Skip to main content
Erschienen in: Computational Mechanics 1-2/2018

13.09.2017 | Original Paper

Finite element formulation with embedded weak discontinuities for strain localization under dynamic conditions

verfasst von: Tao Jin, Hashem M. Mourad, Curt A. Bronkhorst, Veronica Livescu

Erschienen in: Computational Mechanics | Ausgabe 1-2/2018

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

We present an explicit finite element formulation designed for the treatment of strain localization under highly dynamic conditions. A material stability analysis is used to detect the onset of localization behavior. Finite elements with embedded weak discontinuities are employed with the aim of representing subsequent localized deformation accurately. The formulation and its algorithmic implementation are described in detail. Numerical results are presented to illustrate the usefulness of this computational framework in the treatment of strain localization under highly dynamic conditions, and to examine its performance characteristics in the context of two-dimensional plane-strain problems.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

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!

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!

Anhänge
Nur mit Berechtigung zugänglich
Fußnoten
1
The notched bar geometry is often used in problems involving void formation and growth [60, 61]. We use it here to exercise the strain localization capabilities of the present numerical framework, in loading regimes where voiding is generally not observed.
 
Literatur
1.
Zurück zum Zitat Ortiz M, Leroy Y, Needleman A (1987) A finite element method for localized failure analysis. Comput Methods Appl Mech Eng 61:189–214CrossRefMATH Ortiz M, Leroy Y, Needleman A (1987) A finite element method for localized failure analysis. Comput Methods Appl Mech Eng 61:189–214CrossRefMATH
2.
Zurück zum Zitat Rittel D, Wang ZG, Merzer M (2006) Adiabatic shear failure and dynamic stored energy of cold work. Phys Rev Lett 96:075502(4)CrossRef Rittel D, Wang ZG, Merzer M (2006) Adiabatic shear failure and dynamic stored energy of cold work. Phys Rev Lett 96:075502(4)CrossRef
3.
Zurück zum Zitat Bronkhorst CA, Cerreta EK, Xue Q, Maudlin PJ, Mason TA, Gray GT III (2006) An experimental and numerial study of the localization behavior of tantalum and stainless steel. Int J Plast 22:1304–1335CrossRefMATH Bronkhorst CA, Cerreta EK, Xue Q, Maudlin PJ, Mason TA, Gray GT III (2006) An experimental and numerial study of the localization behavior of tantalum and stainless steel. Int J Plast 22:1304–1335CrossRefMATH
4.
Zurück zum Zitat Linder C, Armero F (2007) Finite elements with embedded strong discontinuities for the modeling of failure in solids. Int J Numer Methods Eng 72(12):1391–1433MathSciNetCrossRefMATH Linder C, Armero F (2007) Finite elements with embedded strong discontinuities for the modeling of failure in solids. Int J Numer Methods Eng 72(12):1391–1433MathSciNetCrossRefMATH
5.
Zurück zum Zitat Plohr JN, Plohr BJ (2016) Numerical simulation of systems of shear bands in ductile metal with inclusions. AIP Adv 6(025):008 Plohr JN, Plohr BJ (2016) Numerical simulation of systems of shear bands in ductile metal with inclusions. AIP Adv 6(025):008
6.
Zurück zum Zitat Bronkhorst CA, Gray GT III, Addessio FL, Livescu V, Bourne NK, MacDonald SA, Withers PJ (2016) Response and representation of ductile damage under varying shock loading conditions in tantalum. J Appl Phys 119(085):103 Bronkhorst CA, Gray GT III, Addessio FL, Livescu V, Bourne NK, MacDonald SA, Withers PJ (2016) Response and representation of ductile damage under varying shock loading conditions in tantalum. J Appl Phys 119(085):103
7.
Zurück zum Zitat Mourad HM, Bronkhorst CA, Livescu V, Plohr JN, Cerreta EK (2017) Modeling and simulation framework for dynamic strain localization in elasto-viscoplastic metallic materials subject to large deformations. Int J Plast 88:1–26CrossRef Mourad HM, Bronkhorst CA, Livescu V, Plohr JN, Cerreta EK (2017) Modeling and simulation framework for dynamic strain localization in elasto-viscoplastic metallic materials subject to large deformations. Int J Plast 88:1–26CrossRef
8.
Zurück zum Zitat Wright TW, Batra RC (1985) The initiation and growth of adiabatic shear bands. Int J Plast 1:205–212CrossRef Wright TW, Batra RC (1985) The initiation and growth of adiabatic shear bands. Int J Plast 1:205–212CrossRef
9.
Zurück zum Zitat Anand L, Kim KH, Shawki TG (1987) Onset of shear localization in viscoplastic solids. J Mech Phys Solids 35:407–429CrossRefMATH Anand L, Kim KH, Shawki TG (1987) Onset of shear localization in viscoplastic solids. J Mech Phys Solids 35:407–429CrossRefMATH
10.
Zurück zum Zitat Shawki T, Clifton R (1989) Shear band formation in thermal viscoplastic materials. Mech Mater 8:13–43CrossRef Shawki T, Clifton R (1989) Shear band formation in thermal viscoplastic materials. Mech Mater 8:13–43CrossRef
11.
Zurück zum Zitat Zhou M, Rosakis AJ, Ravichandran G (1996) Dynamically propagating shear bands in impact-loaded prenotched plates—I. Experimental investigations of temperature signatures and propagation speed. J Mech Phys Solids 44:981–1006CrossRef Zhou M, Rosakis AJ, Ravichandran G (1996) Dynamically propagating shear bands in impact-loaded prenotched plates—I. Experimental investigations of temperature signatures and propagation speed. J Mech Phys Solids 44:981–1006CrossRef
12.
Zurück zum Zitat Wright TW (2002) The physics and mathematics of adiabatic shear bands. Cambridge University Press, CambridgeMATH Wright TW (2002) The physics and mathematics of adiabatic shear bands. Cambridge University Press, CambridgeMATH
13.
Zurück zum Zitat Osovski S, Rittel D, Venkert A (2013) The respective influence of microstructural and thermal softening on adiabatic shear localization. Mech Mater 56:11–22CrossRef Osovski S, Rittel D, Venkert A (2013) The respective influence of microstructural and thermal softening on adiabatic shear localization. Mech Mater 56:11–22CrossRef
14.
Zurück zum Zitat Wang BF, Liu ZL, Wang XY, Li ZZ (2014) An EBSD investigation on deformation-induced shear bands in a low nickel austenitic stainless steel under controlled shock-loading conditions. Mater Sci Eng A 610:301–308CrossRef Wang BF, Liu ZL, Wang XY, Li ZZ (2014) An EBSD investigation on deformation-induced shear bands in a low nickel austenitic stainless steel under controlled shock-loading conditions. Mater Sci Eng A 610:301–308CrossRef
15.
Zurück zum Zitat Fish J, Belytschko T (1988) Elements with embedded lozalization zones for large deformation problems. Compos Struct 30:247–256CrossRefMATH Fish J, Belytschko T (1988) Elements with embedded lozalization zones for large deformation problems. Compos Struct 30:247–256CrossRefMATH
16.
Zurück zum Zitat Xue Q, Gray GT III, Henrie BL, Maloy SA, Chen SR (2005) Influence of shock prestraining on the formation of shear localization in 304 stainless steel. Metall Mater Trans A 36:1471–1486CrossRef Xue Q, Gray GT III, Henrie BL, Maloy SA, Chen SR (2005) Influence of shock prestraining on the formation of shear localization in 304 stainless steel. Metall Mater Trans A 36:1471–1486CrossRef
17.
Zurück zum Zitat Belytschko T, Chiang HY, Plaskacz E (1994) High resolution two-dimensional shear band computations: imperfections and mesh dependence. Comput Methods Appl Mech Eng 119(1):1–15CrossRefMATH Belytschko T, Chiang HY, Plaskacz E (1994) High resolution two-dimensional shear band computations: imperfections and mesh dependence. Comput Methods Appl Mech Eng 119(1):1–15CrossRefMATH
18.
Zurück zum Zitat Wilson E, Taylor R, Doherty W, Ghaboussi J (1973) Incompatible displacement models. In: Fenves SJ, Perrone N, Robinson AR, Schnobrich WC (eds) Numerical and computer methods in structural mechanics. Academic Press Inc., New York, pp 43–57 Wilson E, Taylor R, Doherty W, Ghaboussi J (1973) Incompatible displacement models. In: Fenves SJ, Perrone N, Robinson AR, Schnobrich WC (eds) Numerical and computer methods in structural mechanics. Academic Press Inc., New York, pp 43–57
19.
Zurück zum Zitat Hadamard J (1903) Leçons sur la propagation des ondes et les équations de l’hydrodynamique. A. Hermann, ParisMATH Hadamard J (1903) Leçons sur la propagation des ondes et les équations de l’hydrodynamique. A. Hermann, ParisMATH
21.
Zurück zum Zitat Belytschko T, Fish J, Engelmann BE (1988) A finite element with embedded localization zones. Comput Methods Appl Mech Eng 70:59–89CrossRefMATH Belytschko T, Fish J, Engelmann BE (1988) A finite element with embedded localization zones. Comput Methods Appl Mech Eng 70:59–89CrossRefMATH
22.
Zurück zum Zitat Fish J, Belytschko T (1990) A finite element with a unidirectionally enriched strain field for localization analysis. Comput Methods Appl Mech Eng 78(2):181–200MathSciNetCrossRefMATH Fish J, Belytschko T (1990) A finite element with a unidirectionally enriched strain field for localization analysis. Comput Methods Appl Mech Eng 78(2):181–200MathSciNetCrossRefMATH
23.
Zurück zum Zitat Simo JC, Oliver J, Armero F (1993) An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids. Comput Mech 12:277–296MathSciNetCrossRefMATH Simo JC, Oliver J, Armero F (1993) An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids. Comput Mech 12:277–296MathSciNetCrossRefMATH
24.
Zurück zum Zitat Armero F, Garikipati K (1995) Recent advances in the analysis and numerical simulation of strain localization in inelastic solids. In: Owen D, Oñate E, Hinton E (eds) Proceedings of the 4th international conference on computational plasticity: fundamentals and applications, pp 547–561 Armero F, Garikipati K (1995) Recent advances in the analysis and numerical simulation of strain localization in inelastic solids. In: Owen D, Oñate E, Hinton E (eds) Proceedings of the 4th international conference on computational plasticity: fundamentals and applications, pp 547–561
25.
Zurück zum Zitat Oliver J (1995) Continuum modelling of strong discontinuities in solid mechanics using damage models. Comput Mech 17:49–61CrossRefMATH Oliver J (1995) Continuum modelling of strong discontinuities in solid mechanics using damage models. Comput Mech 17:49–61CrossRefMATH
26.
Zurück zum Zitat Oliver J (1996a) Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. Part 1: fundamentals. Int J Numer Methods Eng 39:3575–3600CrossRefMATH Oliver J (1996a) Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. Part 1: fundamentals. Int J Numer Methods Eng 39:3575–3600CrossRefMATH
27.
Zurück zum Zitat Oliver J (1996b) Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. Part 2: numerical simulation. Int J Numer Methods Eng 39:3601–3623CrossRef Oliver J (1996b) Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. Part 2: numerical simulation. Int J Numer Methods Eng 39:3601–3623CrossRef
28.
Zurück zum Zitat Armero F, Garikipati K (1996) An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids. Int J Solids Struct 33(20):2863–2885MathSciNetCrossRefMATH Armero F, Garikipati K (1996) An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids. Int J Solids Struct 33(20):2863–2885MathSciNetCrossRefMATH
29.
Zurück zum Zitat Armero F, Linder C (2008) New finite elements with embedded strong discontinuities in the finite deformation range. Comput Methods Appl Mech Eng 197:3138–3170MathSciNetCrossRefMATH Armero F, Linder C (2008) New finite elements with embedded strong discontinuities in the finite deformation range. Comput Methods Appl Mech Eng 197:3138–3170MathSciNetCrossRefMATH
30.
Zurück zum Zitat Armero F, Linder C (2009) Numerical simulation of dynamic fracture using finite elements with embedded discontinuities. Int J Fract 160:119–141CrossRefMATH Armero F, Linder C (2009) Numerical simulation of dynamic fracture using finite elements with embedded discontinuities. Int J Fract 160:119–141CrossRefMATH
31.
Zurück zum Zitat Armero F, Kim J (2012) Three-dimensional finite elements with embedded strong discontinuities to model material failure in the infinitesimal range. Int J Numer Methods Eng 91:1291–1330MathSciNetCrossRef Armero F, Kim J (2012) Three-dimensional finite elements with embedded strong discontinuities to model material failure in the infinitesimal range. Int J Numer Methods Eng 91:1291–1330MathSciNetCrossRef
32.
Zurück zum Zitat Fries TP, Belytschko T (2010) The extended/generalized finite element method: an overview of the method and its applications. Int J Numer Methods Eng 84:253–304MathSciNetMATH Fries TP, Belytschko T (2010) The extended/generalized finite element method: an overview of the method and its applications. Int J Numer Methods Eng 84:253–304MathSciNetMATH
33.
Zurück zum Zitat Sukumar N, Dolbow J, Moës N (2015) Extended finite element method in computational fracture mechanics: a retrospective examination. Int J Fract 196:189–206CrossRef Sukumar N, Dolbow J, Moës N (2015) Extended finite element method in computational fracture mechanics: a retrospective examination. Int J Fract 196:189–206CrossRef
34.
Zurück zum Zitat Garikipati K, Hughes TJ (1998) A study of strain localization in a multiple scale framework the one-dimensional problem. Comput Methods Appl Mech Eng 159:193–222MathSciNetCrossRefMATH Garikipati K, Hughes TJ (1998) A study of strain localization in a multiple scale framework the one-dimensional problem. Comput Methods Appl Mech Eng 159:193–222MathSciNetCrossRefMATH
35.
Zurück zum Zitat Garikipati K, Hughes T (2000) A variational multiscale approach to strain localization formulation for multidimensional problems. Comput Methods Appl Mech Eng 188:39–60MathSciNetCrossRefMATH Garikipati K, Hughes T (2000) A variational multiscale approach to strain localization formulation for multidimensional problems. Comput Methods Appl Mech Eng 188:39–60MathSciNetCrossRefMATH
37.
Zurück zum Zitat Li S, Liu WK, Qian D, Guduru PR, Rosakis AJ (2001) Dynamic shear band propagation and micro-structure of adiabatic shear band. Comput Methods Appl Mech Eng 191:73–92CrossRefMATH Li S, Liu WK, Qian D, Guduru PR, Rosakis AJ (2001) Dynamic shear band propagation and micro-structure of adiabatic shear band. Comput Methods Appl Mech Eng 191:73–92CrossRefMATH
38.
Zurück zum Zitat Li S, Liu WK, Rosakis AJ, Belytschko T, Hao W (2002) Mesh-free Galerkin simulations of dynamic shear band propagation and failure mode transition. Int J Solids Struct 39:1213–1240CrossRefMATH Li S, Liu WK, Rosakis AJ, Belytschko T, Hao W (2002) Mesh-free Galerkin simulations of dynamic shear band propagation and failure mode transition. Int J Solids Struct 39:1213–1240CrossRefMATH
39.
Zurück zum Zitat Jirásek M (2000) Comparative study on finite elements with embedded discontinuities. Comput Methods Appl Mech Eng 188:307–330CrossRefMATH Jirásek M (2000) Comparative study on finite elements with embedded discontinuities. Comput Methods Appl Mech Eng 188:307–330CrossRefMATH
40.
Zurück zum Zitat Oliver J, Huespe A, Sanchez P (2006) A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM. Comput Methods Appl Mech Eng 195:4732–4752MathSciNetCrossRefMATH Oliver J, Huespe A, Sanchez P (2006) A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM. Comput Methods Appl Mech Eng 195:4732–4752MathSciNetCrossRefMATH
41.
Zurück zum Zitat Borja RI (2008) Assumed enhanced strain and the extended finite element methods: a unification of concepts. Comput Methods Appl Mech Eng 197:2789–2803MathSciNetCrossRefMATH Borja RI (2008) Assumed enhanced strain and the extended finite element methods: a unification of concepts. Comput Methods Appl Mech Eng 197:2789–2803MathSciNetCrossRefMATH
42.
Zurück zum Zitat Wu JY, Li FB, Xu SL (2015) Extended embedded finite elements with continuous displacement jumps for the modeling of localized failure in solids. Comput Methods Appl Mech Eng 285:346–378MathSciNetCrossRef Wu JY, Li FB, Xu SL (2015) Extended embedded finite elements with continuous displacement jumps for the modeling of localized failure in solids. Comput Methods Appl Mech Eng 285:346–378MathSciNetCrossRef
43.
Zurück zum Zitat Dodd B, Bai Y (2012) Adiabatic shear localization: frontiers and advances, 2nd edn. Elsevier, London Dodd B, Bai Y (2012) Adiabatic shear localization: frontiers and advances, 2nd edn. Elsevier, London
44.
Zurück zum Zitat Brun J, Cobbold P (1980) Strain heating and thermal softening in continental shear zones: a review. J Struct Geol 2(1–2):149–158CrossRef Brun J, Cobbold P (1980) Strain heating and thermal softening in continental shear zones: a review. J Struct Geol 2(1–2):149–158CrossRef
45.
Zurück zum Zitat Molinari A, Clifton R (1987) Analytical characterization of shear localization in thermoviscoplastic materials. J Appl Mech 54:806–812CrossRefMATH Molinari A, Clifton R (1987) Analytical characterization of shear localization in thermoviscoplastic materials. J Appl Mech 54:806–812CrossRefMATH
46.
47.
Zurück zum Zitat Rittel D, Landau P, Venkert A (2008) Dynamic recrystallization as a potential cause for adiabatic shear failure. Phys Rev Lett 101:165501(4)CrossRef Rittel D, Landau P, Venkert A (2008) Dynamic recrystallization as a potential cause for adiabatic shear failure. Phys Rev Lett 101:165501(4)CrossRef
49.
Zurück zum Zitat Mourad HM, Bronkhorst CA, Addessio FL, Cady CM, Brown DW, Chen SR, Gray GT III (2014) Incrementally objective implicit integration of hypoelastic–viscoplastic constitutive equations based on the mechanical threshold strength model. Comput Mech 53:941–955MathSciNetCrossRefMATH Mourad HM, Bronkhorst CA, Addessio FL, Cady CM, Brown DW, Chen SR, Gray GT III (2014) Incrementally objective implicit integration of hypoelastic–viscoplastic constitutive equations based on the mechanical threshold strength model. Comput Mech 53:941–955MathSciNetCrossRefMATH
50.
Zurück zum Zitat Hughes TJR, Winget J (1980) Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis. Int J Numer Methods Eng 15:1862–1867MathSciNetCrossRefMATH Hughes TJR, Winget J (1980) Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis. Int J Numer Methods Eng 15:1862–1867MathSciNetCrossRefMATH
51.
Zurück zum Zitat Simo JC, Hughes TJR (1998) Computational inelasticity. Springer, New YorkMATH Simo JC, Hughes TJR (1998) Computational inelasticity. Springer, New YorkMATH
52.
Zurück zum Zitat Follansbee PS, Kocks UF (1988) A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable. Acta Metall 36:81–93CrossRef Follansbee PS, Kocks UF (1988) A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable. Acta Metall 36:81–93CrossRef
53.
Zurück zum Zitat Follansbee PS, Huang JC, Gray GT III (1990) Low-temperature and high-strain-rate deformation of nickel and nickel–carbon alloys and analysis of the constitutive behavior according to an internal state variable model. Acta Metall Mater 38:1241–1254 Follansbee PS, Huang JC, Gray GT III (1990) Low-temperature and high-strain-rate deformation of nickel and nickel–carbon alloys and analysis of the constitutive behavior according to an internal state variable model. Acta Metall Mater 38:1241–1254
54.
Zurück zum Zitat Wang B, Liu Z, Wang B, Zhao S, Sun J (2014) Microstructural evolution in adiabatic shear band in the ultrafine-grained austenitic stainless steel processed by multi-axial compression. Mater Sci Eng A 611:100–107CrossRef Wang B, Liu Z, Wang B, Zhao S, Sun J (2014) Microstructural evolution in adiabatic shear band in the ultrafine-grained austenitic stainless steel processed by multi-axial compression. Mater Sci Eng A 611:100–107CrossRef
55.
Zurück zum Zitat Porter DA, Easterling KE (1992) Phase transformations in metals and alloys, 2nd edn. Chapman & Hall, LondonCrossRef Porter DA, Easterling KE (1992) Phase transformations in metals and alloys, 2nd edn. Chapman & Hall, LondonCrossRef
56.
Zurück zum Zitat Davies CHJ (1997) Growth of nuclei in a cellular automaton simulation of recrystallisation. Scr Mater 36:35–40CrossRef Davies CHJ (1997) Growth of nuclei in a cellular automaton simulation of recrystallisation. Scr Mater 36:35–40CrossRef
57.
Zurück zum Zitat Mourad HM, Garikipati K (2006) Advances in the numerical treatment of grain-boundary migration: coupling with mass transport and mechanics. Comput Methods Appl Mech Eng 196:595–607CrossRefMATH Mourad HM, Garikipati K (2006) Advances in the numerical treatment of grain-boundary migration: coupling with mass transport and mechanics. Comput Methods Appl Mech Eng 196:595–607CrossRefMATH
58.
Zurück zum Zitat Ling X, Belytschko T (2009) Thermal softening induced plastic instability in rate-dependent materials. J Mech Phys Solids 57:788–802CrossRefMATH Ling X, Belytschko T (2009) Thermal softening induced plastic instability in rate-dependent materials. J Mech Phys Solids 57:788–802CrossRefMATH
59.
Zurück zum Zitat Malvern L (1969) Introduction to the mechanics of a continuous medium. Prentice-Hall, Upper Saddle River, NJMATH Malvern L (1969) Introduction to the mechanics of a continuous medium. Prentice-Hall, Upper Saddle River, NJMATH
60.
Zurück zum Zitat Tvergaard V, Needleman A (1984) Analysis of the cup-cone fracture in a round tensile bar. Acta Metall 32:157–169CrossRef Tvergaard V, Needleman A (1984) Analysis of the cup-cone fracture in a round tensile bar. Acta Metall 32:157–169CrossRef
61.
Zurück zum Zitat Huespe A, Needleman A, Oliver J, Sánchez P (2009) A finite thickness band method for ductile fracture analysis. Int J Plast 25:2349–2365CrossRef Huespe A, Needleman A, Oliver J, Sánchez P (2009) A finite thickness band method for ductile fracture analysis. Int J Plast 25:2349–2365CrossRef
62.
Zurück zum Zitat J ager P, Steinmann P, Kuhl E (2008) Modeling three-dimensional crack propagation—a comparison of crack path tracking strategies. Int J Numer Methods Eng 76:1328–1352MathSciNetCrossRefMATH J ager P, Steinmann P, Kuhl E (2008) Modeling three-dimensional crack propagation—a comparison of crack path tracking strategies. Int J Numer Methods Eng 76:1328–1352MathSciNetCrossRefMATH
63.
Zurück zum Zitat Linder C, Armero F (2007) Finite elements with embedded strong discontinuities for the modeling of failure in solids. Int J Numer Methods Eng 72:1391–1433MathSciNetCrossRefMATH Linder C, Armero F (2007) Finite elements with embedded strong discontinuities for the modeling of failure in solids. Int J Numer Methods Eng 72:1391–1433MathSciNetCrossRefMATH
64.
Zurück zum Zitat Hughes TJR (1980) Generalization of selective integration procedures to anisotropic and nonlinear media. Int J Numer Methods Eng 15:1413–1418MathSciNetCrossRefMATH Hughes TJR (1980) Generalization of selective integration procedures to anisotropic and nonlinear media. Int J Numer Methods Eng 15:1413–1418MathSciNetCrossRefMATH
65.
Zurück zum Zitat Belytschko T, Bachrach WE (1986) Efficient implementation of quadrilaterals with high coarse-mesh accuracy. Comput Methods Appl Mech Eng 54:279–301MathSciNetCrossRefMATH Belytschko T, Bachrach WE (1986) Efficient implementation of quadrilaterals with high coarse-mesh accuracy. Comput Methods Appl Mech Eng 54:279–301MathSciNetCrossRefMATH
Metadaten
Titel
Finite element formulation with embedded weak discontinuities for strain localization under dynamic conditions
verfasst von
Tao Jin
Hashem M. Mourad
Curt A. Bronkhorst
Veronica Livescu
Publikationsdatum
13.09.2017
Verlag
Springer Berlin Heidelberg
Erschienen in
Computational Mechanics / Ausgabe 1-2/2018
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-017-1470-8

Weitere Artikel der Ausgabe 1-2/2018

Computational Mechanics 1-2/2018 Zur Ausgabe

Neuer Inhalt