modeled Taylor bar test in 3D. This test consist to launch a metal bar against a rigid surface. In our case, we consider a copper bar with a velocity of 180 m/s. The computation integrates a wide range of nonlinearities:

  • finite strains with the use of GDEF_LOG;
  • a non-linear behavior VMIS_JOHN_COOK whose hardening varies with temperature and the rate of plastic strain;
  • contact based on the CONTINUOUS method;
  • friction via Coulomb’s law.

The figures illustrate the temperature field during the impact with a front view (figure 1) and a view at the impact zone (figure 2).

Figure 1 : Temperature field during the impact, front view.
Figure 2 : Temperature field during the impact, bottom view at the impact zone.