Lattice-based metamaterials are materials that have a defined architecture reminiscent of atomic lattices but at a larger length scale. These materials oftentimes display unique capabilities that can be traced back to their micro-architected design. Modern advances in fabrication techniques together with increasingly environmentally conscious design constraints have motivated research in lattice-based mechanical metamaterials, which offer a range of properties unusual to natural materials. To enable their use, it is mandatory to build a fine understanding of how the composition, geometry and overall morphology of the underlying truss govern the mechanical properties desired and targeted on the macroscopic scale (centimeter to meter). This proposal aims to design, model and test lattice metamaterials that are polarized: while featuring the same microstructure everywhere, they still manage to be soft to indentation on one side but hard on the opposite side. While electric polarization is a classical concept of continuum electrodynamics, mechanical polarization in elastostatics and elastodynamics has escaped the scope of earlier theories. The theory developed through this research effort should thus be a new addition to the body of fundamental knowledge in the field of elasticity. The research will also include support of education through recruiting undergraduate in research and graduate students and increasing exposure of engineering students, and the general public, to revolutionary materials with microstructure.

Isostatic lattices exhibit a number of infinitesimal collapse mechanisms, i.e., zero modes, that are sensitive to pre-set geometric distortions, such as twisting in Kagome lattices. In a topological transition, zero modes shift from being evenly distributed across bulk and edges to overpopulate preferential edges. In that case, the isostatic lattice displays a polarized behavior where it appears soft on one side and hard on the opposite side. The main aim of the present project is to understand the microstructural mechanisms by which polarization emerges and fades on a macroscopic scale. Focus is on polarization effects that remain dominant even when the size of the unit cell becomes infinitesimal in comparison to the whole lattice. Research efforts are structured around two goals: (1) to build a kinematically enriched continuum theory of elasticity, called ?microtwist elasticity?, capable of modeling polarization effects as well as the underlying zero modes quantitatively and qualitatively by employing suitably developed asymptotic homogenization methods; (2) to investigate the range of static and dynamic phenomena predicted by the microtwist theory and to systematically validate these predictions by mechanical testing of fabricated samples. The proposed theory should bring a fundamental new understanding of architected materials with microstructures based on isostatic lattices.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

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University of Missouri-Columbia
United States
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