Friday, December 2, 2022 — 11:30 am — aula M2.3, edificio Matematica
Variational formulation for hierarchies of structured deformations
Abstract: The mechanical theory of first order structured deformations formulated in [2] enriches the purely macroscopic field theory of non-linear elasticity by taking into account the effects of disarrangements that occur at a single submacroscopic level. In [1] a variational formulation for this theory has been successfully provided in the context of special fields of bounded variation.
Taking into account that many natural and man-made physical systems have a rich enough geometrical structure to permit the identification of hierarchies consisting of more than one physically meaningful submacroscopic level, the mechanical theory of structured deformations has been enriched in [3]. This talk aims at presenting a variational framework of these latter theoretical settings.
Joint project with Ana Cristina Barroso, José Matias, Marco Morandotti and David Owen.
References:
[1] R. Choksi and I. Fonseca. Bulk and interfacial energy densities for structured deformations of continua. Arch. Rational Mech. Anal. 138 (1997), 37-103.
[2] G. Del Piero and D. R. Owen. Structured deformations of continua. Arch. Ration. Mech. Anal. 124 (1993), 99-155.
[3] L. Deseri and D. R. Owen. Elasticity with Hierarchical Disarrangements: A Field Theory That Admits Slips and Separations at Multiple Submacroscopic Levels. J. of Elasticity 135 (2019) Issue 1-2, 149-180.