Browsing by Author "Larsen, Christopher J."
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Item Existence for constrained dynamic Griffith fracture with a weak maximal dissipation condition(2015-11-18) Dal Maso, Gianni; Larsen, Christopher J.; Toader, Rodica; MathematicsThere 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.Item Existence for elastodynamic Griffith fracture with a weak maximal dissipation condition(2018-03) Dal Maso, Gianni; Larsen, Christopher J.; Toader, Rodica; MathematicsWe 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.Item Variational fracture with Neumann boundary conditions(SISSA, 2020) Larsen, Christopher J.; Mathematics