Abstract
Filigree lattice structures are sensible to geometrical imperfections and the scatter of material parameters which all depend on the stability of the manufacturing process. The aim of this study is to analyze these effects for polymer lattice structures and incorporate them in a finite element model for robust design. Micrographs of lattice structure slices show a smaller diameter for vertical struts. Basic mechanical tests on bulk material exhibit a tension–compression asymmetry which is captured with a Drucker-Prager material model in simulations. Digital image correlation measurements allow to determine true material properties. Plateau stress and failure strain are a result of the biggest flaw in the specimen. Hence, a new model to determine their probability distribution is proposed. This model outperforms standard approaches deriving the probability distribution from the central moments. A spatial correlation of geometric deviations and scatter of the material is investigated with variography subsequently allowing to model the varying properties with random fields. Simulations of dog-bone specimens show that the probability distributions of material properties are captured well. Also simulations of lattice structures are able to represent the probability distributions of their homogenized mechanical properties. The whole stress–strain response and the failure progression agree well with experimental results.
Highlights
Cellular structures have already been explored in the past [1,2,3], the progress in additive manufacturing over the past decade has further enhanced the excitement, as many manufacturing restrictions are abolished
The outcome of the procedure to determine the correlation length by variography is depicted and the stochastic variations stemming from the local probability density function (PDF) model are demonstrated
The probability distribution of the material properties is validated for dog-bone specimens and transferred to structures with lattice material incorporating geometry variations
Summary
Cellular structures have already been explored in the past [1,2,3], the progress in additive manufacturing over the past decade has further enhanced the excitement, as many manufacturing restrictions are abolished. Tailoring unit cells according to the specified requirements by topology optimization takes full advantage of additive manufacturing [6]. Lattice structures consisting of many unit cells can be seen as metamaterials and are attractive to many disciplines such as heat conduction [7,8,9], medical engineering [10,11], chemical reactors [12,13,14] or structural design [15] to mention a few
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