A Hashin-Shtrikman type semi-analytical homogenization procedure in multiscale modeling to account for coupled problems

  • David Jaworek Institute of Applied Mechanics, RWTH Aachen University
  • Johanna Waimann Institute of Applied Mechanics, RWTH Aachen University
  • Christian Gierden Institute of Applied Mechanics, RWTH Aachen University
  • Stephan Wulfinghoff Institute for Material Science, Kiel University
  • Stefanie Reese Institute of Applied Mechanics, RWTH Aachen University
Keywords: Process signatures, heterogeneous material, homogenization, Hashin-Shtrikman, Talbot-Willis, plasticity


Heterogeneous materials are important for a vast amount of applications e.g. in automotive industry or in aerospace. For instance, when producing components, it can be desired to use materials with a heterogeneous microstructure in order to achieve specific material properties. The resulting properties highly depend on the manufacturing process itself, which can involve mechanical and/or thermal loadings. Therefore, it is necessary to properly depict the microstructural material behavior in order to allow for the calibration of the manufacturing process and for the solution of the inverse problem. Constitutive models can be used to depict the material response in a simplified manner. These simplifications allow for a more flexible use of the model but restrict it to a certain range of applications. Thus, it is beneficial to take the material’s microscopic structure into account and couple its behavior to the macroscopical response. As multiscale methods (e.g. FE2 , FE-FFT) are computationally expensive, semi-analytical homogenization procedures are investigated to account for the transition between different length scales. There are various well known homogenization techniques discussed in literature such as e.g. the Voigt and Reuss bounds, the self-consistent method as well as the Mori-Tanaka method. In our presentation, the focus lies on a Hashin-Shtrikman type formulation in similarity with the one proposed by Wulfinghoff et al. (2018). This homogenization technique will then be applied to a heterogeneous elastoplastic material under mechanical and thermal loading. After presenting the homogenized material model, we will proof its applicability by various numerical calculations.


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