01145nas a2200145   4500008004100000020001400041245007000055210006900125260001500194300001600209490000800225520069900233100002000932856004700952       2020                        eng d  a1618-189100aWeak formulation of elastodynamics in domains with growing cracks0 aWeak formulation of elastodynamics in domains with growing crack  c2020/08/01  a1571 - 15950 v1993 a<p>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.</p>1 aTasso, Emanuele  uhttps://doi.org/10.1007/s10231-019-00932-y