Abstract
A new and efficient method is proposed for the decomposition of finite elements into finite subcells, which are used to obtain an integration scheme allowing to analyse complex microstructure morphologies in regular finite element discretizations. Since the geometry data of reconstructed microstructures are often given as voxel data, it is reasonable to exploit the special properties of the given data when constructing the subcells, i.e. the perpendicularly cornered shape of the constituent interfaces at the microscale. Thus, in order to obtain a more efficient integration scheme, the proposed method aims to construct a significantly reduced number of subcells by aggregating as much voxels as possible to larger cuboids. The resulting methods are analysed and compared with the conventional Octree algorithm. Eventually, the proposed optimal decomposition method is used for a virtual tension test on a reconstructed three-dimensional microstructure of a dual-phase steel, which is afterwards compared to real experimental data.
Highlights
Dual-phase steels (DP steels) belong to the important class of advanced high-strength steels (AHSS), which combine attractive properties such as high tensile strength and formability
Therein, particular focus was on methods for geometries which are given as voxel/pixel data as they are usually the basis of microstructure simulations
The proposed Optimal Decomposition algorithm exploits the perpendicularity of the material interfaces to construct an optimal number of subcells for an individual element by aggregating voxels to larger cuboids independent from constraints used for the Octree strategy
Summary
Dual-phase steels (DP steels) belong to the important class of advanced high-strength steels (AHSS), which combine attractive properties such as high tensile strength and formability. Since our algorithms mainly aim to reduce the number of subcells required for integration, significant savings in computational costs can only be expected whenever the integration domains can suitably be decomposed in the sense of finite cells. This is the case for microstructures with distinct individual phases and/or cavities or pores. Thereby, the fields of properties are intrinsically assumed to be continuous and more or less automatically smoothed by the shape functions This is the approach we follow in our analysis of the real DP steel microstructures, where the graded properties of at least the matrix phase are included this way.
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