Strain orthogonal decomposition implemented within the phase field method with interfacial damage to model fracture in multi-phase heterogeneous materials
Email:
nxlam@utc.edu.vn
Từ khóa:
phase field method, strain orthogonal decomposition, damage, supplemental sub-function, multi-phase heterogeneous structure.
Tóm tắt
In recent times, the phase field method is a robust simulation tool that can predict crack formation and propagation in structures. In brittle and quasi-brittle materials, the strain tensor is decomposed into negative and positive parts corresponding to the compression and tension behaviors when the structure is loaded. In the previous studies related to the phase field method, the strain tensor decompositions do not satisfy the orthogonal condition of these two parts, even if the elastic stiffness tensor is isotropic. This problem leads to inaccuracies in the mechanical behavior of the materials. In this paper, the strain tensor orthogonal condition is applied to the bulk strain tensor parts representing the internal strain of the component phases. This orthogonal condition is implemented into the phase field method with interfacial damage to simulate crack propagation in a sample containing multi-phase heterogeneous materials. Furthermore, the shape and area fraction of these phases are recognized by a supplemental sub-function which was studied in our recent paper from image formats. Through several examples, the obtained results are compared with the relevant numerical ones to demonstrate the correctness and effectiveness of the proposed method.Tài liệu tham khảo
[1]. C. Miehe, M. Hofacker, F. Welschinger, A phase field model for rate-independent crack
propagation: robust algorithmic implementation based on operator splits, Comput. Methods
Appl. Mech. Eng, 199 (2010) 2765-2778. https://doi.org/10.1016/j.cma.2010.04.011
[2]. N. Nguyen, J. Yvonnet, J. Rethorée, A. B. Tran, Identification of fracture models based on phase field for crack propagation in heterogeneous lattices in a context of non-separated scales, Comput. Mech, 63 (2019) 1047–1068. https://doi.org/10.1007/s00466-018-1636-z
[3]. N. Nguyen, A. B. Tran, Study the impact of voids distribution on the initiation and propagation of cracks by a phase field method, Journal of Science and Technology in Civil Engineering, 5 (2017) 100-107.
[4]. T.T. Nguyen, J. Réthoré, M.C. Bainetto, Phase field modelling of anisotropic crack propagation, Eur. J. Mech. A/Solids, 65 (2017) 279-288. https://doi.org/10.1016/j.euromechsol.2017.05.002
[5]. T.T. Nguyen, J. Réthoré, J. Yvonnet, M.C. Bainetto, Multi-phase-field modeling of anisotropic crack propagation for polycrystalline materials, Comput. Mech, 60 (2017) 289-314. https://doi.org/10.1007/s00466-017-1409-0
[6]. B. T. Vu, V. T. Ngo, T. T. Bui, T. T. Tran, A. T. Do, Phase field modeling of crack initiation and propagation in high-strength concrete beams containing nano-silica, Transport and communications science Journal, 72 (2021) 672-686. https://doi.org/10.47869/tcsj.72.6.1
[7]. B. T. Vu, A.T. Tran, D.H. Nguyen, Modeling of crack propagation in multi-phase structure by phase field method with interfacial damage, Transport and communications science Journal, 72 (2021) 911-925. https://doi.org/10.47869/tcsj.72.8.5
[8]. Matlab 2014b programming language. https://www.mathworks.com.
[9]. T.T. Nguyen, J. Yvonnet, Q.Z. Zhu, M. Bornert, C. Chateau, A phase-field method for
computational modeling of interfacial damage interacting with crack propagation
in realistic microstructures obtained by microtomography, Comput. Methods Appl.
Mech. Eng, 312 (2016) 567–95. https://doi.org/10.1016/j.cma.2015.10.007
[10]. Q.C. He, Q. Shao, Closed-form coordinate-free decompositions of the two-dimensional strain and stress for modeling tension-compression dissymmetry. J. Appl. Mech, 86 (2019) 031007. https://doi.org/10.1115/1.4042217
[11]. T.T. Nguyen, J. Yvonnet, Q.Z. Zhu, M. Bornert, C. Chateau, A phase field method to simulate
crack nucleation and propagation in strongly heterogeneous materials from direct imaging of
their microstructure, Eng. Fract. Mech, 139 (2015) 18-39. https://doi.org/10.1016/j.engfracmech.2015.03.045
[12]. G. Lancioni, G. Royer-Carfagni, The variational approach to fracture mechanics. a practical application to the French Panthéon in Paris, J. Elasticity, 95 (2009) 1-30. https://doi.org/10.1007/s10659-009-9189-1
[13]. J. Y. Wu, M. Cervera, A novel positive/negative projection in energy norm for the damage
modeling of quasi-brittle solids, Int. J. Solids Struct, 139 (2018) 250–269. https://doi.org/10.1016/j.ijsolstr.2018.02.004
[14]. B.T. Vu, Modeling and simulation of damage in anisotropic materials by the phase-field
method, PhD Thesis, Paris-Est University, France, (2021).
[15]. C.V. Verhoosel, R. de Borst, A phase-field model for cohesive fracture, Int. J. Numer. Methods Engrg, 96 (2013) 43–62. https://doi.org/10.1002/nme.4553
propagation: robust algorithmic implementation based on operator splits, Comput. Methods
Appl. Mech. Eng, 199 (2010) 2765-2778. https://doi.org/10.1016/j.cma.2010.04.011
[2]. N. Nguyen, J. Yvonnet, J. Rethorée, A. B. Tran, Identification of fracture models based on phase field for crack propagation in heterogeneous lattices in a context of non-separated scales, Comput. Mech, 63 (2019) 1047–1068. https://doi.org/10.1007/s00466-018-1636-z
[3]. N. Nguyen, A. B. Tran, Study the impact of voids distribution on the initiation and propagation of cracks by a phase field method, Journal of Science and Technology in Civil Engineering, 5 (2017) 100-107.
[4]. T.T. Nguyen, J. Réthoré, M.C. Bainetto, Phase field modelling of anisotropic crack propagation, Eur. J. Mech. A/Solids, 65 (2017) 279-288. https://doi.org/10.1016/j.euromechsol.2017.05.002
[5]. T.T. Nguyen, J. Réthoré, J. Yvonnet, M.C. Bainetto, Multi-phase-field modeling of anisotropic crack propagation for polycrystalline materials, Comput. Mech, 60 (2017) 289-314. https://doi.org/10.1007/s00466-017-1409-0
[6]. B. T. Vu, V. T. Ngo, T. T. Bui, T. T. Tran, A. T. Do, Phase field modeling of crack initiation and propagation in high-strength concrete beams containing nano-silica, Transport and communications science Journal, 72 (2021) 672-686. https://doi.org/10.47869/tcsj.72.6.1
[7]. B. T. Vu, A.T. Tran, D.H. Nguyen, Modeling of crack propagation in multi-phase structure by phase field method with interfacial damage, Transport and communications science Journal, 72 (2021) 911-925. https://doi.org/10.47869/tcsj.72.8.5
[8]. Matlab 2014b programming language. https://www.mathworks.com.
[9]. T.T. Nguyen, J. Yvonnet, Q.Z. Zhu, M. Bornert, C. Chateau, A phase-field method for
computational modeling of interfacial damage interacting with crack propagation
in realistic microstructures obtained by microtomography, Comput. Methods Appl.
Mech. Eng, 312 (2016) 567–95. https://doi.org/10.1016/j.cma.2015.10.007
[10]. Q.C. He, Q. Shao, Closed-form coordinate-free decompositions of the two-dimensional strain and stress for modeling tension-compression dissymmetry. J. Appl. Mech, 86 (2019) 031007. https://doi.org/10.1115/1.4042217
[11]. T.T. Nguyen, J. Yvonnet, Q.Z. Zhu, M. Bornert, C. Chateau, A phase field method to simulate
crack nucleation and propagation in strongly heterogeneous materials from direct imaging of
their microstructure, Eng. Fract. Mech, 139 (2015) 18-39. https://doi.org/10.1016/j.engfracmech.2015.03.045
[12]. G. Lancioni, G. Royer-Carfagni, The variational approach to fracture mechanics. a practical application to the French Panthéon in Paris, J. Elasticity, 95 (2009) 1-30. https://doi.org/10.1007/s10659-009-9189-1
[13]. J. Y. Wu, M. Cervera, A novel positive/negative projection in energy norm for the damage
modeling of quasi-brittle solids, Int. J. Solids Struct, 139 (2018) 250–269. https://doi.org/10.1016/j.ijsolstr.2018.02.004
[14]. B.T. Vu, Modeling and simulation of damage in anisotropic materials by the phase-field
method, PhD Thesis, Paris-Est University, France, (2021).
[15]. C.V. Verhoosel, R. de Borst, A phase-field model for cohesive fracture, Int. J. Numer. Methods Engrg, 96 (2013) 43–62. https://doi.org/10.1002/nme.4553
Tải xuống
Chưa có dữ liệu thống kê
Nhận bài
30/03/2022
Nhận bài sửa
16/05/2022
Chấp nhận đăng
16/06/2022
Xuất bản
15/05/2023
Chuyên mục
Công trình khoa học
Kiểu trích dẫn
Vu Ba, T., Nguyen Xuan, L., & Do Anh, T. (1684083600). Strain orthogonal decomposition implemented within the phase field method with interfacial damage to model fracture in multi-phase heterogeneous materials. Tạp Chí Khoa Học Giao Thông Vận Tải, 74(4), 386-399. https://doi.org/10.47869/tcsj.74.4.1
Số lần xem tóm tắt
190
Số lần xem bài báo
112
