title: Mechanical behavior of regular open-cell porous biomaterials made of diamond lattice unit cells.
abstract: Cellular structures with highly controlled micro-architectures are promising materials for orthopedic applications that require bone-substituting biomaterials or implants. The availability of additive manufacturing techniques has enabled manufacturing of biomaterials made of one or multiple types of unit cells. The diamond lattice unit cell is one of the relatively new types of unit cells that are used in manufacturing of regular porous biomaterials. As opposed to many other types of unit cells, there is currently no analytical solution that could be used for prediction of the mechanical properties of cellular structures made of the diamond lattice unit cells. In this paper, we present new analytical solutions and closed-form relationships for predicting the elastic modulus, Poisson׳s ratio, critical buckling load, and yield (plateau) stress of cellular structures made of the diamond lattice unit cell. The mechanical properties predicted using the analytical solutions are compared with those obtained using finite element models. A number of solid and porous titanium (Ti6Al4V) specimens were manufactured using selective laser melting. A series of experiments were then performed to determine the mechanical properties of the matrix material and cellular structures. The experimentally measured mechanical properties were compared with those obtained using analytical solutions and finite element (FE) models. It has been shown that, for small apparent density values, the mechanical properties obtained using analytical and numerical solutions are in agreement with each other and with experimental observations. The properties estimated using an analytical solution based on the Euler-Bernoulli theory markedly deviated from experimental results for large apparent density values. The mechanical properties estimated using FE models and another analytical solution based on the Timoshenko beam theory better matched the experimental observations.
authors.affiliation: Faculty of Mechanical, Maritime, and Materials Engineering, Delft University of Technology (TU Delft), Mekelweg 2, Delft 2628 CD, The Netherlands. Electronic address: s.m.ahmadi@tudelft.nl.
authors.forename: S M
authors.initials: SM
authors.lastname: Ahmadi
authors.affiliation: Faculty of Mechanical, Maritime, and Materials Engineering, Delft University of Technology (TU Delft), Mekelweg 2, Delft 2628 CD, The Netherlands.
authors.forename: G
authors.initials: G
authors.lastname: Campoli
authors.affiliation: Faculty of Mechanical, Maritime, and Materials Engineering, Delft University of Technology (TU Delft), Mekelweg 2, Delft 2628 CD, The Netherlands.
authors.forename: S
authors.initials: S
authors.lastname: Amin Yavari
authors.affiliation: Faculty of Mechanical, Maritime, and Materials Engineering, Delft University of Technology (TU Delft), Mekelweg 2, Delft 2628 CD, The Netherlands.
authors.forename: B
authors.initials: B
authors.lastname: Sajadi
authors.affiliation: KU Leuven, Department of Mechanical Engineering, Section Production Engineering, Machine Design and Automation (PMA), Celestijnenlaan 300B, 3001 Leuven, Belgium; LayerWise NV, Kapeldreef 60, 3001 Leuven, Belgium.
authors.forename: R
authors.initials: R
authors.lastname: Wauthle
authors.affiliation: KU Leuven, Department of Metallurgy and Materials Engineering, Kasteelpark Arenberg 44, PB2450, 3001 Leuven, Belgium.
authors.forename: J
authors.initials: J
authors.lastname: Schrooten
authors.affiliation: Faculty of Mechanical, Maritime, and Materials Engineering, Delft University of Technology (TU Delft), Mekelweg 2, Delft 2628 CD, The Netherlands; Department of Orthopedics and Department of Rheumatology, University Medical Center Utrecht, Heidelberglaan100, 3584CX Utrecht, The Netherlands.
authors.forename: H
authors.initials: H
authors.lastname: Weinans
authors.affiliation: Faculty of Mechanical, Maritime, and Materials Engineering, Delft University of Technology (TU Delft), Mekelweg 2, Delft 2628 CD, The Netherlands.
authors.forename: A A
authors.initials: AA
authors.lastname: Zadpoor
mesh_terms: D000497:Alloys; D001672:Biocompatible Materials / Q000737:chemistry*; D020342:Finite Element Analysis; D055595:Mechanical Phenomena; D008958:Models, Molecular; D008968:Molecular Conformation; D016062:Porosity; D014025:Titanium / Q000737:chemistry*
chemical_list: D000497:Alloys; D001672:Biocompatible Materials; C031462:titanium alloy (TiAl6V4); D014025:Titanium
keywords: Additive manufacturing; Analytical solution; Cellular solids; Diamond cubic; Finite element; Mechanical properties; Porous biomaterials; Selective laser melting