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.

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 Vol- 135 (2019) Issue 1-2, 149-180.

Joint project with Ana Cristina Barroso, José Matias, Marco Morandotti & David Owen

MathematicsPhysics

Audience: researchers in the topic

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Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor).

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