Homogenization for metamaterial design

Unconventional instability mechanisms in elastic structures are examined, revealing bifurcation and postcritical responses that go well beyond classical compression-induced buckling. These include buckling triggered by tensile dead loads, instability driven by configurational forces, and self-restabilization following loss of stability. Additional nonstandard phenomena arise when dry friction induces flutter and divergence, when nonholonomic constraints generate instability under conservative loading, and when instability emerges from the coupling of structures that are individually stable. Postcritical folding mechanisms and the instability of the Reut column further broaden this framework. These effects can be embedded in metamaterials and, through rigorous homogenization, translated into equivalent continua with exotic mechanical responses. Examples include material-level flutter giving rise to hypo-elastic solids without a strain potential, tensile instabilities associated with closed stability domains, and instability-induced restabilization at the continuum scale.

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