Direct \(\mathrm{FE}^2\) for concurrent multilevel modeling of heterogeneous thin plate structures. (English) Zbl 1507.74522
Summary: The \(\mathrm{FE}^2\) method systematically translates macro kinematic constraints to the underlying (micro) RVEs and extracts the effective RVE responses to macro continuum in an energetically consistent manner. In the literature, many researchers have demonstrated the predictive capability of \(\mathrm{FE}^2\) across a wide range of problems. The conventional \(\mathrm{FE}^2\) numerical framework adopts a staggered solution strategy between the macro and micro analyses. This limits the adoption of \(\mathrm{FE}^2\) method by inexperienced researchers/engineers to solve practical engineering problems using commercial FE software. To this end, a Direct \(\mathrm{FE}^2\) method has been proposed in [V. B. C. Tan et al., Comput. Methods Appl. Mech. Eng. 360, Article ID 112694, 19 p. (2020; Zbl 1441.74276)] and implemented in the commercial software ABAQUS, where macro kinematic constraints are applied directly on the RVEs superimposed on the macro elements. This results in a monolithic numerical framework, without the need to write any subroutines. Compared to the conventional \(\mathrm{FE}^2\) implementation using commercial software, the number of floating-point operations is also reduced because the nested FE calculations are condensed into one in Direct \(\mathrm{FE}^2\) [K. Raju, T.-E. Tay and V. B. C. Tan, “A review of the \(\mathrm{FE}^2\) method for composites”, Multiscale and Multidiscip. Model. Exp. and Des. 4, 1–24 (2021; doi:10.1007/s41939-020-00087-x)]. In this contribution focusing on thin plate structures, the Direct \(\mathrm{FE}^2\) method is extended based on Kirchhoff-Love thin plate kinematics and implemented in ABAQUS without the need for subroutines. The performance of the Direct \(\mathrm{FE}^2\) method for this higher order formulation is demonstrated by comparing against reference solutions from direct numerical simulations. Sample files can be downloaded from https://github.com/leonghien/Direct-FE2-thin-plates.git.
Keywords:
direct \(\mathrm{FE}^2\) method; computational homogenization; thin plate structures; reinforced concrete slabsCitations:
Zbl 1441.74276References:
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