TY - RPRT
T1 - On the continuity of the trace operator in GSBV (Ω) and GSBD (Ω)
Y1 - 2018
A1 - Emanuele Tasso
AB - In this paper we present a new result of continuity for the trace operator acting on functions that might jump on a prescribed (n−1)-dimensional set Г, with the only hypothesis of being rectifiable and of finite measure. We also show an application of our result in relation to the variational model of elasticity with cracks, when the associated minimum problems are coupled with Dirichlet and Neumann boundary conditions.
UR - http://preprints.sissa.it/handle/1963/35324
N1 - 27 pages
U1 - 35634
U2 - Mathematics
U4 - 1
ER -
TY - RPRT
T1 - Energy-dissipation balance of a smooth moving crack
Y1 - 2018
A1 - Maicol Caponi
A1 - Ilaria Lucardesi
A1 - Emanuele Tasso
AB - In this paper we provide necessary and sufficient conditions in order to guarantee the energy-dissipation balance of a Mode III crack, growing on a prescribed smooth path. Moreover, we characterize the singularity of the displacement near the crack tip, generalizing the result in [S. Nicaise, A.M. Sandig - J. Math. Anal. Appl., 2007] valid for straight fractures.
UR - http://preprints.sissa.it/handle/1963/35320
U1 - 35630
U2 - Mathematics
U4 - 1
ER -
TY - RPRT
T1 - Weak formulation of elastodynamics in domains with growing cracks
Y1 - 2018
A1 - Emanuele Tasso
AB - In this paper we formulate and study the system of elastodynamics on domains with arbitrary growing cracks. This includes homogeneous Neumann conditions on the crack sets and mixed general Dirichlet-Neumann conditions on the boundary. The only assumptions on the crack sets are to be (n − 1)-rectifiable with finite surface measure, and increasing in the sense of set inclusions. In particular they might be dense, hence the weak formulation must fall outside the usual context of Sobolev spaces and Korn's inequality. We prove existence of a solution both for the damped and undamped systems, while in the damped case we are also able to prove uniqueness and an energy balance.
PB - SISSA
UR - http://preprints.sissa.it/handle/1963/35328
U1 - 35639
U2 - Mathematics
U4 - 1
ER -