Date on Master's Thesis/Doctoral Dissertation


Document Type

Doctoral Dissertation

Degree Name

Ph. D.


Industrial Engineering

Degree Program

Industrial Engineering, PhD

Committee Chair

Yang, Li

Committee Member

Chou, Kevin

Committee Member

Berfield, Thomas

Committee Member

Starr, Thomas

Committee Member

Gerber, Erin

Author's Keywords

additive manufacturing; cellular structure; size effect; material imperfection; mechanical property; failure response


Cellular structures are networks of interconnected struts or walls with porosities and are widely found in many natural load-bearing structures such as plants and bones. Cellular structures offer unique functional characteristics such as high stiffness to weight ratio, tailorable heat transfer coefficient, and enhanced mechanical energy absorption, which makes them highly attractive in various engineering disciplines such as biomedical implants, electrodes, heat exchangers, and lightweight structures. There exists an abundance of literatures that have investigated various mechanical properties of various cellular structures such as Poisson’s ratio, elastic modulus, ultimate strength, yield strength, and failure characteristics. Based on the classic cellular structure model, these mechanical properties are highly dependent on both the relative density and the topologies of the unit cell designs. Cellular structures with higher relative densities generally exhibit higher overall mechanical properties. In addition, there also exist multiple general design rules for cellular unit cell topology designs, such as nodal connectivity-based deformation mechanism and re-entrant auxetic mechanism. However, currently most theoretical knowledge for cellular structures are established based on infinite pattern sizes, i.e. infinite numbers of unit cells along all principal symmetry directions. On the other hand, for the cellular structures with finite sizes that are commonly designed in real-world applications, in addition to relative density and cell topology, the cellular pattern size effects, which are introduced by the non-ideal boundary conditions, also plays important roles in determining the overall mechanical characteristics of the cellular structure. As a result, many equations and conclusions from the classic Ashby and Gibson models cannot be directly applied to these finite-size cellular structures, which significantly limits the designability of cellular structures for various dimension-limited applications. Besides, due to the complex geometry of cellular structures, additive manufacturing (AM) processes have been considered as the only practically viable option for their fabrication, which introduce various manufacturing-related design variables with material properties such as material anisotropy and material imperfection. In order to adequately design for cellular structures realized by AM processes, a modeling approach that enables comprehensive analysis of all these factors are desirable. In this work, an analytical model framework was established for the analysis of mechanical characteristics of the finite-size cellular structure with imperfect local material properties. The model was verified by the experimental results for both mechanical properties and cellular fracture failure propagation patterns with samples fabricated via powder bed fusion (PBF) process. The results showed that the models could not only provide good predictions to both average mechanical properties and their variabilities, but also adequately capture the effects of the finite pattern size effects and local material heterogeneity effects. Based on the established model, the topology-material-mechanical properties of the finite-size AM cellular structures were investigated in detail. More specifically, the effects of pattern size-topology, material anisotropy and the material imperfections were studied systematically. Various new insights were obtained, including: 1. Based on the modeling analysis, the effects of size and topology on the tensile failure behavior of multiple representative cellular structures (2D auxetic, 2D diamond, 2D triangular1 and 2D triangular2) under various geometry design conditions (including cell topology, cell size and number of unit cells) were systematically investigated. It was found that the 2D bending-dominated structures with lower nodal connectivity (number of struts that meet in joints) (2D auxetic and 2D diamond) exhibited a relatively progressive crack propagation pattern, while the 2D stretching-dominated structures with higher nodal connectivity (2D triangular1 and 2D triangular2) appear to exhibit rather catastrophic brittle fracture failure. During the failure fracture propagation, the energy absorption of the 2D stretching-dominated structures were significantly higher than that of the 2D bending-dominated structures. Moreover, for all cellular designs, the tensile failure behaviors tend to converge to more consistent patterns when the cellular structure pattern sizes increase beyond certain thresholds that are dependent on the cellular topology designs. 2. The material anisotropy effects, which are characteristic to AM processes, were explored through both analytical modeling analysis and experiments on three representative 3D cellular structures (auxetic, BCC and octahedral). The established models were verified via experimentation with samples fabricated by electron beam PBF (EB-PBF) process using Ti6Al4V as material, using the material anisotropy information established experimentally using single struts with different build orientations (0°, 15°, 30°, 45°, 60°, 75° and 90°). The predicted mechanical properties of the Ti6Al4V cellular structures showed good agreement with experimental results. It was shown that both the strength and elastic modulus anisotropy of the materials affect the strength of the cellular structures, which must be determined based on the topology design. In addition, the material anisotropy-topology effects on cellular structures of varying cellular pattern sizes were also investigated in order to quantify the pattern size effects. It was also found that the pattern size effects and the material anisotropy effects can be decoupled during the design of the mechanical properties of these cellular structures. 3. The local material property fluctuation caused by the material imperfection is another important factor to consider for adequate design of AM cellular structures. The local material and feature imperfections affect the overall structural properties of cellular structures and are typically unavoidable with the current AM process technologies. Three representative 2D cellular designs including auxetic, diamond and triangular structures were modeled and analyzed based on the established model, which allows for the implementation of heterogeneous material imperfection at full-scale cellular structure level. The material property imperfection was represented by 3 levels of variabilities (2%, 5% and 10%) for both elastic modulus and strength, defined at local cellular element level. Experimental verification using Ti6Al4V cellular structures fabricated via laser PBF (L-PBF) process demonstrated the potential of the established model in providing accurate predictions to the mechanical property variability of the cellular structures. In addition, the results also revealed new insights into the topology-material imperfection coupling relationships for the cellular structures.