Crack nucleation in heterogeneous bars: h- and p-FEM of a phase field model
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Date
2024-09
Publication Type
Journal Article
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yes
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Abstract
Failure initiation and subsequent crack trajectory in heterogeneous materials, such as functionally graded materials and bones, are yet insufficiently addressed. The AT1 phase field model (PFM) is investigated herein in a 1D setting, imposing challenges and opportunities when discretized by h- and p-finite element (FE) methods. We derive explicit PFM solutions to a heterogeneous bar in tension considering heterogeneous E(x) and GIc(x), necessary for verification of the FE approximations. GIc(x) corrections accounting for the element size at the damage zone in h-FEMs are suggested to account for the peak stress underestimation. p-FEMs do not require any such corrections. We also derive and validate penalty coefficient for heterogeneous domains to enforce damage positivity and irreversibility via penalization. Numerical examples are provided, demonstrating that p-FEMs exhibit faster convergence rates comparing to classical h-FEMs. The new insights are encouraging towards p-FEM discretization in a 3D setting to allow an accurate prediction of failure initiation in human bones.
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published
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Journal / series
Computational Mechanics
Volume
74 (3)
Pages / Article No.
661 - 681
Publisher
Springer
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Subject
Crack nucleation; Phase field model
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Notes
Funding
861061 - New strategies for multifield fracture problems across scales in heterogeneous systems for Energy, Health and Transport (EC)