Nonlinear elasticity in 1d periodic structures with disarrangements

Hierarchically organized man-made structures with self-similar and periodic architectures can be designed to exhibit needed overall mechanical behaviors as a result of specific kinematics occurring at one or more scale levels. Also, the response of biomaterials, from the cell to the tissue scale, in terms of growth, remodeling and morphogenesis, can be interpreted as the overall result of interactions and mechanisms concealed at submacroscopic levels. In the perspective of capturing processes and responses in complex materials it is then felt that the Structured Deformations theory could be helpfully exploited to describe biological multiscale dynamics difficult to be caught by means of classical continuum mechanics, as well as to design new composite materials. Driven by this rationale, a first one-dimensional Structured Deformations-based paradigm-exploiting tensile buckling phenomena-is here proposed, in which a whole class of macroscopic behaviors is obtained as the result of a reversible (elastic) kinematics with disarrangements occurring at the submacroscopic level.