Date of Award


Document Type


Degree Name

Master of Science (MS)

Legacy Department

Mechanical Engineering

Committee Member

Dr. Gang Li, Committee Chair

Committee Member

Dr. Georges Fadel

Committee Member

Dr. Lonny Thompson


A Unit Cell Synthesis Method was developed recently for designing meta-materials from unit cell level to achieve prescribed nonlinear deformation response. The method starts with a process of selecting and combining a set of elemental functional geometries (EFG) and elemental structural geometries (ESG) to form the unit cell structure. A subsequent size optimization is performed to obtain an optimal design which provides the targeted nonlinear deformation behavior. While the method is proven effective in producing feasible meta-material designs, the design and optimization of the unit cells relies heavily on nonlinear finite element analysis, which makes the overall process computationally intensive and time consuming. In this work, a semi-analytical approach is developed for predicting the large deformation response of EFGs and their combinations. In this approach, non-dimensional load and deformation parameters are proposed for the EFGs including cantilever, fixed-fixed and circular beams. The deformation parameters are then expressed as nonlinear analytical functions of the load parameters. The load parameters are generalized for each geometry to unify the analytical functions for different dimensions of the geometry. The obtained analytical functions of the EFGs’ deformation behavior are then implemented in the Unit Cell Synthesis Method for meta-material unit cell design. The semi-analytical Unit Cell Synthesis Method is applied in the design of a linear elastic material based meta-material that mimics the nonlinear deformation behavior of a rubber pad under compression. The results show that the analytical deformation functions of the EFGs enable a much more efficient design process of the meta-material.



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.