TY - RPRT T1 - Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition Y1 - 2015 A1 - Gianni Dal Maso A1 - Cristopher J. Larsen A1 - Rodica Toader AB - There are very few existence results for fracture evolution, outside of globally minimizing quasi-static evolutions. Dynamic evolutions are particularly problematic, due to the difficulty of showing energy balance, as well as of showing that solutions obey a maximal dissipation condition, or some similar condition that prevents stationary cracks from always being solutions. Here we introduce a new weak maximal dissipation condition and show that it is compatible with cracks constrained to grow smoothly on a smooth curve. In particular, we show existence of dynamic fracture evolutions satisfying this maximal dissipation condition, subject to the above smoothness constraints, and exhibit explicit examples to show that this maximal dissipation principle can indeed rule out stationary cracks as solutions. UR - http://urania.sissa.it/xmlui/handle/1963/35045 U1 - 35277 U2 - Mathematics U4 - 1 U5 - MAT/05 ER -