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Dynamic Void Growth and Localization Behaviors of Glassy Polymer Using Nonlocal Explicit Finite Element Analysis

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Abstract

This work introduces the nonlocal integral theory into the finite-deformation viscoplastic Gurson-type model for glassy polymer with plastic softening under strain rate loading. In order to improve computational efficiency and numerical robustness, nonlocal averaging on the void volume fraction is coupled with the update of stress and strain using ABAQUS dynamic subtoutines. From two numerical examples using nonlocal FEA on the unnotched square plate and the dumbbell-shaped specimen under tension respectively, the introduced length scale is demonstrated to regularize the dynamic initial-value problem well that remains hyperbolic by predicting the nonlocal void growth, the objective load responses, and the contours of localization bands accurately. In addition, the relationship between the width of localization band and the length scale is also studied.

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References

  1. Sarva SA, Boyce MC (2007) Mechanics of polycarbonate during high-rate tension. J Mech Mater Struct 2(10):1853–1880

    Article  Google Scholar 

  2. Wu PD, Van Der Giessen E (1994) Analysis of shear-band propagation in amorphous glassy-polymers. Inter J Solids Struct. 31(11):1493–1517

    Article  MATH  Google Scholar 

  3. Steenbrink AC, Van Der Giessen E, Wu PD (1997) Void growth in glassy polymers. J Mech Phys Solids 45(3):405–437

    Article  Google Scholar 

  4. Holopainen S (2014) Influence of damage on inhomogeneous deformation behavior of amorphous glassy polymers. Modeling and algorithmic implementation in a finite element setting. Eng Fract Mech 117:28–50

    Article  Google Scholar 

  5. Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth 1. Yield criteria and flow rules for porous ductile media. ASME J Eng Mater Technol 99(1):2–15

    Article  Google Scholar 

  6. Tvergaard V, Needleman A (1984) Analysis of the cup-cone fracture in a round tensile bar. Acta Metall 32(1):157–169

    Article  Google Scholar 

  7. Li HX, Buckley CP (2009) Evolution of strain localization in glassy polymers: a numerical study. Inter J Solids Struct 46(7–8):1607–1623

    Article  MATH  Google Scholar 

  8. Kweon S, Benzerga AA (2013) On the localization of plastic flow in glassy polymers. Euro J Mech A-Solids 39:251–267

    Article  MathSciNet  Google Scholar 

  9. Tvergaard V, Needleman A (2002) Effect of viscoplastic material parameters on polymer indentation. Model Simul Mater Sci Eng 20:065002–065016

    Article  Google Scholar 

  10. Chowdhury KA, Benzerga AA, Talreja R (2008) An analysis of impact-induced deformation and fracture modes in amorphous glassy polymers. Eng Fract Mech 75:3328–3342

    Article  Google Scholar 

  11. Xiao R, Nguyen TD (2016) A thermodynamic modeling approach for dynamic softening in glassy amorphous polymers. Extreme Mech Letters 8:70–77

    Article  Google Scholar 

  12. Eringen AC, Edelen D (1972) On nonlocal elasticity. Inter J Eng Sci 10(3):233–248

    Article  MathSciNet  MATH  Google Scholar 

  13. Pijaudier-Cabot G, Bažant ZP (1987) Nonlocal damage theory. ASCE J Eng Mech 113(10):1512–1533

    Article  MATH  Google Scholar 

  14. Tvergaard V, Needleman A (1995) Effects of nonlocal damage in porous plastic solids. Int J Solids Struct 32:1063–1077

    Article  MATH  Google Scholar 

  15. Reusch F, Svendsen B, Klingbeil D (2003) Local and non-local Gurson-based ductile damage and failure modelling at large deformation. Euro J Mech A ∕Solids 22:779–792

    Article  MATH  Google Scholar 

  16. Enakoutsa K, Leblond JB, Perrin G (2007) Numerical implementation and assessment of a phenomenological nonlocal model of ductile rupture. Comput Methods Appl Mech Eng 196(13–16):1946–1957

    Article  MATH  Google Scholar 

  17. Samal MK, Seidenfuss M, Roos E, Dutta BK, Kushwaha HS (2008) Finite element formulation of a new nonlocal damage model. Finite Elem Anal Des 44:358–371

    Article  Google Scholar 

  18. Zaïri F, Nait-Abdelaziz M, Gloaguen JM, Lefebvre JM (2008) Modelling of the elasto-viscoplastic damage behaviour of glassy polymers. Int J Plast 24:945–965

    Article  MATH  Google Scholar 

  19. Canal LP, Segurado J, Llorca J (2009) Failure surface of epoxy-modified fiber-reinforced composites under transverse tension and out-of-plane shear. Inter J Solids Struct 46(11–12):2265–2274

    Article  MATH  Google Scholar 

  20. Vadillo G, Zaera R, Fernandez-Saez J (2008) Consistent integration of the constitutive equations of Gurson materials under adiabatic conditions. Comput Methods Appl Mech Eng 197(13–16):1280–1295

    Article  MATH  Google Scholar 

  21. Grassl P, Xenos D, Jirásek M, Horák M (2014) Evaluation of nonlocal approaches for modelling fracture near nonconvex boundaries. Inter J Solids Struct 51(18):3239–3251

    Article  Google Scholar 

  22. Hughes TJR (2000) The finite element method: linear static and dynamic finite element analysis. Dover Publications

  23. Benvenuti E, and Tralli A (2003) “Iterative LCP solvers for non-local loading-unloading conditions. Int J Numer “Meth Eng, 58(15):2343–2370

  24. Needleman A (1988) Material rate dependence and mesh sensitivity in localization problems. Comput Methods Appl Mech Eng 67:69–85

    Article  MATH  Google Scholar 

  25. Ahad FR, Enakoutsa K, Solanki KN, Bammann DJ (2014) Nonlocal modeling in high-velocity impact failure of 6061-T6 aluminum. Int J Plast 55:108–132

    Article  Google Scholar 

  26. Bažant ZP, Jirásek M (2002) Nonlocal integral formulations of plasticity and damage: survey of progress. ASCE J Eng Mech 128:1119–1149

    Article  Google Scholar 

  27. Andrade FXC, Ceser De Sa JMA, Andrade Pires FM (2011) Ductile damage nonlocal model of integral-type at finite strains: formulation and numerical issues. Int J Damage Mech 20:515–557

    Article  Google Scholar 

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Funding

This study was supported by the National Natural Science Funding of China (No. 51875512) and the Project of National Key Laboratory of Deep-Sea Manned Equipment of China.

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Correspondence to P. F. Liu.

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Liu, P.F., Li, X.K. Dynamic Void Growth and Localization Behaviors of Glassy Polymer Using Nonlocal Explicit Finite Element Analysis. J Peridyn Nonlocal Model 1, 3–13 (2019). https://doi.org/10.1007/s42102-018-0003-y

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  • DOI: https://doi.org/10.1007/s42102-018-0003-y

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