Research Papers

Comparison of Concurrent Multiscale Methods in the Application of Fracture in Nickel

[+] Author and Article Information
Vincent Iacobellis

e-mail: vincent.iacobellis@mail.utoronto.ca

Kamran Behdinan

e-mail: behdinan@mie.utoronto.ca
Department of Mechanical and
Industrial Engineering,
University of Toronto,
5 King's College Road,
Toronto, ON M5S 3G8, Canada

1Corresponding author.

Manuscript received September 13, 2011; final manuscript received December 5, 2012; accepted manuscript posted January 22, 2013; published online July 12, 2013. Assoc. Editor: Vikram Deshpande.

J. Appl. Mech 80(5), 051003 (Jul 12, 2013) (8 pages) Paper No: JAM-11-1332; doi: 10.1115/1.4023477 History: Received June 28, 2012; Revised September 18, 2012; Accepted January 22, 2013

This paper presents a study of fracture in nickel using multiscale modeling. A comparison of six concurrent multiscale methods was performed in their application to a common problem using a common framework in order to evaluate each method relative to each other. Each method was compared in both a quasi-static case of crack tip deformation as well as a dynamic case in the study of crack growth. Each method was compared to the fully atomistic model with similarities and differences between the methods noted and reasons for these provided. The results showed a distinct difference between direct and handshake coupling methods. In general, for the quasi-static case, the direct coupling methods took longer to run compared to the handshake coupling methods but had less error with respect to displacement and energy. In the dynamic case, the handshake methods took longer to run, but had reduced error most notably when wave dissipation at the atomistic/continuum region was an issue. Comparing each method under common conditions showed that many similarities exist between each method that may be hidden by their original formulation. The comparison also showed the dependency on the application as well as the simulation techniques used in determining the performance of each method.

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Freund, L. B., 1990, Dynamic Fracture Mechanics, Cambridge University Press, Cambridge, UK.
Zhou, S. J., Beazley, D. M., Lomdahl, P. S., and Holian, B. L., 1996, “Large-Scale Molecular Dynamics Simulations of Fracture and Deformation,” J. Comput.-Aided Mater. Des., 3(1–3), pp. 183–186. [CrossRef]
Miller, R. E., and Tadmor, E. B., 2009, “A Unified Framework and Performance Benchmark of Fourteen Multiscale Atomistic/Continuum Coupling Methods,” Model. Simul. Mater. Sci. Eng., 17(5), p. 053001. [CrossRef]
Csányi, G., Albaret, T., Payne.M. C., and De Vita, A., 2004, “Learn on the Fly: A Hybrid Classical and Quantum-Mechanical Molecular Dynamics Simulation,” Phys. Rev. Lett., 93(17), p. 175503. [CrossRef] [PubMed]
Peng, Q., and Lu, G., 2011, “A Comparative Study of Fracture in Al: Quantum Mechanical Versus Empirical Atomistic Description,” J. Mech. Phys. Solids, 59(4), pp. 775–786. [CrossRef]
Curtin, W. A., and Miller, R. E., 2003, “Atomistic/Continuum Coupling in Computational Materials Science,” Model. Simul. Mater. Sci. Eng., 11(3), pp. R33–R68. [CrossRef]
Liu, W. K., Karpov, E. G., Zhang, S., and Park, H. S., 2004, “An Introduction to Computational Nanomechanics and Materials,” Comput. Methods Appl. Mech. Eng., 193(17–20), pp. 1529–1578. [CrossRef]
Park, H. S., and Liu, W. K., 2004, “An Introduction and Tutorial on Multiple-Scale Analysis in Solids,” Comput. Methods Appl. Mech. Eng., 193(17–20), pp. 1733–1772. [CrossRef]
Tadmor, E. B., Ortiz, M., and, Phillips, R., 1996, “Quasicontinuum Analysis of Defects in Solids,” Philos. Mag. A., 73(6), pp. 1529–1563. [CrossRef]
Miller, R., Ortiz, M., Phillips, R., Shenoy, V., and Tadmor, E. B., 1998, “Quasicontinuum Models of Fracture and Plasticity,” Eng. Fract. Mech., 61(3–4), pp. 427–444. [CrossRef]
Dupuy, L. M., Tadmor, E. B., Miller, R. E., and Phillips, R., 2005, “Finite-Temperature Quasicontinuum: Molecular Dynamics Without All the Atoms,” Phys. Rev. Lett., 95(6), pp. 1–4. [CrossRef]
Shilkrot, L. E., Miller, R. E., and Curtin, W. A., 2004, “Multiscale Plasticity Modeling: Coupled Atomistics and Discrete Dislocation Mechanics,” J Mech. Phys. Solids, 52(4), pp. 755–787. [CrossRef]
Qu, S., Shastry, V., Curtin, W. A., and Miller, R. E., 2005, “A Finite-Temperature Dynamic Coupled Atomistic/Discrete Dislocation Method,” Model. Simul. Mater. Sci. Eng., 13(7), pp. 1101–1118. [CrossRef]
Xiao, S. P., and Belytschko, T., 2004, “A Bridging Domain Method for Coupling Continua With Molecular Dynamics,” Comput. Methods Appl. Mech. Eng., 193(17–20), pp. 1645–1669. [CrossRef]
Fish, J., Nuggehally, M. A., Shephard, M. S., Picu, C. R., Badia, S., Parks, M. L., and Gunzburger, M., 2007, “Concurrent AtC Coupling Based on a Blend of the Continuum Stress and the Atomistic Force,” Comput. Methods Appl. Mech. Eng., 196(45–48), pp. 4548–4560. [CrossRef]
Badia, S., Parks, M., Bochev, P., Gunzburger, M., and Lehouc, Q., 2008, “On Atomistic-to-Continuum Coupling by Blending,” Multiscale Model. Simul., 7(1), pp. 381–406. [CrossRef]
Wagner, G. J., and Liu, W. K., 2003, “Coupling of Atomistic and Continuum Simulations Using a Bridging Scale Decomposition,” J. Comput. Phys., 190(1), pp. 249–274. [CrossRef]
Qian, D., Wagner, G. J., and Liu, W. K., 2004, “A Multiscale Projection Method for the Analysis of Carbon Nanotubes,” Comput. Methods Appl. Mech. Eng., 193(17–20), pp. 1603–1632. [CrossRef]
Shenoy, V. B., Miller, R., Tadmor, E. B., Rodney, D., Phillips, R., and Ortiz, M., 1999, “An Adaptive Finite Element Approach to Atomic-Scale Mechanics—The Quasicontinuum Method,” J. Mech. Phys. Solids, 47(3), pp. 611–642. [CrossRef]


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Fig. 1

Interface for (a) direct atomistic/continuum coupling. White circles are pad atoms and black circles are regular atoms, (b) handshake atomistic/continuum coupling. White circles are pad atoms, gray circles are handshake atoms, and black circles are regular atoms.

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Fig. 2

Dimensions and boundary conditions for fracture study

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Fig. 3

Mesh for fracture simulation: (a) model 1, (b) model 2, (c) model 3

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Fig. 4

(a) y-displacement plot for exact solution, (b) deformed crack with blunting and partial dislocations

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Fig. 5

Displacement error plots for direct coupling methods

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Fig. 6

Displacement error plots for handshake coupling methods

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Fig. 7

Mesh for fracture simulation: (a) model 1, (b) model 2, (c) model 3

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Fig. 8

(a) Final crack position, (b) stress around crack tip

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Fig. 9

Crack tip displacement versus simulation time for model 3

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Fig. 10

Crack tip displacement versus simulation time for three models of BDM



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