2022/08/24 by Ana Cristina Barroso, Barroso, Ana Cristina, José Matías +7
Engineering · Materials Science · #74A60 (49J45 #74M99) #Composite Material Mechanics #Composite Structure Analysis and Optimization #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlocal and gradient elasticity in micro/nano structures #Optimization and Control (math.OC)
paper · pdf · doi:10.48550/arxiv.2208.11785
openalex publication_date 2022/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.