A transformative periodic structure includes a plurality of elastomeric or elasto-plastic periodic solids that experiences a transformation in the structural configuration upon application of a critical macroscopic stress or strain. The transformation alters the geometric pattern changing the spacing and the shape of the features within the transformative periodic structure. For the case of elastomeric periodic structures upon removal of the critical macroscopic stress or strain, the transformative periodic solids are recovered to their original form. For the case of elasto-plastic periodic structures upon removal of the critical macroscopic stress or strain, the new pattern is retained. Polymeric periodic solids can be recovered to their original form by heating or plasticizing.