Formulation and analysis of a functional equation describing a moving one-dimensional elastic phase boundary
Author:
Thomas J. Pence
Journal:
Quart. Appl. Math. 45 (1987), 293-304
MSC:
Primary 73D99; Secondary 35R35
DOI:
https://doi.org/10.1090/qam/895099
MathSciNet review:
895099
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: Certain elastic solids when subjected to sufficiently high loads abruptly change their mechanical properties and yet continue to respond elastically to further loading. In one dimension such mechanically induced elastic phase transitions may be due to a nonmonotonic stress-strain relationship. This appears to be particularly true for certain mineral crystals, such as calcite.
D. E. Grady, R. E. Hollenbach, and K. W. Schuler, Compression wave studies in calcite rock, J. Geophys. Res. 83, 2839–2849 (1978)
- J. L. Ericksen, Equilibrium of bars, J. Elasticity 5 (1975), no. 3-4, 191–201 (English, with French summary). Special issue dedicated to A. E. Green. MR 471528, DOI https://doi.org/10.1007/BF00126984
- Richard D. James, Co-existent phases in the one-dimensional static theory of elastic bars, Arch. Rational Mech. Anal. 72 (1979/80), no. 2, 99–140. MR 545514, DOI https://doi.org/10.1007/BF00249360
- Richard D. James, The propagation of phase boundaries in elastic bars, Arch. Rational Mech. Anal. 73 (1980), no. 2, 125–158. MR 556559, DOI https://doi.org/10.1007/BF00258234
- Thomas J. Pence, On the emergence and propagation of a phase boundary in an elastic bar with a suddenly applied end load, J. Elasticity 16 (1986), no. 1, 3–42. MR 835364, DOI https://doi.org/10.1007/BF00041064
- James Serrin, Phase transitions and interfacial layers for van der Waals fluids, Recent methods in nonlinear analysis and applications (Naples, 1980) Liguori, Naples, 1981, pp. 169–175. MR 819030
- M. Slemrod, Admissibility criteria for propagating phase boundaries in a van der Waals fluid, Arch. Rational Mech. Anal. 81 (1983), no. 4, 301–315. MR 683192, DOI https://doi.org/10.1007/BF00250857
- R. Hagan and M. Slemrod, The viscosity-capillarity criterion for shocks and phase transitions, Arch. Rational Mech. Anal. 83 (1983), no. 4, 333–361. MR 714979, DOI https://doi.org/10.1007/BF00963839
- A. M. Skobeev, On the theory of unloading waves, J. Appl. Math. Mech. 26 (1963), 1605–1616. MR 0159488, DOI https://doi.org/10.1016/0021-8928%2862%2990195-8
R. J. Clifton and S. R. Bodner, An analysis of longitudinal elastic-plastic pulse propagation, J. Appl. Mech. 33, 248–255 (1966)
- Michael P. Mortell and Brian R. Seymour, Exact solutions of a functional equation arising in nonlinear wave propagation, SIAM J. Appl. Math. 30 (1976), no. 4, 587–596. MR 407479, DOI https://doi.org/10.1137/0130052
D. E. Grady, R. E. Hollenbach, and K. W. Schuler, Compression wave studies in calcite rock, J. Geophys. Res. 83, 2839–2849 (1978)
J. L. Ericksen, Equilibrium of bars, J. Elasticity 5, 191–201 (1975)
R. D. James, Co-existent phases in the one-dimensional static theory of elastic bars, Arch. Rat. Mech. Anal. 72, 99–140 (1979)
R. D. James, The propagation of phase boundaries in elastic bars, Arch. Rat. Mech. Anal. 73, 125–150 (1980)
T. J. Pence, On the emergence and propagation of a phase boundary in an elastic bar with a suddenly applied end load, J. Elasticity 16, 3–42 (1986)
J. Serrin, Phase transitions and interfacial layers for van der Waals fluids, in Proceedings of SAFA IV Conference, Recent Methods in Nonlinear Analysis and Applications, Naples, March 21–28, 1980 (A. Canfora, S. Rionero, C. Sbordone, C. Trombetti, Eds.)
M. Slemrod, Admissibility criteria for propagating phase boundaries in a van der Waals fluid, Arch. Rat. Mech. Anal. 81, 301–315 (1983)
R. Hagan and M. Slemrod, The viscosity—capillarity criterion for shocks and phase transitions, Arch. Rat. Mech. Anal. 83, 333–361 (1983)
A. M. Skobeev, On the theory of unloading waves, Appl. Math. Mech., PMM, 26, 1605–1615 (1963)
R. J. Clifton and S. R. Bodner, An analysis of longitudinal elastic-plastic pulse propagation, J. Appl. Mech. 33, 248–255 (1966)
M. P. Mortell and B. R. Seymour, Exact solutions of a functional equation arising in nonlinear wave propagation, SIAM J. Appl. Math. 30, 587–596 (1976)
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
73D99,
35R35
Retrieve articles in all journals
with MSC:
73D99,
35R35
Additional Information
Article copyright:
© Copyright 1987
American Mathematical Society
