Accepted Paper

Inserted: 13 may 2025
Last Updated: 3 oct 2025

Journal: Indiana University Mathematics Journal
Year: 2025

Abstract:

The response of many materials to applied forces and boundary constraints depends upon internal geometric changes at multiple submacroscopic levels. Hierarchical structured deformations provide a mathematical setting for the description of such changes and for the variational determination of the corresponding energetic response. The research in this article provides substantial refinements and broadenings of the mathematical setting both for the underlying geometrical structure and for the variational analysis of energetic response. The mathematical tools employed in this research include the global method for relaxation and establish the equivalence of a relaxed energy obtained via relaxation under simultaneous geometrical changes at all levels and a relaxed energy obtained via iterated relaxations proceeding from the deepest submacroscopic level successively to the macroscopic level.

Keywords: Integral representation, energy minimization, Structured deformations, hierarchies, global method for relaxation

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