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Volume 13, Issue 1
Framework and Numerical Algorithm for a Phase Field Fracture Model

S. Karthik, A. Nasedkina, A. Nasedkin & A. Rajagopal

East Asian J. Appl. Math., 13 (2023), pp. 162-176.

Published online: 2023-01

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  • Abstract

A phase field fracture model for quasi-brittle material in 2D is implemented in Abaqus software. The phase field damage variables 0 and 1 define undamaged and damaged regions of the material and simplify crack surface tracking. On the other hand, one has to use a fine spatial discretization for the smooth distribution of the phase field variable regularized by a small length scale parameter, which makes the method computationally expensive. At the fully damaged regions both the stiffness and stress reach zero. The displacements and damage are determined by a staggered approach, and a few standard benchmark fracture problems are used to demonstrate the work of the phase field fracture model under consideration.

  • AMS Subject Headings

65M10, 78A48

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-13-162, author = {Karthik , S.Nasedkina , A.Nasedkin , A. and Rajagopal , A.}, title = {Framework and Numerical Algorithm for a Phase Field Fracture Model}, journal = {East Asian Journal on Applied Mathematics}, year = {2023}, volume = {13}, number = {1}, pages = {162--176}, abstract = {

A phase field fracture model for quasi-brittle material in 2D is implemented in Abaqus software. The phase field damage variables 0 and 1 define undamaged and damaged regions of the material and simplify crack surface tracking. On the other hand, one has to use a fine spatial discretization for the smooth distribution of the phase field variable regularized by a small length scale parameter, which makes the method computationally expensive. At the fully damaged regions both the stiffness and stress reach zero. The displacements and damage are determined by a staggered approach, and a few standard benchmark fracture problems are used to demonstrate the work of the phase field fracture model under consideration.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.280921.270722}, url = {http://global-sci.org/intro/article_detail/eajam/21307.html} }
TY - JOUR T1 - Framework and Numerical Algorithm for a Phase Field Fracture Model AU - Karthik , S. AU - Nasedkina , A. AU - Nasedkin , A. AU - Rajagopal , A. JO - East Asian Journal on Applied Mathematics VL - 1 SP - 162 EP - 176 PY - 2023 DA - 2023/01 SN - 13 DO - http://doi.org/10.4208/eajam.280921.270722 UR - https://global-sci.org/intro/article_detail/eajam/21307.html KW - Phase field method, fracture, sharp crack, staggered approach and nonlinear finite element method. AB -

A phase field fracture model for quasi-brittle material in 2D is implemented in Abaqus software. The phase field damage variables 0 and 1 define undamaged and damaged regions of the material and simplify crack surface tracking. On the other hand, one has to use a fine spatial discretization for the smooth distribution of the phase field variable regularized by a small length scale parameter, which makes the method computationally expensive. At the fully damaged regions both the stiffness and stress reach zero. The displacements and damage are determined by a staggered approach, and a few standard benchmark fracture problems are used to demonstrate the work of the phase field fracture model under consideration.

S. Karthik, A. Nasedkina, A. Nasedkin & A. Rajagopal. (2023). Framework and Numerical Algorithm for a Phase Field Fracture Model. East Asian Journal on Applied Mathematics. 13 (1). 162-176. doi:10.4208/eajam.280921.270722
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