|dc.description.abstract||Topology optimization is a demonstrated tool for the design of components with enhanced mechanical properties. Despite tremendous advances in topology optimization methods over the past 25 years, however, the vast majority of topology optimization work assumes linear elastic governing mechanics. This dissertation proposes algorithms for designing components and cellular materials with optimized properties governed by nonlinear mechanics.
Optimizing for properties in the nonlinear regime poses several challenges, both fundamental and practical. The general ill-posedness of maximum stiffness formulations leads to numerical instabilities of solution mesh dependence, well-known for problems governed by linear mechanics and persisting for problems governed by nonlinear mechanics. Other instabilities are associated with modeling low density elements and include stress singularities and excessive element distortion. Computational expense must also be addressed, as the large dimensionality of topology optimization problems coupled with iterative nonlinear finite element analysis becomes computationally prohibitive. These issues are circumvented herein using projection-based topology optimization methods that enable separation of the analysis and design spaces and subsequent manipulation of the spaces to achieve stability and efficiency as needed. While similar approaches proposed in literature have shown significant sensitivity to user-defined optimization parameters, the nature of the nonlinear projection is shown to provide more robust and stable performance in the context of nonlinear mechanics.
The proposed algorithms are then used to design periodic cellular materials with optimized nonlinear response properties, including maximized energy absorption considering geometric and material nonlinearities. Effective elastic properties and symmetry of the bulk material are estimated using elastic homogenization under the assumption of infinite periodicity. Nonlinear properties are estimated using finite periodicity. This leads to a unit cell topology optimization problem with analysis conducted over two different domains. The target material system is a Bulk Metallic Glass cellular material whose constituent properties are approximated with an elastoplastic material model. Several new topologies are presented that are shown to offer improved nonlinear performance when compared to topologies optimized for elastic properties and traditional honeycomb patterns.||en_US