Analytical relationships for prediction of the mechanical properties of additively manufactured porous biomaterials

Abstract

Recent developments in additive manufacturing techniques have motivated an increasing number of researchers to study regular porous biomaterials that are based on repeating unit cells. The physical and mechanical properties of such porous biomaterials have therefore received increasing attention during recent years. One of the areas that have revived is analytical study of the mechanical behavior of regular porous biomaterials with the aim of deriving analytical relationships that could predict the relative density and mechanical properties of porous biomaterials, given the design and dimensions of their repeating unit cells. In this article, we review the analytical relationships that have been presented in the literature for predicting the relative density, elastic modulus, Poisson's ratio, yield stress, and buckling limit of regular porous structures based on various types of unit cells. The reviewed analytical relationships are used to compare the mechanical properties of porous biomaterials based on different types of unit cells. The major areas where the analytical relationships have improved during the recent years are discussed and suggestions are made for future research directions. © 2016 Wiley Periodicals, Inc. J Biomed Mater Res Part A: 104A: 3164–3174, 2016.

Design and Structure–Function Characterization of 3D Printed Synthetic Porous Biomaterials for Tissue Engineering

“…Of the subset of literature that does seek to address structure–function relationships, very few are systematic or definitive enough to develop strong and useful relationships. This fact was also noted by Zadpoor . Given this, the following review will first give a general background on printing methods and materials used in tissue engineering.…”

“…For biomedical applications, corrosion resistance is an important consideration in selecting material, in addition to strength and fatigue resistance. Currently, the most widely used metallic material for 3D printing for biomedical applications is titanium alloy (Ti‐6Al‐4V), due to its high strength and corrosion resistance . There is also a smaller set of studies using 3D printing methods for fabrication of scaffolds made of cobalt–chromium (CoCr), tantalum (Ta), and nitinol (NiTi).…”

“…The present review will focus solely on 3D printed materials, as this groundbreaking technology permits the creation of architectures vastly different from prior methods, and is subject to many unique limitations of its own. Some prior reviews have pointed out the need for good structure–function understanding, and some have even touched on related portions of the existing literature. [6,7b,8] However, this review will provide a broader summary of the existing literature in which the mechanical or biological performance of a 3D printed porous scaffold was examined as a function of its architecture.…”

The Static and Fatigue Behavior of AlSiMg Alloy Plain, Notched, and Diamond Lattice Specimens Fabricated by Laser Powder Bed Fusion

“…For the mechanical properties, analytical models exist, allowing the prediction of the elastic moduli, yield, and ultimate stresses of regular lattice structures as functions of the cell type, porosity, and properties of the base material [1,12,13]. Usual assumptions consider lattice structure struts as bars transmitting normal efforts (stretching dominated behavior) or beams transmitting bending moments (bending dominated behavior) [13][14][15]. The more three-dimensional the stress state becomes, as it occurs with relatively dense lattices, the more complicated the numerical methods applied for their modeling must be [16,17].…”

Mechanobiological Approach to Design and Optimize Bone Tissue Scaffolds 3D Printed with Fused Deposition Modeling: A Feasibility Study

“…The regular scaffolds include unit cell configurations all with the same shape and dimensions that are regularly replicated in the scaffold volume [1,2]. Analytical solutions were recently developed that put in relationship the equivalent material properties of the entire scaffold with the dimensions and the material properties of the single unit cell [3][4][5][6]. The irregular ones include pores differently shaped and dimensioned and present a geometry that can be described with statistical parameters [7][8][9] but not in a precise form [10].…”