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Open AccessArticle

Mesh-Based and Meshfree Reduced Order Phase-Field Models for Brittle Fracture: One Dimensional Problems

1
Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam
2
Department of Mathematical Sciences, School of Science, RMIT University, Melbourne, Victoria 3000, Australia
3
Department of Civil Engineering, Monash University, Clayton, Victoria 3800, Australia
4
State Key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou 510641, China
5
Department of Aerospace Engineering, Ho Chi Minh City University of Technology, Ho Chi Minh City 700000, Vietnam
*
Authors to whom correspondence should be addressed.
Materials 2019, 12(11), 1858; https://doi.org/10.3390/ma12111858
Received: 17 May 2019 / Revised: 4 June 2019 / Accepted: 5 June 2019 / Published: 8 June 2019
(This article belongs to the Special Issue Randomness and Uncertainty)
Modelling brittle fracture by a phase-field fracture formulation has now been widely accepted. However, the full-order phase-field fracture model implemented using finite elements results in a nonlinear coupled system for which simulations are very computationally demanding, particularly for parametrized problems when the randomness and uncertainty of material properties are considered. To tackle this issue, we present two reduced-order phase-field models for parametrized brittle fracture problems in this work. The first one is a mesh-based Proper Orthogonal Decomposition (POD) method. Both the Discrete Empirical Interpolation Method (DEIM) and the Matrix Discrete Empirical Interpolation Method ((M)DEIM) are adopted to approximate the nonlinear vectors and matrices. The second one is a meshfree Krigingmodel. For one-dimensional problems, served as proof-of-concept demonstrations, in which Young’s modulus and the fracture energy vary, the POD-based model can speed up the online computations eight-times, and for the Kriging model, the speed-up factor is 1100, albeit with a slightly lower accuracy. Another merit of the Kriging’s model is its non-intrusive nature, as one does not need to modify the full-order model code. View Full-Text
Keywords: phase-field theory; brittle fracture; Reduced-Order Model (ROM); Kriging model; Proper Orthogonal Decomposition (POD) phase-field theory; brittle fracture; Reduced-Order Model (ROM); Kriging model; Proper Orthogonal Decomposition (POD)
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Nguyen, N.-H.; Nguyen, V.P.; Wu, J.-Y.; Le, T.-H.-H.; Ding, Y. Mesh-Based and Meshfree Reduced Order Phase-Field Models for Brittle Fracture: One Dimensional Problems. Materials 2019, 12, 1858.

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