00762nas a2200121   4500008004100000245009200041210006900133520032400202100002100526700002600547700001900573856004800592       2018                        en  d00aExistence for elastodynamic Griffith fracture with a weak maximal dissipation condition0 aExistence for elastodynamic Griffith fracture with a weak maxima3 aWe 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.1 aDal Maso, Gianni1 aLarsen, Cristopher J.1 aToader, Rodica  uhttp://preprints.sissa.it/handle/1963/3530801267nas a2200121   4500008004100000245009800041210006900139520082000208100002101028700002601049700001901075856005101094       2015                        en  d00aExistence for constrained dynamic Griffith fracture with a weak maximal dissipation condition0 aExistence for constrained dynamic Griffith fracture with a weak 3 aThere 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.1 aDal Maso, Gianni1 aLarsen, Cristopher J.1 aToader, Rodica  uhttp://urania.sissa.it/xmlui/handle/1963/3504501004nas a2200133   4500008004100000245007400041210006900115260003400184520055100218653001800769100002100787700002600808856003600834       2011                        en  d00aExistence for wave equations on domains with arbitrary growing cracks0 aExistence for wave equations on domains with arbitrary growing c  bEuropean Mathematical Society3 aIn 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.10aWave equation1 aDal Maso, Gianni1 aLarsen, Cristopher J.  uhttp://hdl.handle.net/1963/4284