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

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. (c) 2016 Wiley Periodicals, Inc. J Biomed Mater Res Part A: 104A: 3164-3174, 2016.