Stress relaxation, creep, failure and hysteresis in a linear elastic material with voids. (English) Zbl 0535.73080
Summary: The author studies several specific boundary-value problems in a theory recently proposed to model linear elastic materials with voids [S. C. Cowin and J. W. Nunziato, ibid. 13, 125-147 (1983; Zbl 0523.73008)]. It is shown that, in addition to the known fact that the model exhibits stress relaxation, it also exhibits creep, hysteresis, and a phenomenon which can be interpreted as failure. In order to maintain plausible physical behavior, the author suggests an a priori inequality not contained in the original theory.
MSC:
| 74R99 | Fracture and damage |
| 74C99 | Plastic materials, materials of stress-rate and internal-variable type |
| 74D05 | Linear constitutive equations for materials with memory |
| 74D10 | Nonlinear constitutive equations for materials with memory |
| 74B10 | Linear elasticity with initial stresses |
| 74B99 | Elastic materials |
| 74H99 | Dynamical problems in solid mechanics |
Keywords:
constant solution; asymptotic solution; nonexistence after finite time; boundary-value problems; linear elastic materials with voids; stress relaxation; creep; hysteresis; failure; a priori inequalityCitations:
Zbl 0523.73008References:
| [1] | J.W. Nunziato and S.C. Cowin, A nonlinear theory of elastic materials with voids, Archive for Rational Mechanics and Analysis 72 (1979) 175. · Zbl 0444.73018 · doi:10.1007/BF00249363 |
| [2] | S.C. Cowin and J.W. Nunziato, Linear elastic materials with voids, Journal of Elasticity 13 (1983) 125. · Zbl 0523.73008 · doi:10.1007/BF00041230 |
| [3] | M.A. Goodman and S.C. Cowin, A continuum theory for granular materials, Archive for Rational Mechanics and Analysis 44 (1972) 249. · Zbl 0243.76005 · doi:10.1007/BF00284326 |
| [4] | S.L. Passman, D.E. Grady and J.B. Rundle, The role of inertia in the fracture of rock, Journal of Applied Physics 51(8) (1980) 4070. · doi:10.1063/1.328257 |
| [5] | R.J. Atkin, S.C. Cowin and N. Fox, On boundary conditions for polar materials, Zeitschrift für angewandte Mathematik und Physik 28 (1977) 1017. · Zbl 0385.76003 · doi:10.1007/BF01601669 |
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