Top

Computational Mechanics

Published in:

31-01-2020 | Original Paper

An enriched finite volume formulation for the simulation of ductile material failure under shock loading

Authors: Marie Gorecki, Guillaume Peillex, Laurianne Pillon, Nicolas Moës

Published in: Computational Mechanics | Issue 5/2020

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

A method is proposed to model failure under shock loading. Finite Volume schemes are known to be efficient to take into account the density variations in the shock regions. The proposed method, called eXtended Finite Volume (XFV), is able to model failure in a finite volume framework. The material degradation is modeled using a cohesive zone model to dissipate the amount of energy required to create new surfaces. The XFV method allows to locate the cohesive surface inside elements and to introduce a displacement jump inside the cracked cells without remeshing, in an explicit dynamics finite volume framework. Attention is paid to the mass lumping and scheme stability. The XFV method is validated to simulate a plate impact experiment. It shows the ability to reproduce spall patterns and free surface velocities. However, numerical stability issues still need to be fixed before being able to compare the simulation with experimental data.

previous article Non-localised contact between beams with circular and elliptical cross-sections

next article Application of PDS–FEM to simulate dynamic crack propagation and supershear rupture

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

\(\sigma _{N0}\) depictes the cohesive traction projected on the cohesive surface, as a force per unit surface.

Cases A and E are limit cases respectively approaching a linear cohesive law and a Dugdale model. However, in the implementation of the cohesive model in Hesione code, it is not possible to choose \(\delta _1 = 0 \) or \(\delta _1 = \delta _{Nc}\). These values have therefore been approximated to get \(\delta _1 \approx 0 \) and \( \delta _1 \approx \delta _{Nc} \).

Once again, cases A and E are limit cases corresponding respectively to a linear cohesive law and a Dugdale model.

Roy G (2003) Vers une modélisation approfondie de l’endommagement ductile dynamique: investigation expérimentale d’une nuance de tantale et développements théoriques. PhD thesis, Poitiers

Besson J (2010) Continuum models of ductile fracture: a review. Int J Damage Mech 19(1):3–52

Johnson JN (1981) Dynamic fracture and spallation in ductile solids. J Appl Phys 52(4):2812–2825

Czarnota C, Jacques N, Mercier S, Molinari A (2008) Modelling of dynamic ductile fracture and application to the simulation of plate impact tests on tantalum. J Mech Phys Solids 56(4):1624–1650

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

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

Bargellini R, Besson J, Lorentz E, Michel-Ponnelle S (2009) A non-local finite element based on volumetric strain gradient: application to ductile fracture. Comput Mater Sci 45(3):762–767

Ambati M, Gerasimov T, De Lorenzis L (2015) Phase-field modeling of ductile fracture. Comput Mech 55(5):1017–1040MathSciNetMATH

Dugdale DS (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8(2):100–104

10.

Needleman A (1987) A continuum model for void nucleation by inclusion debonding. J Appl Mech 54(3):525–531MATH

11.

Gullerud AS, Gao X, Dodds RH Jr, Haj-Ali R (2000) Simulation of ductile crack growth using computational cells: numerical aspects. Eng Fract Mech 66(1):65–92

12.

Moës N, Stolz C, Bernard P-E, Chevaugeon N (2011) A level set based model for damage growth: the thick level set approach. Int J Numer Methods Eng 86(3):358–380MathSciNetMATH

13.

Stershic AJ, Dolbow JE, Moës N (2017) The thick level-set model for dynamic fragmentation. Eng Fract Mech 172:39–60

14.

Zhang H, Li L, An X, Ma G (2010) Numerical analysis of 2-d crack propagation problems using the numerical manifold method. Eng Anal Bound Elem 34(1):41–50MathSciNetMATH

15.

Terada K, Asai M, Yamagishi M (2003) Finite cover method for linear and non-linear analyses of heterogeneous solids. Int J Numer Methods Eng 58(9):1321–1346MATH

16.

Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46(1):131–150MathSciNetMATH

17.

Hansbo A, Hansbo P (2004) A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Comput Methods Appl Mech Eng 193(33):3523–3540MathSciNetMATH

18.

Areias PM, Belytschko T (2006) A comment on the article “A finite element method for simulation of strong and weak discontinuities in solid mechanics” by a. hansbo and p. hansbo [comput. methods appl. mech. engrg. 193 (2004) 3523–3540]. Comput Methods Appl Mech Eng 195(9):1275–1276MATH

19.

Rozycki P, Moës N, Bechet E, Dubois C (2008) X-fem explicit dynamics for constant strain elements to alleviate mesh constraints on internal or external boundaries. Comput Methods Appl Mech Eng 197(5):349–363MATH

20.

Song J-H, Areias P, Belytschko T (2006) A method for dynamic crack and shear band propagation with phantom nodes. Int J Numer Methods Eng 67(6):868–893MATH

21.

Menouillard T, Rethore J, Combescure A, Bung H (2006) Efficient explicit time stepping for the extended finite element method (x-fem). Int J Numer Methods Eng 68(9):911–939MathSciNetMATH

22.

Elguedj T, Gravouil A, Maigre H (2009) An explicit dynamics extended finite element method. Part 1: mass lumping for arbitrary enrichment functions. Comput Methods Appl Mech Eng 198(30):2297–2317MATH

23.

Menouillard T, Rethore J, Moes N, Combescure A, Bung H (2008) Mass lumping strategies for x-fem explicit dynamics: application to crack propagation. Int J Numer Methods Eng 74(3):447–474MathSciNetMATH

24.

VonNeumann J, Richtmyer RD (1950) A method for the numerical calculation of hydrodynamic shocks. J Appl Phys 21(3):232–237MathSciNetMATH

25.

Wilkins M L (1963) Calculation of elastic-plastic flow. Technical report, California Univ Livermore Radiation Lab

26.

Flament J, Perlat J-P (2011) Méthode de couplage euler-lagrange pour la dynamique rapide. In 10e colloque national en calcul des structures

27.

Longère P, Dragon A (2013) Description of shear failure in ductile metals via back stress concept linked to damage-microporosity softening. Eng Fract Mech 98:92–108

28.

Desgraz JC, Lascaux P (1976) Stabilite de la discretisation des equations de l’hydrodynamique lagrangienne 2d. Computing Methods in Applied Sciences. Springer, Berlin, pp 510–529

29.

Grüneisen E (1912) Theorie des festen zustandes einatomiger elemente. Ann Phys 344(12):257–306MATH

30.

McQueen RG, Marsh SP, Taylor JW, Fritz JN, Carter WJ (1970) The equation of state of solids from shock wave studies. In: High velocity impact phenomena, vol 293, pp 293–417

31.

Steinberg D, Cochran S, Guinan M (1980) A constitutive model for metals applicable at high-strain rate. J Appl Phys 51(3):1498–1504

32.

Wilkins ML (1980) Use of artificial viscosity in multidimensional fluid dynamic calculations. J Comput Phys 36(3):281–303MathSciNetMATH

33.

Tvergaard V, Hutchinson JW (1992) The relation between crack growth resistance and fracture process parameters in elastic-plastic solids. J Mech Phys Solids 40(6):1377–1397MATH

34.

Scheider I (2009) Derivation of separation laws for cohesive models in the course of ductile fracture. Eng Fract Mech 76(10):1450–1459

35.

Baranger J, Maitre J-F (1996) Connection between finite volume and mixed finite element methods. ESAIM Math Modell Numer Anal 30(4):445–465MathSciNetMATH

36.

Chan RK-C (1975) A generalized arbitrary Lagrangian–Eulerian method for incompressible flows with sharp interfaces. J Comput Phys 17(3):311–331MATH

37.

Buy F, Llorca F (2002) Shock wave effects in copper: design of an experimental device for post recovery mechanical testing. In: AIP conference proceedings, vol 620. AIP, pp 319–322

38.

Courant R, Friedrichs K, Lewy H (1928) Über die partiellen differenzengleichungen der mathematischen physik. Math Ann 100(1):32–74MathSciNetMATH

Title: An enriched finite volume formulation for the simulation of ductile material failure under shock loading
Authors: Marie Gorecki
Guillaume Peillex
Laurianne Pillon
Nicolas Moës
Publication date: 31-01-2020
Publisher: Springer Berlin Heidelberg
Published in: Computational Mechanics / Issue 5/2020
Print ISSN: 0178-7675
Electronic ISSN: 1432-0924
DOI: https://doi.org/10.1007/s00466-020-01818-0

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 5/2020

Isogeometric analysis of thin Reissner–Mindlin shells: locking phenomena and B-bar method

Mixed peridynamic formulations for compressible and incompressible finite deformations

Strain gradient finite element model for finite deformation theory: size effects and shear bands

Method for real-time simulation of haptic interaction with deformable objects using GPU-based parallel computing and homogeneous hexahedral elements

A phase-field model of thermo-elastic coupled brittle fracture with explicit time integration

A consistent strain-based beam element with quaternion representation of rotations