Second-order cone interior-point method for quasistatic and moderate dynamic cohesive fracture by S. Vavasis, , M. R. Hirmand
\ Cohesive fracture is among the few techniques able to
\ model complex fracture nucleation and propagation
\ with a sharp (nonsmeared) representation
\ of the crack.\ Implicit time-stepping schemes are often favored
\ in mechanics due to their ability to take larger time steps in
\ quasistatic and moderate dynamic problems.\ Furthermore,
\ initially rigid cohesive models are typically preferred when
\ the location of the crack is not known in advance, since
\ initially elastic models artificially lower the material stiffness.
\ It is challenging to include an initially rigid
\ cohesive model in an implicit scheme because
\ the initiation of fracture corresponds
\ to a nondifferentiability of the underlying potential.\ In
\ this work, an interior-point method is proposed for implicit time
\ stepping of initially rigid cohesive
\ fracture.\ It uses techniques developed for convex second-order
\ cone programming for the nonconvex problem at hand.\ The underlying cohesive model
\ is taken from Papoulia (2017) and is based on a nondifferentiable
\ energy function.\ That previous work proposed an algorithm based on successive
\ smooth approximations to the nondifferential objective for solving
\ the resulting optimization problem.\ It is argued herein that cone
\ programming can capture the nondifferentiability without smoothing,
\ and the resulting cone formulation is amenable to interior-point
\ algorithms.\ A further benefit of the formulation is that other
\ conic inequality constraints are straightforward to incorporate.
\ Computational results are provided showing that certain contact
\ constraints can be easily handled and that the
\ method is practical.
\
}, url = {https://arxiv.org/abs/1909.10641}, author = {Vavasis, Stephen and Papoulia, Katerina and Hirmand, M. Reza} }