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Journal article
Bound-constrained optimization using Lagrange multiplier for a length scale insensitive phase field fracture model
Engineering fracture mechanics [e-journal], v 310, 110496
20 Sep 2024
Featured in Collection : Research Supported by Drexel Libraries' OA Programs
Abstract
The classical phase field model using the second-order geometric function 𝛼(𝜑) = 𝜑2 (i.e., AT2 model), where 𝜑 ∈ [0,1] is an auxiliary phase field variable representing material damage state, has wide applications in static and dynamic scenarios for brittle materials, but nonlinearity and inelasticity are found in its stress–strain curve. The phase field model using the linear geometric function 𝛼(𝜑) = 𝜑 (i.e., AT1 model), can avoid this, and a linear elastic threshold is available in its stress–strain curve. However, both AT2 and AT1 models are length scale sensitive phase field models, which could have difficulty in adjusting fracture strength and crack band simultaneously through a single parameter (the length scale). In this paper, a generalized quadratic geometric function (linear combination of AT1 and AT2 models) is used in the phase field model, where the extra parameter in this geometric function makes it a length scale insensitive phase field model. Similar to the AT1 model, negative phases can happen in the proposed generalized quadratic geometric function model. To solve this problem, a boundconstrained optimization using the Lagrange multiplier is derived, and the Karush–Kuhn–Tucker (KKT) conditions change from strain energy and maximum history strain energy (an indirect method acting on phase) to phase and Lagrange multiplier (a direct method acting on phase). Several simulations successfully validated the proposed model. A single element analysis and a bar under cyclic loading show the different stress–strain curves obtained from different models. A simulation of Mode I Brazilian test is compared with the experiment conducted by the authors, and two more simulations of Mode II shear test and mixed mode PMMA tensile test are compared with results from the literature.
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Details
- Title
- Bound-constrained optimization using Lagrange multiplier for a length scale insensitive phase field fracture model
- Creators
- Ahmad Raeisi Najafi (Corresponding Author) - Drexel University, Mechanical Engineering and MechanicsLi Meng - Drexel University, Mechanical Engineering and MechanicsHsiao Wei Lee - Drexel University, Mechanical Engineering and MechanicsChristopher Sales - Drexel University, C. and J. Nyheim Plasma InstituteYaghoob “Amir” Farnam - Drexel University, Civil, Architectural, and Environmental Engineering
- Publication Details
- Engineering fracture mechanics [e-journal], v 310, 110496
- Publisher
- Elsevier
- Number of pages
- 21
- Grant note
- DARPA, United States: D23AC00043-00 This work was financed by DARPA, United States (Award Instrument Number: D23AC00043-00) and was performed at Drexel University in the Multiscale Computational Mechanics and Biomechanics (MCMB) Lab. Special thanks to Dr. Matthew Pava, Dr. Jayan Rammohan from DARPA/Biological Technologies Office, and Dr. Claretta Sullivan from Air Force Research Laboratories. All simulations were conducted on Picotte, Drexel University's primary high-performance computing cluster, and on the clusters and PCs in the MCMB lab.
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- C. and J. Nyheim Plasma Institute; Civil, Architectural, and Environmental Engineering; Mechanical Engineering and Mechanics
- Web of Science ID
- WOS:001320527600001
- Scopus ID
- 2-s2.0-85204344299
- Other Identifier
- 991021902710204721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mechanics