Natural stress rate

Durban, David; Baruch, Menahem

doi:10.1090/qam/99647

Natural stress rate

Authors: David Durban and Menahem Baruch
Journal: Quart. Appl. Math. 35 (1977), 55-61
DOI: https://doi.org/10.1090/qam/99647
MathSciNet review: QAM99647
Full-text PDF Free Access

Abstract | References | Additional Information

Abstract: A three-dimensional definition of the natural stress rate is suggested. The behavior of a hypoelastic material of grade zero based on the natural stress rate is analyzed for the case of simple extension. The results of the theoretical analysis agree with existing experimental data for urethane rubber. An interesting relation between the natural stress rate and stress rates suggested by Truesdell and Hill is given. The paper is written in full tensorial notation which is especially suitable when rates of tensor are considered.

William Prager, An elementary discussion of definitions of stress rate, Quart. Appl. Math. 18 (1960/61), 403–407. MR 116567, DOI https://doi.org/10.1090/S0033-569X-1961-0116567-4
L. I. Sedov, Different definitions of the rate of change of a tensor, J. Appl. Math. Mech. 24 (1960), 579–586. MR 0119549, DOI https://doi.org/10.1016/0021-8928%2860%2990165-9
E. F. Masur, On the definition of stress rate, Quart. Appl. Math. 19 (1961/62), 160–163. MR 133969, DOI https://doi.org/10.1090/S0033-569X-1961-0133969-0

D. Durban, A rate approach to the behavior of elasto-plastic structures, D.Sc. Thesis (in Hebrew) Technion-Israel Institute of Technology, Haifa, 1975

D. Durban and M. Baruch, Incremental behavior of an elasto-plastic Continuum, TAE Report No. 193, Technion-Israel Institute of Technology, Haifa, 1975

V. J. Parks and A. J. Durelli, Natural stress, Int. J. Non-Linear Mechanics 4, 7–16 (1969)

V. I. Bloch, Theory of elasticity (in Russian), Kharkov, 1964

C. Truesdell, The simplest rate theory of pure elasticity, Comm. Pure Appl. Math. 8 (1955), 123–132. MR 68411, DOI https://doi.org/10.1002/cpa.3160080109
R. Hill, Uniqueness in general boundary-value problems for elastic or inelastic solids, J. Mech. Phys. Solids 9 (1961), 114–130. MR 118020, DOI https://doi.org/10.1016/0022-5096%2861%2990029-1

R. Hill, Constitutive inequalities for isotropic elastic solids under finite strain, Proc. Roy. Soc. Lond. A314, 457–472 (1970)