Finite element simulation of quasi-static tensile fracture in nonlinear strain-limiting solids with the phase-field approach. Lee, S., Yoon, H. C., & Mallikarjunaiah, S. Journal of Computational and Applied Mathematics, 399:113715, 2022. ![Finite element simulation of quasi-static tensile fracture in nonlinear strain-limiting solids with the phase-field approach [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper doi abstract bibtex We investigate a quasi-static tensile fracture in nonlinear strain-limiting solids by coupling with the phase-field approach. A classical model for the growth of fractures in an elastic material is formulated in the framework of linear elasticity for deformation systems. This linear elastic fracture mechanics (LEFM) model is derived based on the assumption of small strain. However, the boundary value problem formulated within the LEFM and under traction-free boundary conditions predicts large singular crack-tip strains. Fundamentally, this result is directly in contradiction with the underlying assumption of small strain. In this work, we study a theoretical framework of nonlinear strain-limiting models, which are algebraic nonlinear relations between stress and strain. These models are consistent with the basic assumption of small strain. The advantage of such framework over the LEFM is that the strain remains bounded even if the crack-tip stress tends to the infinity. Then, employing the phase-field approach, the distinct predictions for tensile crack growth can be governed by the model. Several numerical examples to evaluate the efficacy and the performance of the model and numerical algorithms structured on finite element method are presented. Detailed comparisons of the strain, fracture energy with corresponding discrete propagation speed between the nonlinear strain-limiting model and the LEFM for the quasi-static tensile fracture are discussed.
@article{LEE2022113715,
title = {Finite element simulation of quasi-static tensile fracture in nonlinear strain-limiting solids with the phase-field approach},
journal = {Journal of Computational and Applied Mathematics},
volume = {399},
pages = {113715},
year = {2022},
issn = {0377-0427},
doi = {https://doi.org/10.1016/j.cam.2021.113715},
url = {https://www.sciencedirect.com/science/article/pii/S037704272100337X},
author = {Sanghyun Lee and Hyun Chul Yoon and S.M. Mallikarjunaiah},
keywords = {Strain-limiting model, Nonlinear elasticity, LEFM, Fracture propagation, Phase-field, Finite element method},
abstract = {We investigate a quasi-static tensile fracture in nonlinear strain-limiting solids by coupling with the phase-field approach. A classical model for the growth of fractures in an elastic material is formulated in the framework of linear elasticity for deformation systems. This linear elastic fracture mechanics (LEFM) model is derived based on the assumption of small strain. However, the boundary value problem formulated within the LEFM and under traction-free boundary conditions predicts large singular crack-tip strains. Fundamentally, this result is directly in contradiction with the underlying assumption of small strain. In this work, we study a theoretical framework of nonlinear strain-limiting models, which are algebraic nonlinear relations between stress and strain. These models are consistent with the basic assumption of small strain. The advantage of such framework over the LEFM is that the strain remains bounded even if the crack-tip stress tends to the infinity. Then, employing the phase-field approach, the distinct predictions for tensile crack growth can be governed by the model. Several numerical examples to evaluate the efficacy and the performance of the model and numerical algorithms structured on finite element method are presented. Detailed comparisons of the strain, fracture energy with corresponding discrete propagation speed between the nonlinear strain-limiting model and the LEFM for the quasi-static tensile fracture are discussed.}
}
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C.","Mallikarjunaiah, S."],"bibdata":{"bibtype":"article","type":"article","title":"Finite element simulation of quasi-static tensile fracture in nonlinear strain-limiting solids with the phase-field approach","journal":"Journal of Computational and Applied Mathematics","volume":"399","pages":"113715","year":"2022","issn":"0377-0427","doi":"https://doi.org/10.1016/j.cam.2021.113715","url":"https://www.sciencedirect.com/science/article/pii/S037704272100337X","author":[{"firstnames":["Sanghyun"],"propositions":[],"lastnames":["Lee"],"suffixes":[]},{"firstnames":["Hyun","Chul"],"propositions":[],"lastnames":["Yoon"],"suffixes":[]},{"firstnames":["S.M."],"propositions":[],"lastnames":["Mallikarjunaiah"],"suffixes":[]}],"keywords":"Strain-limiting model, Nonlinear elasticity, LEFM, Fracture propagation, Phase-field, Finite element method","abstract":"We investigate a quasi-static tensile fracture in nonlinear strain-limiting solids by coupling with the phase-field approach. A classical model for the growth of fractures in an elastic material is formulated in the framework of linear elasticity for deformation systems. This linear elastic fracture mechanics (LEFM) model is derived based on the assumption of small strain. However, the boundary value problem formulated within the LEFM and under traction-free boundary conditions predicts large singular crack-tip strains. Fundamentally, this result is directly in contradiction with the underlying assumption of small strain. In this work, we study a theoretical framework of nonlinear strain-limiting models, which are algebraic nonlinear relations between stress and strain. These models are consistent with the basic assumption of small strain. The advantage of such framework over the LEFM is that the strain remains bounded even if the crack-tip stress tends to the infinity. Then, employing the phase-field approach, the distinct predictions for tensile crack growth can be governed by the model. Several numerical examples to evaluate the efficacy and the performance of the model and numerical algorithms structured on finite element method are presented. Detailed comparisons of the strain, fracture energy with corresponding discrete propagation speed between the nonlinear strain-limiting model and the LEFM for the quasi-static tensile fracture are discussed.","bibtex":"@article{LEE2022113715,\ntitle = {Finite element simulation of quasi-static tensile fracture in nonlinear strain-limiting solids with the phase-field approach},\njournal = {Journal of Computational and Applied Mathematics},\nvolume = {399},\npages = {113715},\nyear = {2022},\nissn = {0377-0427},\ndoi = {https://doi.org/10.1016/j.cam.2021.113715},\nurl = {https://www.sciencedirect.com/science/article/pii/S037704272100337X},\nauthor = {Sanghyun Lee and Hyun Chul Yoon and S.M. Mallikarjunaiah},\nkeywords = {Strain-limiting model, Nonlinear elasticity, LEFM, Fracture propagation, Phase-field, Finite element method},\nabstract = {We investigate a quasi-static tensile fracture in nonlinear strain-limiting solids by coupling with the phase-field approach. A classical model for the growth of fractures in an elastic material is formulated in the framework of linear elasticity for deformation systems. This linear elastic fracture mechanics (LEFM) model is derived based on the assumption of small strain. However, the boundary value problem formulated within the LEFM and under traction-free boundary conditions predicts large singular crack-tip strains. Fundamentally, this result is directly in contradiction with the underlying assumption of small strain. In this work, we study a theoretical framework of nonlinear strain-limiting models, which are algebraic nonlinear relations between stress and strain. 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