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 for both the damped and undamped systems, while in the damped case we are also able to prove uniqueness and an energy balance.

Weak formulation of elastodynamics in domains with growing cracks / Tasso, E.. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 199:4(2020), pp. 1571-1595. [10.1007/s10231-019-00932-y]

Weak formulation of elastodynamics in domains with growing cracks

Tasso E.
2020-01-01

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–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 for both the damped and undamped systems, while in the damped case we are also able to prove uniqueness and an energy balance.
199
4
1571
1595
10.1007/s10231-019-00932-y
Tasso, E.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/125101
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