A ?parallel universe? scheme for crack nucleation in the phase field approach to fracture

被引:8
作者
Chen, Yihao [1 ]
Shen, Yongxing [1 ,2 ,3 ]
机构
[1] Shanghai Jiao Tong Univ, Univ Michigan, Shanghai Jiao Tong Univ Joint Inst, Shanghai 200240, Peoples R China
[2] Shanghai Key Lab Digital Maintenance Bldg & Infras, Shanghai 200240, Peoples R China
[3] Shanghai Jiao Tong Univ, Global Inst Future Technol, Solid State Battery Res Ctr, Shanghai 200240, Peoples R China
基金
中国国家自然科学基金; 上海市自然科学基金;
关键词
Phase field for fracture; Global minimization; Crack nucleation; Newton method; BRITTLE-FRACTURE; FORMULATION;
D O I
10.1016/j.cma.2022.115708
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
Crack nucleation is crucial in many industrial applications. The phase field method for fracture transforms the crack nucleation problem into a minimization problem of the sum of the elastic potential energy and the crack surface energy. Due to the polyconvexity of the formulation, starting from a crackless solid, a standard Newton iteration may lead to a solution with no crack, even though a cracked solution has a lower total energy. As such, the critical load for cracking is highly overestimated. Here, we propose an algorithm termed "parallel universe" algorithm to capture the global minimum. This algorithm has two key ingredients: (a) a necessary condition for cracking solely based on the current crackless solution, and (b) beginning from when this condition is met, Newton iteration with two initial guesses, a crackles one and a cracked one, will both be performed and the converged candidate solution with lower energy is accepted as the solution at that load step. Once the cracked candidate solution is accepted, the crackless one is discarded, i.e., only one universe is retained. This cracked initial guess is obtained only once for all load steps by solving a series of similar minimization problems with a progressively reduced critical crack energy release rate. Numerical examples with isotropic and anisotropic critical crack energy release rates indicate that the proposed algorithm is more reliable (as there is no need to retrace) and more efficient than the standard Newton iteration and a well-known backtracking algorithm.(c) 2022 Elsevier B.V. All rights reserved.
引用
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页数:16
相关论文
共 12 条
[1]  
Allgower E. L., 2003, Introduction to Numerical Continuation Methods
[2]   Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments [J].
Amor, Hanen ;
Marigo, Jean-Jacques ;
Maurini, Corrado .
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 2009, 57 (08) :1209-1229
[3]   Numerical experiments in revisited brittle fracture [J].
Bourdin, B ;
Francfort, GA ;
Marigo, JJ .
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 2000, 48 (04) :797-826
[4]   The variational approach to fracture [J].
Bourdin, Blaise ;
Francfort, Gilles A. ;
Marigo, Jean-Jacques .
JOURNAL OF ELASTICITY, 2008, 91 (1-3) :5-148
[5]  
Bourdin B, 2007, INTERFACE FREE BOUND, V9, P411
[6]   Revisiting brittle fracture as an energy minimization problem [J].
Francfort, GA ;
Marigo, JJ .
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 1998, 46 (08) :1319-1342
[7]  
FRASER A. S., 1957, AUSTRALIAN JOUR BIOL SCI, V10, P484
[8]   Second-order phase-field formulations for anisotropic brittle fracture [J].
Gerasimov, Tymofiy ;
De Lorenzis, Laura .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2022, 389
[9]   OPTIMIZATION BY SIMULATED ANNEALING [J].
KIRKPATRICK, S ;
GELATT, CD ;
VECCHI, MP .
SCIENCE, 1983, 220 (4598) :671-680
[10]   A recursive multilevel trust region method with application to fully monolithic phase-field models of brittle fracture [J].
Kopanicakova, Alena ;
Krause, Rolf .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2020, 360