Abstract
Introduction
Integrating additively manufactured structures, such as porous lattices into implants has numerous potential benefits, such as custom mechanical properties, porosity for osseointegration/fluid flow as well as improved fixation features.
Component anisotropic stiffness can be controlled through varying density and lattice orientation. This is useful due to the influence of load on bone remodelling. Matching implant and bone anisotropy/stiffness may help reduce problems such as stress shielding and prevent implant loosening. It is therefore beneficial to be able to design AM parts with a desired anisotropic stiffness.
In this study we present a method that predicts the anisotropic stiffness of an additively manufactured lattice structure from its CAD data, and validate this model with experimental testing. The model predicts anisotropic stiffness in terms of density (ρ), fabric (M) and fabric eigen values (m) and is matched to stiffness data of the structure in 3 principal directions, based on an orthotropic assumption. This model was described in terms of 10 constants and had the form shown in Equation 1.
Methods
A stochastic line structure was formed in CAD by joining pseudo-random points generated using the Poisson-disk method Lines at an angle lower than 30° to the x-y plane removed to allow for AM manufacturing. Lines were converted to struts with 330 µm diameter.
Second order fabric tensors were determined from CAD files of the AM specimens using the mean intercept length (MIL), the gold standard for determining a measure of the ‘average orientation’ of material within trabecular bone structures.
10 × 10 × 12 mm specimens of the CAD model were manufactured on a Renishaw AM250 powder bed fusion machine. The structure was built in 10 different orientations to enable stiffness measurement in 10 different directions (n=5 for each direction). Compression testing in a servohydraulic materials testing machine was performed according to ISO13314 with LVDTs used to measure displacement to remove compliance effects. Stress-strain curves were obtained and elastic moduli were estimated from a hysteresis loop in the load application, from 70% to 20% of the plateau stress.
Specimen density and fabric data were fit to the observed stiffnesses using least squares linear regression. Experimental stiffnesses of the structure in 10 directions were compared to the model to evaluate the accuracy of model predictions.
Results & Discussion
The model predicted the stiffness of the structure across all 10 orientations to within 13% absolute error compared to the observed stiffness data, with an R2 value of 0.969. The three dimensional stiffness plot formed by the model was similar to the experimental data, displaying an hourglass shape. Our model is the first to predict the anisotropic stiffness of stochastic structures and will be highly useful in predicting stiffness of lattice structures and could also be applied to bone to measure anisotropic stiffness.
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