Abstract
The work deals on computational design of structural materials by resorting to computational homogenization and topological optimization techniques. The goal is then to minimize the structural (macro-scale) compliance by appropriately designing the material distribution (microstructure) at a lower scale (micro-scale), which, in turn, rules the mechanical properties of the material. The specific features of the proposed approach are: (1) The cost function to be optimized (structural stiffness) is defined at the macro-scale, whereas the design variables defining the micro-structural topology lie on the low scale. Therefore a coupled, two-scale (macro/micro), optimization problem is solved unlike the classical, single-scale, topological optimization problems. (2) To overcome the exorbitant computational cost stemming from the multiplicative character of the aforementioned multiscale approach, a specific strategy, based on the consultation of a discrete material catalog of micro-scale optimized topologies (Computational Vademecum) is used. The Computational Vademecum is computed in an offline process, which is performed only once for every constitutive-material, and it can be subsequently consulted as many times as desired in the online design process. This results into a large diminution of the resulting computational costs, which make affordable the proposed methodology for multiscale computational material design. Some representative examples assess the performance of the considered approach.
Highlights
In the last decades, topological structural optimization has gained considerable importance in the Computational Mechanics field
The work deals on computational design of structural materials by resorting to computational homogenization and topological optimization techniques
The specific features of the proposed approach are: (1) The cost function to be optimized is defined at the macro-scale, whereas the design variables defining the micro-structural topology lie on the low scale
Summary
Topological structural optimization has gained considerable importance in the Computational Mechanics field. The former is based on analytical expansion theories, the latter seems to fit more naturally into the FEM context, specially due to its variational framework They lead to a FE2 problem where standard FEM discretizations of the elastic equations are considered at both the macro and micro-scales. Highly demanding applications require better accuracy of the constitutive modeling To overcome this difficulty, multi-scale techniques, based on homogenization theories, aim at representing heterogeneities of the small length scale lμ by taking mean values of the micro-scale material properties. The second consequence of the Hill-Mandel principle is the equilibrium equation of the RVE σμ : δμ = 0 ∀δμ ∈ Vμ This result points out that the fluctuations do not produce work, i.e. they have zero internal energy.
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