@article {2020, title = {On the blow-up of GSBV functions under suitable geometric properties of the jump set}, journal = {Advances in Calculus of Variations}, year = {2020}, month = {2020}, url = {https://doi.org/10.1515/acv-2019-0068}, author = {Emanuele Tasso} } @article {2020, title = {On the continuity of the trace operator in GSBV (Ω) and GSBD (Ω)}, journal = {ESAIM: COCV}, volume = {26}, year = {2020}, month = {2020///}, url = {https://doi.org/10.1051/cocv/2019014}, author = {Emanuele Tasso} } @article {2020, title = {Energy-dissipation balance of a smooth moving crack}, volume = {483}, year = {2020}, month = {2020/03/15/}, pages = {123656}, abstract = {

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 [10] valid for straight fractures.

}, keywords = {Energy-dissipation balance, Fracture dynamics, Wave equation in time-dependent domains}, isbn = {0022-247X}, url = {https://www.sciencedirect.com/science/article/pii/S0022247X19309242}, author = {Maicol Caponi and Ilaria Lucardesi and Emanuele Tasso} } @article {2020, title = {Weak formulation of elastodynamics in domains with growing cracks}, volume = {199}, year = {2020}, month = {2020/08/01}, pages = {1571 - 1595}, abstract = {

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{\textendash}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{\textquoteright}s inequality. We prove existence of a solution for both the damped and undamped systems, while in the damped case we are also able to prove uniqueness and an energy balance.

}, isbn = {1618-1891}, url = {https://doi.org/10.1007/s10231-019-00932-y}, author = {Emanuele Tasso} }