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Research Papers

An Inertia-Based Stabilizing Method for Quasi-Static Simulation of Unstable Crack Initiation and Propagation

[+] Author and Article Information
Y. C. Gu

Department of Civil Engineering,
Zhejiang University,
Zijingang Campus,
Hangzhou 310058, China

J. Jung

Department of Mechanical and
Aerospace Engineering,
University of Miami,
Coral Gables, FL 33124

Q. D. Yang

Department of Mechanical and
Aerospace Engineering,
University of Miami,
Coral Gables, FL 33124
e-mail: qdyang@miami.edu

W. Q. Chen

Department of Civil Engineering,
Zhejiang University,
Zijingang Campus,
Hangzhou 310058, China;
Department of Engineering Mechanics,
Zhejiang University,
Yuquan Campus,
Hangzhou 310027, China

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received June 5, 2015; final manuscript received July 6, 2015; published online July 22, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(10), 101010 (Jul 22, 2015) Paper No: JAM-15-1301; doi: 10.1115/1.4031010 History: Received June 05, 2015

In this paper, an inertia-based stabilizing method is proposed to overcome the loss of numerical convergence in quasi-static simulations of fracture problems with unstable (fast or dynamic) crack propagation. The method guarantees unconditional convergence as the time increment step progressively decreases and it does not need any numerical damping or other solution enhancement parameters. It has been demonstrated, through direct simulations of several numerical examples with severe local or global instabilities, that the proposed method can effectively and efficiently overcome severe instability points unconditionally and regain stability if there exist mechanisms for stable crack propagation after passing through such instability points. In all the numerical tests, the new method outperforms other solution enhancement techniques, such as numerical damping, arc-length method, and implicit dynamic simulation method, in the solution accuracy and numerical robustness.

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Figures

Grahic Jump Location
Fig. 1

(a) An elastic bar with stress (σ) smaller than its cohesive strength (σ∧), (b) upon satisfaction of σ =  σ∧, the bar is separated by a cohesive fracture process with a cohesive law as shown in (c), (c) three cohesive laws with identical toughness but different cohesive strength values, and (d) illustration of analytical solutions with stable (curve #1) and unstable (curve #3) fracture processes. Curve #2 is the critical transition point between stable and unstable conditions.

Grahic Jump Location
Fig. 2

Illustration of the element augmentation from (a) a regular element with possible different material domains, to (b) an A-FE with two quadrilateral subdomains, or to (c) an A-FE with one triangular subdomain and one pentagonal subdomain

Grahic Jump Location
Fig. 3

(a) The single A-FE under displacement-controlled loading; (b) comparison of simulated load–displacement curves obtained with current stabilizing and standard numerical damping (displacement-controlled loading); (c) simulated load and displacement as functions of pseudotime obtained with inertia-based stabilizing method under load-controlled lading; (d) simulated load and displacement as functions of pseudotime obtained with numerical damping method

Grahic Jump Location
Fig. 4

A DCB with an initial small flaw under symmetric opening load or displacement

Grahic Jump Location
Fig. 5

(a) Simulated load-point load versus displacement curves with three different cohesive strength values and (b) the pseudotime increment size (automatically determined by abaqus) as functions of displacement

Grahic Jump Location
Fig. 6

Contour plots of ε22 at three different time instances: (a) just before the crack starts to propagate (corresponding to the peak load point 1 in Fig. 5(a)); (b) immediately after the crack jump (corresponding to the load drop point 2 in Fig. 5(a)); and (c) steady-state crack propagation (point 3 in Fig. 5(a))

Grahic Jump Location
Fig. 7

(a) A-FEM simulated load-point P ∼ Δ curve (left axis) and the associated (Δt ∼ Δ) curve (right-vertical axis) and (b) contour plots of ε22 at five different time increments corresponding to the five points at the load–displacement curve in (a)

Grahic Jump Location
Fig. 8

(a) Comparison of simulated load–displacement curves obtained with current method and with the implicit dynamic under displacement-controlled loading and (b) comparison of simulated load and displacement as functions of pseudotime obtained with the current and the implicit dynamic under load-controlled lading

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