5. Digital implementation in Code_Aster

In general, monocrystalline behaviors are integrated into Runge-Kutta methods for explicit integration, and into the « plasti » environment for implicit integration [R5.03.14]. For their part, the orientation tensors of the sliding systems are all defined in routine LCMMSG providing the global coordinate tensor for the nth system in the family provided whose name is provided by the calling routine.

To add a new single-crystal behavior, or simply a new flow or work hardening law, you need to define its parameters in DEFI_MATERIAU. Depending on the case (flow, isotropic or kinematic work hardening), it is necessary to add the reading of these parameters in the routines LCMAFL, LCMAEI, LCMAEC. For integration, simply write the definition of increases in internal variables in the routines LCMMFE (flow), LCMMFC (kinematic work hardening), and LCMMFI (isotropic work hardening), for explicit integration to work.

Implicit integration also uses the LCMMFE, LCMMFC, and LCMMFI routines. It also requires defining the derivatives of the equations in relation to the various variables. The derivatives are to be written in routines LCMMJF (derivatives of the flow equation), LCMMJI (derivatives of the isotropic work hardening relationship) and LCMMJC (derivatives of the kinematic work hardening relationship).

For more details on the architecture for resolving crystalline behaviors, see [D5.04.02].