Chapter 4. Computational Design and Modeling of Linear and Nonlinear Elastic Tissue Engineering Scaffold Triply Periodic Minimal Surface (TPMS) Porous Architecture

Abstract

The concept of “functional tissue engineering” proposes that biomaterial scaffolds should be developed with mechanical properties that approximate those of native tissues. This can present a challenge as soft tissues exhibit at a minimum nonlinear elastic properties. The question becomes how to computationally estimate effective properties for scaffolds made from nonlinear materials and whether these nonlinear effective properties can be estimated from linear homogenization analysis. In this chapter, contact analyses are performed for both Triply Minimal Periodic Surface (TPMS) and P Schwartz architecture for 1×1×1 to 5×5×5 repeated unit cells for both linear and nonlinear (Neo-Hookean) base materials. These are compared to linear homogenization analyses for the same scaffold architecture. Results show that nonlinear effective properties show the same trend of decreasing material coefficients as linear effective properties as scaffold porosity increases. Furthermore, linear homogenization resulted bounded both linear and nonlinear multi-cell contact analyses. The results provide an initial insight into the behavior of porous scaffolds made from nonlinear materials as well as suggesting that linear homogenization estimates can be used as initial bounds for nonlinear effective properties of porous scaffolds.