Phase field modelling combined with optimization algorithm for maximizing the resistance in two-phase composites
Email:
thanhvb@utc.edu.vn
Từ khóa:
phase field modelling, topology optimization, strain orthogonal decomposition, fracture, composite structures.
Tóm tắt
Recently, the phase field modelling is widely used to model and simulate material damage. In present work, we present a framework of the topology optimization combined with the phase-field modelling with/ without interfacial damage for optimizing the damage resistance of the inclusion-matrix composites. The first phase field method with the interfacial damage described by the phase field variable d(x) and an interfacial phase field variable β(x), thus the crack occurs in the interaction between the bulk fracture and the interfacial one; the second phase field method without the interfacial damage describes the crack by using only a damage variable d(x), thus the crack initiates at the points where stress concentration occurs (damage only occurring in the phases). Extended bi-directional evolutionary structural optimization algorithm (BESO) is used to optimize the inclusion distribution in order to reduce its volume while keeping the fracture resistance value of the initial design unchanged. Moreover, the strain tensor orthogonal decompositions are implemented into the phase field methods to improve the inaccuracy in the mechanical behavior of the materials. We compare the inclusion optimal distribution, the crack propagation and the fracture resistance between the proposed models through several numerical examples.Tài liệu tham khảo
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[13]. B. T. Vu, Modeling and simulation of damage in anisotropic materials by the phase-field
method, PhD Thesis, Paris-Est University, France, (2021).
[14]. 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
[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
[16]. T. T. Nguyen, J. Yvonnet, M. Bornert, C. Chateau, K. Sab, R. Romani, R. Le Roy, On the
choice of parameters in the phase field method for simulating crack initiation with experimental validation, Int. J. Fracture, 197 (2016) 213-226. https://doi.org/10.1007/s10704-016-0082-1
Royal Society London Series A, 221 (1921) 163-198. https://doi.org/10.1098/rsta.1921.0006
[2]. G. R. Irwin, Analysis of stress and strains near the end of a crack traversing a plate, J. Appl.
Mech, 24 (1957) 361-364.
[3]. G. A. Francfort, J. J. Marigo, Revisiting brittle fracture as an energy minimization problem, J.
Mech. Phys. Solids, 46 (1998) 1319-1342. https://doi.org/10.1016/S0022-5096(98)00034-9
[4]. D. Mumford, J. Shah, Optimal approximations by piecewise smooth functions and associated
variational problems, Commun. Pure. Appl. Math, 42 (1989) 577-685. https://doi.org/ 10.1002/cpa.3160420503
[5]. B. Bourdin, J. J. Marigo, C. Maurini, P. Sicsic, Morphogenesis and propagation of complex
cracks induced by thermal shocks, Phys. Rev. Lett, 112 (2014) 014301. https://doi.org/10.1103/PhysRevLett.112.014301
[6]. 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
[7]. 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
[8]. 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
[9]. 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
[10]. L. Xia, P. Breitkopf, Recent advances on topology optimization of multiscale nonlinear structures, Arch. Comput. Methods Eng, 24 (2017) 227–249. https://doi.org/10.1007/s11831-016-9170-7
[11]. L. Xia, D. C. Da, J. Yvonnet, Topology optimization for maximizing the fracture resistance of quasi-brittle composites, Comput. Methods Appl. Mech. Eng, 332 (2018) 234–254. https://doi.org/10.1016/j.cma.2017.12.021
[12]. D. C. Da, J. Yvonnet, L. Xia, G. Li, Topology optimization of particlematrix composites for optimal fracture resistance taking into account interfacial damage, Int. J. Numer. Methods Eng, 115 (2018) 604–626. https://doi.org/10.1002/nme.5818
[13]. B. T. Vu, Modeling and simulation of damage in anisotropic materials by the phase-field
method, PhD Thesis, Paris-Est University, France, (2021).
[14]. 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
[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
[16]. T. T. Nguyen, J. Yvonnet, M. Bornert, C. Chateau, K. Sab, R. Romani, R. Le Roy, On the
choice of parameters in the phase field method for simulating crack initiation with experimental validation, Int. J. Fracture, 197 (2016) 213-226. https://doi.org/10.1007/s10704-016-0082-1
Tải xuống
Chưa có dữ liệu thống kê
Nhận bài
12/12/2022
Nhận bài sửa
20/04/2023
Chấp nhận đăng
14/05/2023
Xuất bản
15/05/2023
Chuyên mục
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Kiểu trích dẫn
Vu Ba, T. (1684083600). Phase field modelling combined with optimization algorithm for maximizing the resistance in two-phase composites. Tạp Chí Khoa Học Giao Thông Vận Tải, 74(4), 428-444. https://doi.org/10.47869/tcsj.74.4.4
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