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Homogenization driven design of lightweight structures for additive manufacturing

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Abstract

The diffusion of design tools suitable for regular lattice structures was recently stimulated by the spread of additive manufacturing technologies that enable the fabrication of complex geometries, exceeding the limits of traditional manufacturing methods. Fillet radii play a fundamental role in the design of lattice materials, reducing the stress concentration and improving fatigue life. However, only simplified beam and 2D models are available in the literature, which are unable to capture the actual stiffness and stress concentrations in the cell nodes of the 3-D beam based lattice structures with fillets. In this paper, four types of polyamide 12 cells, fabricated by selective laser sintering technology, based on cylindrical elements, are studied by finite element (FE) analysis, evaluating the influence of struts and fillet radii on the mechanical properties. In order to study a single cell, specific boundary conditions, simulating the presence of adjacent cells, were adopted in FE analysis. As a result, a model describing mechanical properties as a function of geometrical characteristics is obtained. By this model, it is possible to replace the complex shape of a lattice structure with its boundary, simplifying numerical analyses. This approach, called homogenization, is very useful in the design process of lightweight structures and can be adopted in optimization strategies. Numerical outcomes show that the effect of fillet radius is not negligible, especially in cells having a large number of struts. Moreover, experimental tests were also carried out showing a good agreement with the numerical analysis. Finally, an interactive design process for lattice structures based on experimental and numerical outcomes is proposed.

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Abbreviations

E :

Young modulus

G :

Shear modulus

ν :

Poisson’s ratio

R :

Beam radius

r :

Fillet radius

L :

Cell dimension

∆ :

Displacement

σ :

Tensile stress

ε :

Tensile strain

τ :

Shear stress

γ :

Shear strain

F :

Force

ρ :

Relative density or volume fraction

V :

Actual cell volume

V 0 :

Volume occupied by the cell

E 0, G 0, ν 0, σ 0 :

Mechanical properties of the bulk material

E ef, G ef, ν ef, σ ef, τ ef :

Effective mechanical properties of the virtual material of a cell

R 2 :

Coefficient of determination

BCC :

Body-centered cubic

BCCZ :

Body-centered cubic with vertical pillars

SC :

Simple cubic

RBCC :

Reinforced body-centered cubic

GA :

Modified Gibson–Ashby

OT :

Octet-truss

FE :

Finite element

AM :

Additive manufacturing

PA 12 :

Polyamide 12

SLM :

Selective laser melting

SLS :

Selective laser sintering

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Acknowledgements

The authors gratefully acknowledge generous in-kind support from 3Dfast Srl and Andrea Sandi for fabricating test parts and Mario Saraceni of Enginlab Srl for the tensile test machine. This work was partially supported by the Grants “FSE 2105-116-2216-2016” by Regione Veneto and “BIRD175287/17” by Department of Civil, Environmental and Architectural Engineering ICEA—University of Padua.

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Authors and Affiliations

  1. Laboratory of Design Tools and Methods in Industrial Engineering, Department of Civil, Environmental and Architectural Engineering, University of Padua, Via Venezia, 1, 35131, Padua, Italy

    Gianpaolo Savio, Andrea Curtarello, Stefano Rosso & Gianmaria Concheri

  2. Laboratory of Design Tools and Methods in Industrial Engineering, Department of Management and Engineering, University of Padua, Stradella S. Nicola, 3, 36100, Vicenza, Italy

    Roberto Meneghello

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  1. Gianpaolo Savio
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Correspondence to Gianpaolo Savio.

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Savio, G., Curtarello, A., Rosso, S. et al. Homogenization driven design of lightweight structures for additive manufacturing. Int J Interact Des Manuf 13, 263–276 (2019). https://doi.org/10.1007/s12008-019-00543-0

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