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  5. This work presents a comprehensive methodology for designing meta-materials with desired non-linear elastic behaviors. The approach employs a modified asymptotic expansion based homogenization method for topology optimization with finite deformation. Design and optimization of meta-materials for targeted non-linear elastic response under various loading conditions is explored. 
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  6. Starting from a network of discrete beams, topology optimized structures are produced by simultaneously optimizing each beam’s width and the locations of each node within the network. Due to the sparse nature of a beam network and by utilizing gradient descent results in a drastic reduction in computational cost compared to existing methods. Two different optimization objectives are investigated: minimization of the strain energy occurring from loading, often referred to compliance minimization; and the design of structures with prescribed mechanical responses to an applied load. 
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