Computational homogenization analysis in finite plasticity Simulation of texture development in polycrystalline materials

Kröner, 1960, Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen, Arch. Rat. Mech. Anal., 4, 273, 10.1007/BF00281393 Teodosiu, 1970, A dynamic theory of dislocations and its applications to the theory of the elastic-plastic continuum, Vol. II, 837 Rice, 1971, Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity, J. Mech. Phys. Solids, 19, 433, 10.1016/0022-5096(71)90010-X Mandel, 1972, Plasticité Classique et Viscoplasticité Teodosiu, 1976, A finite theory of the elastoviscoplasticity of single crystals, Int. J. Engrg. Sci., 14, 713, 10.1016/0020-7225(76)90027-6 Hill, 1982, Perspectives in the mechanics of elastoplastic crystals, J. Mech. Phys. Solids, 30, 5, 10.1016/0022-5096(82)90010-2 Havner, 1982, The theory of finite plastic deformation of crystalline solids, 265 Havner, 1992 Asaro, 1983, Micromechanics of crystals and polycrystals, Adv. Appl. Mech., 23, 1, 10.1016/S0065-2156(08)70242-4 Kocks, 1970, The relation between polycrystal deformation and single crystal deformation, Metall. Trans., 1, 1121, 10.1007/BF02900224 Kocks, 1975, Thermodynamics and kinetics of slip, Prog. Mat. Sci., 19 Hutchinson, 1976, Elastic-plastic behaviour of polycrystalline metals and composites, 319, 247 Chang, 1981, An experimental study of shear localization in aluminium-copper single crystals, Acta Metall., 29, 241, 10.1016/0001-6160(81)90103-6 Hull, 1984 Cuitiño, 1992, Computational modelling of single crystals, Modell. Simul. Mater. Sci. Engrg., 1, 225, 10.1088/0965-0393/1/3/001 Bassani, 1993, Plastic flow of crystals, Adv. Appl. Mech., 30, 191, 10.1016/S0065-2156(08)70175-3 Asaro, 1985, Texture development and strain hardening in rate dependent polycrystals, Acta Metall., 33, 923, 10.1016/0001-6160(85)90188-9 Harren, 1989, Nonuniform deformations in polycrystals and aspects of the validity of the Taylor model, J. Mech. Phys. Solids, 191, 10.1016/0022-5096(89)90010-0 Mathur, 1989, On modeling the development of crystallographic texture in bulk forming processes, Int. J. Plasticity, 5, 67, 10.1016/0749-6419(89)90020-X Kalidindi, 1992, Crystallographic texture development in bulk deformation processing of FCC metals, J. Mech. Phys. Solids, 40, 537, 10.1016/0022-5096(92)80003-9 Kumar, 1996, The simulation of texture evolution with finite elements of orientation space. Part I. Development and Part II. Application to planar crystals, Comput. Methods Appl. Mech. Engrg., 130, 227, 10.1016/0045-7825(95)00904-3 Kumar, 1996, The simulation of texture evolution with finite elements of orientation space. Part I. Development and Part II. Application to planar crystals, Comput. Methods Appl. Mech. Engrg., 130, 247, 10.1016/0045-7825(95)00903-5 Kothari, 1998, Elasto-viscoplastic constitutive equations for polycrystalline metals: application to tantalum, J. Mech. Phys. Solids, 46, 51, 10.1016/S0022-5096(97)00037-9 Taylor, 1938, Plastic strain in metals, J. Inst. Metals, 62, 307 Hill, 1972, On constitutive macro-variables for heterogeneous solids at finite strain, 326, 131 Hill, 1985, On the micro-to-macro transition in constitutive analyses of elastoplastic response at finite strains, 98, 579 Hassanizadeh, 1979, General conservation equations for multi-phase systems: Part I. Averaging procedure and Part II. Mass, momenta, energy, and entropy equations, Adv. Water Res., 2, 131, 10.1016/0309-1708(79)90025-3 Hassanizadeh, 1979, General conservation equations for multi-phase systems: Part I. Averaging procedure and Part II. Mass, momenta, energy, and entropy equations, Adv. Water Res., 2, 191, 10.1016/0309-1708(79)90035-6 Suquet, 1986, Elements of homogenization for inelastic solid mechanics, 272, 193 Krawietz, 1986, Materialtheorie Maugin, 1992 Nemat-Nasser, 1993, Micromechanics: Overall properties of heterogeneous materials Koiter, 1960, General theorems of elasto-plastic solids Borja, 1993, Discrete micromechanics of elastoplastic crystals, Int. J. Numer. Methods Engineering, 36, 3815, 10.1002/nme.1620362205 Anand, 1996, A computational procedure for rate-independent crystal plasticity, J. Mech. Phys. Solids, 44, 525, 10.1016/0022-5096(96)00001-4 Miehe, 1996, Multisurface thermoplasticity for single crystals at large strains in terms of Eulerian vector updates, Int. J. Solids Struct., 33, 1981, 10.1016/0020-7683(95)00274-X Miehe, 1996, Exponential map algorithm for stress updates in anisotropic multiplicative elastoplasticity for single crystals, Int. J. Numer. Methods Engrg., 39, 3367, 10.1002/(SICI)1097-0207(19961015)39:19<3367::AID-NME4>3.0.CO;2-7 Schröder, 1997, Aspects of computational rate-independent crystal plasticity, Comput. Mater. Sci., 9, 168, 10.1016/S0927-0256(97)00072-4 Simó, 1992, Associative coupled thermoplasticity at finite strains: formulation, numerical analysis and implementation, Comput. Methods Appl. Mech. Engrg., 98, 41, 10.1016/0045-7825(92)90170-O Miehe, 1995, A theory of large-strain isotropic thermoplasticity based on metric transformation tensors, Arch. Appl. Mech., 66, 45 Miehe, 1995, Entropic thermoelasticity at finite strains, Comput. Methods Appl. Mech. Engrg., 120, 243, 10.1016/0045-7825(94)00057-T Miehe, 1996, Numerical computation of algorithmic (consistent) tangent moduli in large-strain computational inelasticity, Comput. Methods Appl. Mech. Engrg., 134, 223, 10.1016/0045-7825(96)01019-5 Simó, 1985, Variational and projection methods for the volume constraint in finite deformation elasto-plasticity, Comput. Methods Appl. Mech. Engrg., 51, 177, 10.1016/0045-7825(85)90033-7 Miehe, 1994, Aspects of the formulation and finite element implementation of large strain isotropic elasticity, Int. J. Numer. Methods Engrg., 37, 1981, 10.1002/nme.1620371202 Miehe, 1994, On the representation of Prandtl—Reuss tensors within the framework of multiplicative elasto-plasticity, Int. J. Plasticity, 10, 609, 10.1016/0749-6419(94)90025-6 Peirce, 1982, An analysis of nonuniform and localized deformation in ductile single Crystals, Acta Metall., 30, 1087, 10.1016/0001-6160(82)90005-0 Perzyna, 1988, Temperature and rate dependent theory of plasticity of crystalline solids, Revue de Physique Appliquée, 23, 445, 10.1051/rphysap:01988002304044500 Luenberger, 1984 Simó, 1998, Non-smooth multisurface plasticity and viscoplasticity, Int. J. Numer. Methods Engrg., 26, 2161, 10.1002/nme.1620261003 Golub, 1993 Press, 1992, Numerical Recipies C. Miehe and J. Schröder, A comparative study of rate-independent and rate-dependent crystal plasticity, Int. J. Numer. Methods Engrg., in press. Zienkiewicz, 1989, Vol. 2 Müller, 1993, Plastische Anisotropic polykristalliner Materialien als Folge der Texturentwicklung Bertram, 1999, Texture development of aluminum polycrystals under finite plastic deformations, 127 Hosford, 1993, The Mechanics of Crystals and Textured Polycrytals, Oxford Engineering Science Series Reed-Hill, 1992 Wriggers, 1994, Contact constraints within coupled thermomechanical analysis—a finite element model, Comput. Methods Appl. Mech. Engrg., 113, 301, 10.1016/0045-7825(94)90051-5