×

A variational constitutive model for porous metal plasticity. (English) Zbl 1102.74007

Summary: This paper presents a variational formulation of viscoplastic constitutive updates for porous elastoplastic materials. The material model combines von Mises plasticity with volumetric plastic expansion as induced, e.g., by the growth of voids and defects in metals. The finite deformation theory is based on the multiplicative decomposition of the deformation gradient and an internal variable formulation of continuum thermodynamics. By the use of logarithmic and exponential mappings the stress update algorithms are extended from small strains to finite deformations. Thus the time-discretized version of the porous-viscoplastic constitutive updates is described in a fully variational manner. The range of behavior predicted by the model and the performance of the variational update are demonstrated by its application to the forced expansion and fragmentation of U-6%Nb rings.

MSC:

74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74G65 Energy minimization in equilibrium problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ball JM (1982) Discontinuous equilibrium solutions and cavitation in non-linear elasticity. Philos T Roy Soc A 306(1496): 557–611 · Zbl 0513.73020 · doi:10.1098/rsta.1982.0095
[2] Barbee TW, Seaman L, Crewdson R, Curran D (1972) Dynamic fracture criteria for ductile and brittle metals. J Mater 7(3):393–401 · doi:10.1007/BF02403402
[3] Beachem CD, Yoder GR (1973) Elastic-plastic fracture by homogeneous microvoid coalescence tearing along alternating shear planes. Metall Trans 4(4):1145–1153 · doi:10.1007/BF02645619
[4] Becker R (2002) Ring fragmentation predictions using the Gurson model with material stability conditions as failure criteria. Int J Solids Struct 39(13–14):3555–3580 · Zbl 1087.74621
[5] Belak J (1998) On the nucleation and growth of voids at high strain-rates. J Comput-Aided Mater 5:193–206
[6] Cortes R (1992) Dynamic growth of microvoids under combined hydrostatic and deviatoric stresses. Int J Solids Struct 29(13):1637–1645 · Zbl 0825.73559 · doi:10.1016/0020-7683(92)90013-J
[7] Cuitino A, Ortiz M (1992) A material-independent method for extending stress update algorithms from small-strain plasticity to finite plasticity with multiplicative kinematics. Eng Comput 9:255–263
[8] Glushak BL, Koritskaya SV, Trunin IR (2000) Numerical analysis of damage accumulation in copper under dynamic load. Chem Phys Rep 18(10–11):1835–1841
[9] Grady DE, Benson DA (1983) Fragmentation of metal rings by electromagnetic loading. Exp Mech 23(4):393–400 · doi:10.1007/BF02330054
[10] 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 T ASME 99(1):2–15 · doi:10.1115/1.3443401
[11] Hackl K (1997) Generalized standard media and variational principles in classical and finite strain elastoplasticity. J Mech Phys Solids 45(5):667–688 · Zbl 0974.74512 · doi:10.1016/S0022-5096(96)00110-X
[12] Huang Y, Hutchinson JW, Tvergaard V (1991) Cavitation instabilities in elastic plastic solids. J Mech Phys Solids 39(2):223–241 · doi:10.1016/0022-5096(91)90004-8
[13] Leblond JB, Roy G (2000) A model for dynamic ductile behavior applicable for arbitrary triaxialities. CR Acad Sci II B 328(5):381–386 · Zbl 1001.74041
[14] Lee EH (1969) Elastic-plastic deformation at finite strains. J Appl Mech 36(1):1–6 · Zbl 0179.55603
[15] Lubliner J (1972) On the thermodynamic foundations of non-linear solid mechanics. Int J Nonlinear Mech 7:237–254 · Zbl 0265.73005 · doi:10.1016/0020-7462(72)90048-0
[16] Mercier S, Molinari A (2000) Micromechanics of void growth at high rates. J Phys IV 10(P9):415–420 · doi:10.1051/jp4:2000969
[17] Molinari A, Mercier S (2001) Micromechanical modelling of porous materials under dynamic loading. J Mech Phys Solids 49(7):1497–1516 · Zbl 0989.74008 · doi:10.1016/S0022-5096(01)00003-5
[18] Ortiz M, Molinari A (1992) Effect of strain-hardening and rate sensitivity on the dynamic growth of a void in a plastic material. J Apll Mech -T ASME 59(1):48–53 · Zbl 0761.73089
[19] Ortiz M, Radovitzky RA, Repetto EA (2001) The computation of the exponential and logarithmic mappings and their first and second linearizations. Int J Numer Meth Eng 52(12):1431–1441 · Zbl 0995.65053 · doi:10.1002/nme.263
[20] Ortiz M, Stainier L (1999) The variational formulation of viscoplastic constitutive updates. Comput Method Appl Meth Eng 171(3–4):419–444 · Zbl 0938.74016
[21] Perzyna P (1986) Internal state variable description of dynamic fracture of ductile solids. Int J Solids Struct 22(7):797–818 · doi:10.1016/0020-7683(86)90123-X
[22] Radovitzky R, Ortiz M (1999) Error estimation and adaptive meshing in strongly nonlinear dynamic problems. Comput Method Appl M 172(1–4):203–240 · Zbl 0957.74058
[23] Thomason PF (1990) Ductile fracture of metals. Pergamon Press, New York
[24] Thomason PF (1999) Ductile spallation fracture and the mechanics of void growth and coalescence under shock-loading conditions. Acta Mater 47(13): 3633–3643 · doi:10.1016/S1359-6454(99)00223-2
[25] Tong W, Ravichandran G (1995) Inertial effects on void growth in porous viscoplastic materials. J Appl Mech T ASME 62(3):633–639 · doi:10.1115/1.2895993
[26] Tvergaard V (1990) Material failure by void growth to coalescence. Adv Appl Mech 27:83–151 · Zbl 0728.73058 · doi:10.1016/S0065-2156(08)70195-9
[27] Tvergaard V, Huang Y, Hutchinson JW (1992) Cavitation instabilities in a power hardening elastic-plastic solid. Eur J Mech A Solid 11(2):215–231
[28] Tvergaard V, Needleman A (1984) Analysis of the cup-cone fracture in a round tensile bar. Acta Metall 32(1):157–169 · doi:10.1016/0001-6160(84)90213-X
[29] Yang Q, Mota A, Ortiz M (2005) A class of variational strain-localization finite elements. Int J Numer Meth Eng, 62(8):1013–1037 · Zbl 1081.74045
[30] Zurek AK, Thissell WR, Tonks DL, Hixson R, Addessio F (1997) Quantification of damage evolution for a micromechanical model of ductile fracture in spallation of tantalum. J Phys IV 7(C3):903–908 · doi:10.1051/jp4:19973152
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.