Tailoring of Microstructural Nonlinear Constitutive Laws

Brianna MacNider, University of California, San Diego

Photo of Brianna MacNider

Nonlinearities have been used to realize novel phenomenon and enhanced performance in materials systems, including wave effects1, locomotion2, topologically protected edge modes3, and impact mitigation and energy trapping4,5. However, there is currently no consistent methodology to physically realize a desired type of nonlinearity, leaving treatment of such systems scattered and opportunistic. Most nonlinear systems are analyzed analytically, contain active components with control input, or begin from a premise of a known nonlinear response to study. If a specific interesting or functionally ideal nonlinearity is identified that does not correspond to a known nonlinear mechanism, there exist few approaches to design and incorporate it into an experimental system.

Topology optimization has been used in the past to design microstructures for specific desired effective material properties using geometric nonlinearities6. It has even been used to tailor single force-displacement pairs in the pursuit of snap-through or bi-stability7. However, there exists no method to tailor a continuum geometry’s entire force-displacement curve for a desired nonlinearity. We present a level set topology optimization approach that can tailor unit cell constitutive laws for desired nonlinearities. By combining initial geometries designed using mechanical insights into geometric nonlinearity with topology optimization, microstructures are successfully optimized for a range of target nonlinear curves. This approach enables promising future work in designing systems capable of any nonlinear behavior tailored for the desired functionality, through incorporation into mass-spring chains or lattices of unit cells.


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Abstract Author(s): Brianna MacNider, H. Alicia Kim, Nicholas Boechler