The variational modeling of hierarchical structured deformations
Abstract
Hierarchical (first-order) structured deformations are studied from the variational point of view. The main contributions of the present research are the first steps, at the theoretical level, to establish a variational framework to minimize mechanically relevant energies defined on hierarchical structured deformations. Two results are obtained here: (i) an approximation theorem and (ii) the assignment of an energy to a hierarchical structured deformation by means of an iterative procedure. This has the effect of validating the proposal made in [Deseri & Owen: Elasticity with hierarchical disarrangements: a field theory that admits slips and separations at multiple submacroscopic levels. J.~Elast., 135 (2019), 149--182] to study deformations admitting slips and separations at multiple submacroscopic levels. An explicit example is provided to illustrate the behavior of the proposed iterative procedure and relevant directions for future research are highlighted.
Cite
@article{arxiv.2208.11785,
title = {The variational modeling of hierarchical structured deformations},
author = {Ana Cristina Barroso and José Matias and Marco Morandotti and David R. Owen and Elvira Zappale},
journal= {arXiv preprint arXiv:2208.11785},
year = {2022}
}
Comments
In memory of Jerry Ericksen, whose broad and deep scientific contributions and leadership never cease to evoke admiration and to provide inspiration