Some recent results on the convergence of damage to fracture

Conti, Sergio; Focardi, Matteo; Iurlano, Flaviana

doi:10.4171/rlm/722

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2017

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“…In this paper, we contribute to this topic by studying three different problems. Some of these results have been announced in [22].…”

Section: Introductionmentioning

confidence: 95%

Which special functions of bounded deformation have bounded variation?

Conti¹,

Focardi²,

Iurlano³

2017

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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Abstract. Functions of bounded deformation (BD) arise naturally in the study of fracture and damage in a geometrically linear context. They are related to functions of bounded variation (BV ), but are less well understood. We discuss here the relation to BV under additional regularity assumptions, which may require the regular part of the strain to have higher integrability or the jump set to have finite area or the Cantor part to vanish. On the positive side, we prove that BD functions which are piecewise affine on a Caccioppoli partition are in GSBV , and we prove that SBD p functions are approximately continuous H n−1 -a.e. away from the jump set. On the negative side, we construct a function which is BD but not in BV and has distributional strain consisting only of a jump part, and one which has a distributional strain consisting of only a Cantor part.

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“…In this paper, we contribute to this topic by studying three different problems. Some of these results have been announced in [22].…”

Section: Introductionmentioning

confidence: 95%