Date of Completion


Embargo Period



Dr. Mei Wei, Dr. Horea Ilies

Field of Study

Mechanical Engineering


Master of Science

Open Access

Open Access


Bone scaffold porosity and stiffness play a critical role in the success of critical-size bone defect rehabilitation. In this work, we present a computational procedure to design ceramic bone scaffolds to provide adequate mechanical support and foster bone healing. The scaffolds considered in our study consist of a lattice of curved rods fabricated via direct ink writing. We develop cellular solids models of the scaffold's effective elastic constants as functions of its geometric parameters, up to some unknown coefficients. To determine numeric values for these coefficients, we execute a computational design of experiments whereby effective elastic properties are obtained using numerical homogenization with the finite element method. In order to automate these experiments and circumvent re-meshing for every scaffold geometry, we project a representative volume element of the scaffold onto a fixed uniform mesh and assign an ersatz material for the analysis. Then, through a nonlinear least-squares regression, we fit the cellular solids models to the data set generated in this manner. Once calibrated, we use these models in conjunction with efficient gradient-based optimization methods to design patient-specific scaffolds (i.e., shape, location, and loading) by varying geometric parameters that can be controlled in the fabrication, namely the separation between rods in the lattice, and the orientation of the tangent vector to the rod axis. The optimization procedure renders element-wise values of rod separation and tangent vector orientation. As this representation is not amenable to fabrication, lastly, we generate the final scaffold geometry by posing a differential equation whose solution is a function such that its level set lines at specified values correspond to the directrices of the rods in the scaffold. We explore two problem formulations: maximization of stiffness of a mandible implant with a constraint on porosity, and maximization of porosity with a stiffness constraint equivalent to the stiffness of the bone native to the defect site.

Major Advisor

Dr. Julian Norato