Zoning Method for Efficient Material Properties Calculation

When material models are enhanced by calculating additional effects such as microstructure evolution for every Gauss point and time step, considerable numerical effort must be expected. Interfacing third-party software from within user defined material subroutines can even be more time consuming. In many applications, however, considerable parts of the material domain give similar results. Strain, strain rate and temperature are the most important properties for the material behavior. During the thermo-mechanical processing such as rolling and especially extrusion, material deformation is concentrated in small areas. This means that strain, strain rate and thus temperature remain almost constant for large parts of the material during most of the simulation runtime. The idea behind the zoning method proposed in present work and implemented into LS-DYNA® user defined subroutine is to calculate material properties only once for an individual zone. By adaptively subdividing the material domain due to e.g. strain, strain rate and/or temperature results, runtime used for calculation and interfacing of third party software can be effectively saved. A comparison between history variables from the last call of the zoning method with current values can be even used to reduce the number of calculations over time. Elements are dynamically clustered using adaptive zoning and element iteration is thus reduced to elements with evolving values. For elements without major changes of relevant quantities or sufficiently small deviations to already computed data, existing values are used. The effectiveness of the proposed zoning method is demonstrated for a case of 2D compression test of a cylindrical sample. A cylindrical specimen made of a standard AA2024 alloy is compressed at elevated temperature to a certain degree. For calculation of a flow stress an in-house dislocation density based model is implemented into a user-defined elastoviscoplastic material model. Based on the elemental dislocation density, the material domain is separated in individual zones and calculated results are mapped to all elements covered by the respective zone. In the end, the third-party software (herein MatCalc©) is called to calculate the local fraction of precipitates in a given zone. The results have shown that it is possible to consider microchemistry at reasonable costs.