Skip to main content
Erschienen in: Computational Mechanics 1/2016

01.01.2016 | Original Paper

A phase-field model for ductile fracture at finite strains and its experimental verification

verfasst von: Marreddy Ambati, Roland Kruse, Laura De Lorenzis

Erschienen in: Computational Mechanics | Ausgabe 1/2016

Einloggen

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

search-config
loading …

Abstract

In this paper, a phase-field model for ductile fracture previously proposed in the kinematically linear regime is extended to the three-dimensional finite strain setting, and its predictions are qualitatively and quantitatively compared with several experimental results, both from ad-hoc tests carried out by the authors and from the available literature. The proposed model is based on the physical assumption that fracture occurs when a scalar measure of the accumulated plastic strain reaches a critical value, and such assumption is introduced through the dependency of the phase-field degradation function on this scalar measure. The proposed model is able to capture the experimentally observed sequence of elasto-plastic deformation, necking and fracture phenomena in flat specimens; the occurrence of cup-and-cone fracture patterns in axisymmetric specimens; the role played by notches and by their size on the measured displacement at fracture; and the sequence of distinct cracking events observed in more complex specimens.

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!

Literatur
1.
Zurück zum Zitat Besson J (2010) Continuum models of ductile fracture: a review. Int J Damage Mech 19(1):3–52CrossRef Besson J (2010) Continuum models of ductile fracture: a review. Int J Damage Mech 19(1):3–52CrossRef
2.
Zurück zum Zitat Trädegard A, Nilsson F, Östlund S (1998) FEM-remeshing technique applied to crack growth problems. Comput Methods Appl Mech Eng 160:115–131CrossRefMATH Trädegard A, Nilsson F, Östlund S (1998) FEM-remeshing technique applied to crack growth problems. Comput Methods Appl Mech Eng 160:115–131CrossRefMATH
3.
Zurück zum Zitat Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth: part I—yield criteria and flow rules for porous ductile media. J Eng Mater Technol 99:2–15CrossRef Gurson AL (1977) Continuum theory of ductile rupture by void nucleation and growth: part I—yield criteria and flow rules for porous ductile media. J Eng Mater Technol 99:2–15CrossRef
4.
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
5.
Zurück zum Zitat Lemaitre J (1985) A Continuous damage mechanics model for ductile fracture. J Eng Mater Technol 107:83–89CrossRef Lemaitre J (1985) A Continuous damage mechanics model for ductile fracture. J Eng Mater Technol 107:83–89CrossRef
7.
Zurück zum Zitat Bazant ZP, Pijaudier-Cabot G (1988) Non-local continuum damage. Localization, instability and convergence. J Appl Mech 55:287–294CrossRefMATH Bazant ZP, Pijaudier-Cabot G (1988) Non-local continuum damage. Localization, instability and convergence. J Appl Mech 55:287–294CrossRefMATH
8.
Zurück zum Zitat Peerlings RHJ, De Borst R, Brekelmans WAM, De Vree JHP, Spee I (1996) Some observations on localisation in non-local and gradient damage models. Eur J Mech 15A(6):937–953 Peerlings RHJ, De Borst R, Brekelmans WAM, De Vree JHP, Spee I (1996) Some observations on localisation in non-local and gradient damage models. Eur J Mech 15A(6):937–953
9.
Zurück zum Zitat Enakoutsa K, Leblond JB, Perrin G (2007) Numerical implementation and assessment of a phenomenological non-local model of ductile rupture. Comput Methods Appl Mech Eng 196(13–16):1946–1957CrossRefMATH Enakoutsa K, Leblond JB, Perrin G (2007) Numerical implementation and assessment of a phenomenological non-local model of ductile rupture. Comput Methods Appl Mech Eng 196(13–16):1946–1957CrossRefMATH
10.
Zurück zum Zitat Reusch F, Svendsen B, Klingbeil D (2003) Local and non-local Gurson-based ductile damage and failure modelling at large deformation. Eur J Mech 22A:779–792CrossRef Reusch F, Svendsen B, Klingbeil D (2003) Local and non-local Gurson-based ductile damage and failure modelling at large deformation. Eur J Mech 22A:779–792CrossRef
11.
Zurück zum Zitat Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46(1):131–150CrossRefMATH Moës N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46(1):131–150CrossRefMATH
12.
Zurück zum Zitat Ortiz M, Pandolfi A (1999) Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Int J Numer Methods Eng 44(9):1267–1282CrossRefMATH Ortiz M, Pandolfi A (1999) Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Int J Numer Methods Eng 44(9):1267–1282CrossRefMATH
13.
Zurück zum Zitat Alfano G, Crisfield MA (2001) Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues. Int J Numer Methods Eng 50:1701–1736CrossRefMATH Alfano G, Crisfield MA (2001) Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues. Int J Numer Methods Eng 50:1701–1736CrossRefMATH
14.
Zurück zum Zitat Dimitri R, De Lorenzis L, Wriggers P, Zavarise G (2014) NURBS- and T-spline-based isogeometric cohesive zone modeling of interface debonding. Comput Mech 54:369–388MathSciNetCrossRefMATH Dimitri R, De Lorenzis L, Wriggers P, Zavarise G (2014) NURBS- and T-spline-based isogeometric cohesive zone modeling of interface debonding. Comput Mech 54:369–388MathSciNetCrossRefMATH
15.
Zurück zum Zitat Scheider I, Brocks W (2003) Simulation of cup-cone fracture using the cohesive model. Eng Fract Mech 70(14):1943–1961CrossRef Scheider I, Brocks W (2003) Simulation of cup-cone fracture using the cohesive model. Eng Fract Mech 70(14):1943–1961CrossRef
16.
Zurück zum Zitat Seabra MRR, Sustarić P, Cesar de Sa JMA, Rodić T (2013) Damage driven crack initiation and propagation in ductile metals using XFEM. Comput Mech 52:161–179MathSciNetCrossRefMATH Seabra MRR, Sustarić P, Cesar de Sa JMA, Rodić T (2013) Damage driven crack initiation and propagation in ductile metals using XFEM. Comput Mech 52:161–179MathSciNetCrossRefMATH
17.
Zurück zum Zitat Broumand P, Khoei AR (2013) The extended finite element method for large deformation ductile fracture problems with a non-local damage-plasticity model. Eng Fract Mech 112–113:97–125CrossRef Broumand P, Khoei AR (2013) The extended finite element method for large deformation ductile fracture problems with a non-local damage-plasticity model. Eng Fract Mech 112–113:97–125CrossRef
18.
Zurück zum Zitat Crété JP, Longère P, Cadou JM (2014) Numerical modelling of crack propagation in ductile materials combining the GTN model and X-FEM. Comput Methods Appl Mech Eng 275:204–233CrossRefMATH Crété JP, Longère P, Cadou JM (2014) Numerical modelling of crack propagation in ductile materials combining the GTN model and X-FEM. Comput Methods Appl Mech Eng 275:204–233CrossRefMATH
19.
Zurück zum Zitat Francfort GA, Marigo JJ (1998) Revisiting brittle fractures as an energy minimization problem. J Mech Phys Solids 46:1319–1342MathSciNetCrossRefMATH Francfort GA, Marigo JJ (1998) Revisiting brittle fractures as an energy minimization problem. J Mech Phys Solids 46:1319–1342MathSciNetCrossRefMATH
21.
Zurück zum Zitat Bourdin B, Francfort GA, Marigo JJ (2000) Numerical experiments in revisited brittle fracture. J Mech Phys Solids 48:797–826MathSciNetCrossRefMATH Bourdin B, Francfort GA, Marigo JJ (2000) Numerical experiments in revisited brittle fracture. J Mech Phys Solids 48:797–826MathSciNetCrossRefMATH
22.
Zurück zum Zitat Amor H, Marigo JJ, Maurini C (2009) Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments. J Mech Phys Solids 57:1209–1229CrossRefMATH Amor H, Marigo JJ, Maurini C (2009) Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments. J Mech Phys Solids 57:1209–1229CrossRefMATH
23.
Zurück zum Zitat Kuhn C, Müller R (2010) A continuum phase field model for fracture. Eng Fract Mech 77:3625–3634CrossRef Kuhn C, Müller R (2010) A continuum phase field model for fracture. Eng Fract Mech 77:3625–3634CrossRef
24.
Zurück zum Zitat Miehe C, Hofacker M, Welschinger F (2010) A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits. Comput Methods Appl Mech Eng 199:2765–2778MathSciNetCrossRefMATH Miehe C, Hofacker M, Welschinger F (2010) A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits. Comput Methods Appl Mech Eng 199:2765–2778MathSciNetCrossRefMATH
25.
Zurück zum Zitat Borden MJ, Hughes TJR, Landis CM, Verhoosel CV (2014) A higher-order phase-field model for brittle fracture: formulation and analysis within the isogeometric analysis framework. Comput Methods Appl Mech Eng 273:100–118MathSciNetCrossRefMATH Borden MJ, Hughes TJR, Landis CM, Verhoosel CV (2014) A higher-order phase-field model for brittle fracture: formulation and analysis within the isogeometric analysis framework. Comput Methods Appl Mech Eng 273:100–118MathSciNetCrossRefMATH
26.
Zurück zum Zitat Ambati M, Gerasimov T, De Lorenzis L (2014) A review on phase-field models of brittle fracture and a new fast hybrid formulation. Comput Mech 55:383–405CrossRef Ambati M, Gerasimov T, De Lorenzis L (2014) A review on phase-field models of brittle fracture and a new fast hybrid formulation. Comput Mech 55:383–405CrossRef
27.
Zurück zum Zitat Duda FP, Ciarbonetti A, Sanchez PJ, Huespe AE (2014) A phase-field/gradient damage model for brittle fracture in elastic-plastic solids. Int J Plast 65:269–296CrossRef Duda FP, Ciarbonetti A, Sanchez PJ, Huespe AE (2014) A phase-field/gradient damage model for brittle fracture in elastic-plastic solids. Int J Plast 65:269–296CrossRef
28.
Zurück zum Zitat Borden MJ (2012) Isogeometric analysis of phase-field models for dynamic brittle and ductile fracture. PhD dissertation, The University of Texas at Austin Borden MJ (2012) Isogeometric analysis of phase-field models for dynamic brittle and ductile fracture. PhD dissertation, The University of Texas at Austin
29.
Zurück zum Zitat Miehe C, Hofacker M, Schänzel L, Aldakheel F (2014) Phase field modeling of fracture in multi-physics problems. Part II. Coupled brittle-to-ductile failure criteria and crack propagation in thermo-elastic-plastic solids. Comput Methods Appl Mech Eng 294:486–522 Miehe C, Hofacker M, Schänzel L, Aldakheel F (2014) Phase field modeling of fracture in multi-physics problems. Part II. Coupled brittle-to-ductile failure criteria and crack propagation in thermo-elastic-plastic solids. Comput Methods Appl Mech Eng 294:486–522
30.
Zurück zum Zitat Ambati M, Gerasimov T, De Lorenzis L (2015) Phase-field modeling of ductile fracture. Comput Mech 55:1017–1040 Ambati M, Gerasimov T, De Lorenzis L (2015) Phase-field modeling of ductile fracture. Comput Mech 55:1017–1040
31.
Zurück zum Zitat Alessi R, Marigo JJ, Vidoli S (2014) Gradient damage models coupled with plasticity and nucleation of cohesive cracks. Arch Ration Mech Anal 214:575–615MathSciNetCrossRefMATH Alessi R, Marigo JJ, Vidoli S (2014) Gradient damage models coupled with plasticity and nucleation of cohesive cracks. Arch Ration Mech Anal 214:575–615MathSciNetCrossRefMATH
32.
Zurück zum Zitat Alessi R, Marigo JJ, Vidoli S (2015) Gradient damage models coupled with plasticity: variational formulation and main properties. Mech Mater 80:351–367CrossRef Alessi R, Marigo JJ, Vidoli S (2015) Gradient damage models coupled with plasticity: variational formulation and main properties. Mech Mater 80:351–367CrossRef
33.
Zurück zum Zitat Wick D, Wick T, Hellmig RJ, Christ HJ (2015) Numerical simulations of crack propagation in screws with phase-field modeling. RICAM-Report No. 2015–11 Wick D, Wick T, Hellmig RJ, Christ HJ (2015) Numerical simulations of crack propagation in screws with phase-field modeling. RICAM-Report No. 2015–11
34.
Zurück zum Zitat Miehe C, Schänzel LM (2014) Phase field modeling of fracture in rubbery polymers: part I: finite elasticity coupled with brittle failure. J Mech Phys Solids 65:93–113MathSciNetCrossRef Miehe C, Schänzel LM (2014) Phase field modeling of fracture in rubbery polymers: part I: finite elasticity coupled with brittle failure. J Mech Phys Solids 65:93–113MathSciNetCrossRef
35.
Zurück zum Zitat Hesch C, Weinberg K (2014) Thermodynamically consistent algorithms for a finite-deformation phase-field approach to fracture. Int J Numer Methods Eng 99:906–925MathSciNetCrossRef Hesch C, Weinberg K (2014) Thermodynamically consistent algorithms for a finite-deformation phase-field approach to fracture. Int J Numer Methods Eng 99:906–925MathSciNetCrossRef
36.
Zurück zum Zitat Clayton JD, Knap J (2014) A geometrically nonlinear phase field theory of brittle fracture. Int J Fract 189:139–148CrossRef Clayton JD, Knap J (2014) A geometrically nonlinear phase field theory of brittle fracture. Int J Fract 189:139–148CrossRef
37.
Zurück zum Zitat Mesgarnejad A, Bourdin B, Khonsari MM (2015) Validation simulations for the variational approach to fracture. Comput Methods Appl Mech Eng 290:420–437MathSciNetCrossRef Mesgarnejad A, Bourdin B, Khonsari MM (2015) Validation simulations for the variational approach to fracture. Comput Methods Appl Mech Eng 290:420–437MathSciNetCrossRef
38.
Zurück zum Zitat Xiao H, Bruhns OT, Meyers A (2006) Elastoplasticity beyond small deformations. Acta Mech 182:31–111CrossRefMATH Xiao H, Bruhns OT, Meyers A (2006) Elastoplasticity beyond small deformations. Acta Mech 182:31–111CrossRefMATH
40.
Zurück zum Zitat Simo JC (1988) A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. Part I: continuum formulation. Comput Methods Appl Mech Eng 66:199–219MathSciNetCrossRefMATH Simo JC (1988) A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. Part I: continuum formulation. Comput Methods Appl Mech Eng 66:199–219MathSciNetCrossRefMATH
41.
Zurück zum Zitat Simo JC, Hughes TJR (1998) Computational inelasticity. Springer, New YorkMATH Simo JC, Hughes TJR (1998) Computational inelasticity. Springer, New YorkMATH
42.
Zurück zum Zitat Holzapfel GA (2000) Nonlinear solid mechanics. Wiley, ChichesterMATH Holzapfel GA (2000) Nonlinear solid mechanics. Wiley, ChichesterMATH
43.
Zurück zum Zitat Voce E (1955) A practical strain hardening function. Metallurgia 51:219–226 Voce E (1955) A practical strain hardening function. Metallurgia 51:219–226
44.
Zurück zum Zitat Simo JC (1988) A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. Part II: computational aspects. Comput Methods Appl Mech Eng 68:1–31CrossRefMATH Simo JC (1988) A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. Part II: computational aspects. Comput Methods Appl Mech Eng 68:1–31CrossRefMATH
45.
Zurück zum Zitat Guo J, Zhao S, Murakami R, Zang S (2013) Experimental and numerical investigation for ductile fracture of Al-alloy 5052 using modified Rousselier model. Comput Mater Sci 71:115–123CrossRef Guo J, Zhao S, Murakami R, Zang S (2013) Experimental and numerical investigation for ductile fracture of Al-alloy 5052 using modified Rousselier model. Comput Mater Sci 71:115–123CrossRef
46.
Zurück zum Zitat Simo JC, Rifai MS (1990) A class of mixed assumed strain methods and the method of incompatible modes. Int J Numer Methods Eng 29:1595–1638MathSciNetCrossRefMATH Simo JC, Rifai MS (1990) A class of mixed assumed strain methods and the method of incompatible modes. Int J Numer Methods Eng 29:1595–1638MathSciNetCrossRefMATH
47.
Zurück zum Zitat Simo JC, Armero F (1992) Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes. Int J Numer Methods Eng 33:1413–1449MathSciNetCrossRefMATH Simo JC, Armero F (1992) Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes. Int J Numer Methods Eng 33:1413–1449MathSciNetCrossRefMATH
48.
Zurück zum Zitat Hughes TJR (1980) Generalization of selective integration procedure to anisotropic and nonlinear media. Int J Numer Methods Eng 15:1413–1418CrossRefMATH Hughes TJR (1980) Generalization of selective integration procedure to anisotropic and nonlinear media. Int J Numer Methods Eng 15:1413–1418CrossRefMATH
49.
Zurück zum Zitat Hughes TJR (2000) The finite element method: linear static and dynamic finite element analysis. Dover Publications, Mineola Hughes TJR (2000) The finite element method: linear static and dynamic finite element analysis. Dover Publications, Mineola
50.
Zurück zum Zitat Simo JC, Taylor RL, Pister KS (1985) Variational and projection methods for the volume contraint in finite deformation elastoplasticity. Comput Methods Appl Mech Eng 51:177–208MathSciNetCrossRefMATH Simo JC, Taylor RL, Pister KS (1985) Variational and projection methods for the volume contraint in finite deformation elastoplasticity. Comput Methods Appl Mech Eng 51:177–208MathSciNetCrossRefMATH
51.
Zurück zum Zitat de Souza Neto EA, Peric D, Dutko M, Owen DRJ (1996) Design of simple low order finite elements for large strain analysis of nearly incompressible solids. Int J Solids Struct 33:3277–3296CrossRefMATH de Souza Neto EA, Peric D, Dutko M, Owen DRJ (1996) Design of simple low order finite elements for large strain analysis of nearly incompressible solids. Int J Solids Struct 33:3277–3296CrossRefMATH
52.
Zurück zum Zitat Elguedj T, Bazilevs Y, Calo VM, Hughes TJR (2008) B-bar and F-bar projection methods for nearly incompressible linear and non-linear elasticity and plasticity based on higher-order NURBS elements. Comput Methods Appl Mech Eng 197:2732–2762CrossRefMATH Elguedj T, Bazilevs Y, Calo VM, Hughes TJR (2008) B-bar and F-bar projection methods for nearly incompressible linear and non-linear elasticity and plasticity based on higher-order NURBS elements. Comput Methods Appl Mech Eng 197:2732–2762CrossRefMATH
53.
Zurück zum Zitat Elguedj T, Hughes TJR (2014) Isogeometric analysis of nearly incompressible large strain plasticity. Comput Methods Appl Mech Eng 268:388–416MathSciNetCrossRefMATH Elguedj T, Hughes TJR (2014) Isogeometric analysis of nearly incompressible large strain plasticity. Comput Methods Appl Mech Eng 268:388–416MathSciNetCrossRefMATH
54.
Zurück zum Zitat Tvergaard V, Needleman A (1984) Analysis of the cup-cone fracture in a round tensile bar. Comput Methods Appl Mech Eng 32:157–169 Tvergaard V, Needleman A (1984) Analysis of the cup-cone fracture in a round tensile bar. Comput Methods Appl Mech Eng 32:157–169
55.
Zurück zum Zitat Bao Y, Wierzbicki T (2004) On fracture locus in the equivalent strain and stress triaxiality space. Int J Mech Sci 46:81–98CrossRef Bao Y, Wierzbicki T (2004) On fracture locus in the equivalent strain and stress triaxiality space. Int J Mech Sci 46:81–98CrossRef
56.
Zurück zum Zitat Wierzbicki T, Bao Y, Lee YW, Bai Y (2005) Calibration and evaluation of seven fracture models. Int J Mech Sci 47:719–743CrossRef Wierzbicki T, Bao Y, Lee YW, Bai Y (2005) Calibration and evaluation of seven fracture models. Int J Mech Sci 47:719–743CrossRef
57.
Zurück zum Zitat Mediavilla J, Peerlings RHJ, Geers MGD (2006) Discrete crack modelling of ductile fracture driven by non-local softening plasticity. Int J Numer Methods Eng 66(4):661–688CrossRefMATH Mediavilla J, Peerlings RHJ, Geers MGD (2006) Discrete crack modelling of ductile fracture driven by non-local softening plasticity. Int J Numer Methods Eng 66(4):661–688CrossRefMATH
58.
Zurück zum Zitat Xue L (2007) Damage accumulation and fracture initiation in uncracked ductile solids subject to triaxial loading. Int J Solids Struct 44:5163–5181CrossRefMATH Xue L (2007) Damage accumulation and fracture initiation in uncracked ductile solids subject to triaxial loading. Int J Solids Struct 44:5163–5181CrossRefMATH
59.
Zurück zum Zitat Boyce BL (2014) The Sandia fracture challenge: blind round robin predictions of ductile tearing. Int J Fract 186:5–68CrossRef Boyce BL (2014) The Sandia fracture challenge: blind round robin predictions of ductile tearing. Int J Fract 186:5–68CrossRef
60.
Zurück zum Zitat Guo J (2013) An experimental and numerical investigation on damage evolution and ductile fracture mechanism of aluminum alloy. PhD dissertation, The University of Tokushima Guo J (2013) An experimental and numerical investigation on damage evolution and ductile fracture mechanism of aluminum alloy. PhD dissertation, The University of Tokushima
61.
Zurück zum Zitat Gerasimov T, De Lorenzis L (subm.) A line-search assisted monolithic approach for phase-field computing of brittle fracture Gerasimov T, De Lorenzis L (subm.) A line-search assisted monolithic approach for phase-field computing of brittle fracture
Metadaten
Titel
A phase-field model for ductile fracture at finite strains and its experimental verification
verfasst von
Marreddy Ambati
Roland Kruse
Laura De Lorenzis
Publikationsdatum
01.01.2016
Verlag
Springer Berlin Heidelberg
Erschienen in
Computational Mechanics / Ausgabe 1/2016
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-015-1225-3

Weitere Artikel der Ausgabe 1/2016

Computational Mechanics 1/2016 Zur Ausgabe

Neuer Inhalt