@article{YoonLeeMudd2021,
author={Yoon, Hyun C.
and Lee, Sanghyun
and Mallikarjunaiah, S. M.},
title={Quasi-static anti-plane shear crack propagation in nonlinear strain-limiting elastic solids using phase-field approach},
journal={International Journal of Fracture},
year={2021},
month={Jan},
day={02},
abstract={We study a quasi-static evolution of anti-plane crack with the nonlinear strain-limiting model using the phase-field approach. The nonlinear strain-limiting models, a subclass of the implicit constitutive relations, allow the linearized strain value to remain small even if the stress value tends to infinity. To compute the quasi-static crack, we solve the constrained energy minimization for the nonlinear bulk energy coupled with diffusive crack energy. An iterative staggered scheme (L-scheme) is employed for coupling the nonlinear mechanics and phase-field, and augmented Lagrangian is utilized to accommodate crack irreversibility. Several numerical experiments of the proposed framework substantiate the bounded strain in the neighborhood of the crack-tip for both static and quasi-static cracks. The comparisons of bulk and the crack energies and the discrete crack-tip speed between the LEFM and our model are presented.},
issn={1573-2673},
doi={10.1007/s10704-020-00501-y},
url={https://doi.org/10.1007/s10704-020-00501-y}
}

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