On approximation theorem for structured deformations from BV(Omega)

0443122 - MÚ 2016 RIV IT eng J - Journal Article
Šilhavý, Miroslav
On approximation theorem for structured deformations from BV(Omega).
Mathematics and Mechanics of Complex Systems. Roč. 3, č. 1 (2015), s. 83-100. ISSN 2326-7186
R&D Projects: GA ČR GA201/09/0473
Institutional support: RVO:67985840
Keywords : structured deformation * fracture * approximations
Subject RIV: BA - General Mathematics
http://msp.org/memocs/2015/3-1/p04.xhtml

This note deals with structured deformations introduced by Del Piero and Owen. As treated in the present paper, a structured deformation is a pair .(g,G) where g is a macroscopic deformation giving the position of points of the body and G represents deformations without disarrangements. Here g is a map of bounded variation on the reference region, and G is a Lebesgue-integrable tensorvalued map. For structured deformations of this level of generality, an approximating sequence gk of simple deformations is constructed from the space of maps of special bounded variation on which converges in the strongly to (g,G) and for which the sequence of total variations of gk is bounded. The condition is optimal. Further, in the second part of this note, the limit relation of Del Piero and Owen is established on the above level of generality.
Permanent Link: http://hdl.handle.net/11104/0245878