Automated simulation of voxel-based microstructures based on enhanced finite cell approach
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O R I G I NA L
Yannick F. Fangye
· Niklas Miska
· Daniel Balzani
Automated simulation of voxel-based microstructures based on enhanced finite cell approach
Received: 2 January 2020 / Accepted: 7 June 2020 © The Author(s) 2020
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. Keywords Dual-phase steel · Voxel-based microstructures · Finite cells · Multiscale simulation
1 Introduction 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. DP steels are therefore suitable for applications in many engineering fields, e.g. in the automotive industry for an improvement in the crash safety and stability whilst the overall weight is reduced. The advantageous material properties are directly dependent on the interactions of the individual microscopic constituents, which arise from a specific production process, see, e.g. Al-Abbasi and Nemes [1], Pierman et al. [25], Kim and Lee [17] and Davies [6]. The microstructure of DP steel consists of hard martensitic inclusions embedded in a ductile ferritic matrix. A crucial step in the production of DP steels is the rapid cooling of hot-rolled steel that induces the transformation from austenite to martensite. These transformation is responsible for graded material properties in the ferrite matrix as found in Brands et al. [4]. Due to the complexity of their microstructure, the modelling and simulation of structures made of DP steels is not straightforward. Since a phenomenological model to appropriately describe the effective material response is difficult to design, homogenization approaches taking the morphology of the microstructure into account are more suitable, see, e.g. Golanski et al. [14], Moulinec and Suquet [23] or Miehe et al. [21]. A direct two-scale homogenization scheme is the FE2 method, where a microscopic boundary value problem is solved at each integration point of the macroscopic finite elements, cf., e.g. Smit et al. [33], Feyel [10,11], Feyel and C
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