Determining Brittle Fracture Paths with Strain Splitting Using Shape Optimization Algorithms
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Fracture propagation phenomena can frequently be modelled by a minimization of energy of the system. The minimization of this energy can be achieved in different manners, where each has its own advantages and drawbacks. In this presentation, we interpret the fracture as a shape, where the shape represents a part of the boundary of the system, and apply shape optimization algorithms to minimize the stored energy in the system. We consider brittle material and rely on Griffith's criterion to describe resistance to fracture. The shape optimization algorithm chosen here relies on mathematical concepts that incorporate structure on the space of shapes, the so-called shape space, and therefore provides a mathematical framework for the optimization. Numerical simulations for two-dimensional tension and shear tests with strain splitting to omit unphysical fracture paths will be performed and discussed.
