Hencky’s logarithmic strain and dual stress–strain and strain–stress relations in isotropic finite hyperelasticity
Tài liệu tham khảo
Anand, 1979, On H. Hencky’s approximate strain-energy function for moderate deformations, J. Appl. Mech., 46, 78, 10.1115/1.3424532
Anand, 1986, Moderate deformations in extension-torsion of incompressible isotropic elastic materials, J. Mech. Phys. Solids, 34, 293, 10.1016/0022-5096(86)90021-9
Bažant, 1998, Easy-to-compute tensors with symmetric inverse approximating Hencky finite strain and its rate, J. Engng. Mater. Techn., 120, 131, 10.1115/1.2807001
Blume, 1992, On the form of the inverted stress–strain law for isotropic hyperelastic solids, Int. J. Non-linear Mech., 27, 413, 10.1016/0020-7462(92)90009-V
de Boer, 1967, Die elastisch-plastische Biegung eines Plattenstreifens aus inkompressiblem Werkstoff bei endlichen Formänderungen, Ing.-Arch., 36, 145, 10.1007/BF00532152
de Boer, 1969, Zur Berechnung der Eigenspannungen bei einem durch endliche Biegung verformten inkompressiblen Plattenstreifen, Acta Mech., 146, 10.1007/BF01182256
Bonet, 1997
Bruhns, 1970, Die Berücksichtigung einer isotropen Werkstoffverfestigung bei der elastisch-plastischen Blechbiegung mit endlichen Formänderungen, Ing.-Arch., 39, 63, 10.1007/BF00532629
Bruhns, 1971, Elastoplastische Scheibenbiegung bei endlichen Formänderungen, Z. Angew. Math. Mech., 51, T101
Bruhns, 1969, Elastisch-plastische Biegung eines Plattenstreifens bei endlichen Formänderungen, Ing.-Arch., 38, 141, 10.1007/BF00532951
Bruhns, 1999, Self-consistent Eulerian rate type elastoplasticity models based upon the logarithmic stress rate, Int. J. Plasticity, 15, 479, 10.1016/S0749-6419(99)00003-0
Bruhns, 2001, The Hencky model of elasticity: a study on Poynting effect and stress response in torsion of tubes and rods, Arch. Mech., 52, 489
Bruhns, 2001, A self-consistent Eulerian rate type model for finite deformation elastoplasticity with isotropic damage, Int. J. Solids Struct., 38, 657, 10.1016/S0020-7683(00)00094-9
Chiskis, 2000, Linear stress–strain relations in nonlinear elasticity, Acta Mech., 146, 109, 10.1007/BF01178798
Curnier, 1991, Generalized strain and stress measures: critical survey and new results, Engng. Trans., 39, 461
Eterovic, 1990, A hyperelastic-based large strain elasto-plastic constitutive formulation with combined isotropic-kinematic hardening using the logarithmic stress and strain measures, Int. J. Num. Meth. Engng., 30, 1099, 10.1002/nme.1620300602
Fitzjerald, 1980, A tensorial Hencky measure of strain and strain rate for finite deformations, J. Appl. Phys., 51, 5111, 10.1063/1.327428
Freed, 1995, Natural strain, J. Engng. Mater. Techn., 117, 379, 10.1115/1.2804729
Gurtin, 1981
Hencky, 1928, Über die Form des Elastizitätsgesetzes bei ideal elastischen Stoffen, Z. Techn. Phys., 9, 215
Hencky, 1931, The law of elasticity for isotropic and quasi-isotropic substances by finite deformations, J. Rheology, 2, 169, 10.1122/1.2116361
Hencky, 1933, The elastic behaviour of vulcanized rubber, Rubber Chem. Techn., 6, 217, 10.5254/1.3547545
Hill, 1968, Constitutive inequalities for simple materials, J. Mech. Phys. Solids, 16, 229, 10.1016/0022-5096(68)90031-8
Hill, 1970, Constitutive inequalities for isotropic elastic solids under finite strain, Proc. R. Soc. Lond. A, 326, 131, 10.1098/rspa.1972.0001
Hill, 1978, Aspect of invariance in solid mechanics, Adv. Appl. Mech., 18, 1, 10.1016/S0065-2156(08)70264-3
Hoger, 1987, The stress conjugate to logarithmic strain, Int. J. Solids Struct., 23, 1645, 10.1016/0020-7683(87)90115-6
Kollmann, 1997, Viscoplastic shells: theory and numerical analysis, Arch. Mech., 49, 477
Miehe, 1998, A formulation of finite elastoplasticity based on dual co- and contravariant eigenvector triads normalized with respect to a plastic metric, Comp. Meth. Appl. Mech. Engng., 159, 223, 10.1016/S0045-7825(97)00273-9
Miehe, 1994, Associative multiplicative elasto-plasticity: formulation and aspects of the numerical implementation including stability analysis, Comput. Struct., 52, 969, 10.1016/0045-7949(94)90081-7
Ogden, 1970, Compressible isotropic elastic solids under finite strain-constitutive inequalities, Quart. J. Mech. Appl. Math., 23, 457, 10.1093/qjmam/23.4.457
Ogden, 1984
Raniecki, 1984, Isotropic elasto-plastic solids at finite strain and arbitrary pressure, Arch. Mech., 36, 687
Sansour, 2001, On the dual variable of the logarithmic strain tensor, the dual variable of the Cauchy stress tensor, and related issues, Int. J. Solids Struct., 38, 9221, 10.1016/S0020-7683(01)00073-7
Schieck, 1995, The appropriate corotational rate, exact formula for the plastic spin and constitutive model for finite elastoplasticity, Int. J. Solids Struct., 32, 3643, 10.1016/0020-7683(95)00007-W
Šilhavý, 1997
Stören, 1975, Localized necking in thin sheets, J. Mech. Phys. Solids, 23, 421, 10.1016/0022-5096(75)90004-6
Stumpf, 1994, Theory and analysis of shells undergoing finite elastic–plastic strains and rotations, Acta Mech., 106, 1, 10.1007/BF01300941
Truesdell, 1965, The non-linear field theories of mechanics
Weber, 1990, Finite deformation constitutive equations and a time integration procedure for isotropic, hyperelastic–viscoplastic solids, Comp. Meth. Appl. Mech. Engng., 79, 173, 10.1016/0045-7825(90)90131-5
Xiao, 1997, Hypo-elasticity model based upon the logarithmic stress rate, J. Elasticity, 47, 51, 10.1023/A:1007356925912
Xiao, 1997, Logarithmic strain, logarithmic spin and logarithmic rate, Acta Mech., 124, 89, 10.1007/BF01213020
Xiao, 1998, Strain rates and material spins, J. Elasticity, 52, 1, 10.1023/A:1007570827614
Xiao, 1999, Existence and uniqueness of the integrable-exactly hypoelastic equation τ∘*=λ(D)I+2GD and its significance to finite inelasticity, Acta Mech., 138, 31, 10.1007/BF01179540
Xiao, 2000, The choice of objective rates in finite elastoplasticity: general results on the uniqueness of the logarithmic rate, Proc. R. Soc. Lond. A, 456, 1865, 10.1098/rspa.2000.0591