A micromechanical approach to numerical modeling of yielding of open-cell porous structures under compressive loads
Today, interconnected open-cell porous structures made of titanium and its alloys are replacing the prevalent solid metals used in bone substitute implants. The advent of additive manufacturing techniques has enabled manufacturing of open-cell structures with arbitrary micro-structural geometry. In this paper, rhombic dodecahedron structures manufactured using SLM technique and tested by Amin Yavari et al. (2014) are investigated numerically using ANSYS and LS-DYNA finite element codes for the modeling of the elastic and postyielding behavior of the lattice structure, respectively. Implementing a micro-mechanical approach to the numerical modeling of the yielding behavior of open-cell porous materials is the main contribution of this work.One of the advantages of micro-mechanical modeling of an open-cell structure is that, in contrast to the macro-mechanical finite element modeling, it is not necessary to obtain several material constants for different foam material models through heavy experimental tests. The results of the study showed that considering the irregularity in defining the cross-sections of the struts decreases both the yielding stress and densification strain of the numerical structure to the values obtained from the experimental tests. Moreover, the stress-strain curve of the irregular structure was much smoother in two points of yielding and densification, which is also observable in experimental plots. Considering the irregularity in the structure also decreased the elastic modulus of the lattice structure by about 20-30%. The post-densification modulus was more influenced by irregularity as it was decreased by more than 50%. In summary, it was demonstrated that using beam elements with variable cross-sections for constructing open-cell biomaterials could result in numerical results sufficiently close to the experimental data.
Keywords: rhombic dodecahedron, additive manufacturing, micro-structure, porous biomaterials, implant, finite element