Design of a meta-material with targeted nonlinear deformation response

The M1 Abrams tank contains track pads consist of a high density rubber. This rubber fails prematurely due to heat buildup caused by the hysteretic nature of elastomers. It is therefore desired to replace this elastomer by a meta-material that has equivalent nonlinear deformation characteristics without this primary failure mode. A meta-material is an artificial material in the form of a periodic structure that exhibits behavior that differs from its constitutive material. After a thorough literature review, topology optimization was found as the only method used to design meta-materials. Further investigation determined topology optimization as an infeasible method to design meta-materials with the targeted nonlinear deformation characteristics. Therefore, a method was developed in this thesis to logically and systematically design meta-material unit cells using engineering principles to achieve the desired nonlinear response. This method, called the Unit Cell Synthesis Method, requires the designer to have a fundamental understanding of the geometric nonlinearity of an elemental geometry. One or more of these elemental geometries are then systematically combined into a unit cell. A size optimization is performed on promising unit cell concepts to tune the geometry and converge its response towards that of the target. Application of this method was successful in generating a meta-material to meet the response of the rubber pad. The method represented in this thesis is meant to serve as a framework for future designers to develop meta-materials for nonlinear targeted responses.