TY - RPRT
T1 - Existence for elastodynamic Griffith fracture with a weak maximal dissipation condition
Y1 - 2018
A1 - Gianni Dal Maso
A1 - Cristopher J. Larsen
A1 - Rodica Toader
AB - We consider a model of elastodynamics with fracture evolution, based on energy-dissipation balance and a maximal dissipation condition. We prove an existence result in the case of planar elasticity with a free crack path, where the maximal dissipation condition is satisfied among suitably regular competitor cracks.
UR - http://preprints.sissa.it/handle/1963/35308
U1 - 35616
U2 - Mathematics
U4 - 1
U5 - MAT/05
ER -
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 -
TY - JOUR
T1 - Existence for wave equations on domains with arbitrary growing cracks
JF - Rend. Lincei Mat. Appl. 22 (2011) 387-408
Y1 - 2011
A1 - Gianni Dal Maso
A1 - Cristopher J. Larsen
KW - Wave equation
AB - In this paper we formulate and study scalar wave equations on domains with arbitrary growing cracks. This includes a zero Neumann condition on the crack sets, and the only assumptions on these sets are that they have bounded surface measure and are growing in the sense of set inclusion. In particular, they may be dense, so the weak formulations must fall outside of the usual weak formulations using Sobolev spaces. We study both damped and undamped equations, showing existence and, for the damped equation, uniqueness and energy conservation.
PB - European Mathematical Society
UR - http://hdl.handle.net/1963/4284
U1 - 4015
U2 - Mathematics
U3 - Functional Analysis and Applications
U4 - -1
ER -