@article {21100, title = {Second-order cone interior-point method for quasistatic and moderate dynamic cohesive fracture}, journal = {Comput. Meth. Appl. Mech. Engr.}, volume = {358}, year = {2020}, note = {Arxiv version: https://arxiv.org/abs/1909.10641}, pages = {112633}, abstract = {

Second-order cone interior-point method for quasistatic and moderate dynamic cohesive fracture by S. Vavasis, K. Papoulia, 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} }