A set of invariants are presented for transverse-isotropic materials whose gradients produce strain fields, instead of deformation fields as is typically the case. Finite-strain theories for elastic and K-BKZ-type viscoelastic solids are derived. Shear-free and simple shearing deformations are employed to illustrate the constitutive theory.
Issue Section:
Technical Papers
1.
Spencer, A. J. M., 1972, Deformations of Fibre-reinforced Materials, Clarendon Press, Oxford.
2.
Leonov
, A. I.
, 2000
, “On the Conditions of Potentiality in Finite Elasticity and Hypo-Elasticity
,” Int. J. Solids Struct.
, 37
, pp. 2565
–2576
.3.
Coleman
, B. D.
, 1964
, “Thermodynamics of Materials With Memory
,” Arch. Ration. Mech. Anal.
, 17
, pp. 1
–46
.4.
Gurtin
, M. E.
, and Sternberg
, E.
, 1962
, “On the Linear Theory of Viscoelasticity
,” Arch. Ration. Mech. Anal.
, 11
, pp. 291
–356
.5.
Kaye, A., 1962, “Non-Newtonian Flow in Incompressible Fluids,” Technical Report 134, The College of Aeronautics, Cranfield.
6.
Bernstein
, B.
, Kearsley
, E. A.
, and Zapas
, L. J.
, 1963
, “A Study of Stress Relaxation With Finite Strain
,” Trans. Soc. Rheol.
, 7
, pp. 391
–410
.7.
Truesdell
, C.
, 1958
, “Geometric Interpretation for the Reciprocal Deformation Tensors
,” Q. J. Appl. Math.
, 15
, pp. 434
–435
.8.
Doyle, T. C., and Ericksen, J. E., 1956, “Nonlinear Elasticity,” in Advances in Applied Mechanics, 4, H. L. Dryden and T. von Ka´rma´n, editors, Academic Press, New York, pp. 53–115.
9.
Bazˇant
, Z. P.
, 1998
, “Easy-to-Compute Tensors With Symmetric Inverse Approximating Hencky Finite Strain and Its Rate
,” ASME J. Eng. Mater. Technol.
, 120
, pp. 131
–136
.10.
Hencky
, H.
, 1928
, “U¨ber die Form des Elastizita¨tsgesetzes bei ideal elastischen Stoffen
,” Z. Tech. Phys. (Leipzig)
, 9
, pp. 215
–220
.11.
Hoger
, A.
, 1986
, “The Material Time Derivative of Logarithmic Strain
,” Int. J. Solids Struct.
, 22
, pp. 1019
–1032
.Copyright © 2004
by ASME
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