On a Model of Nonlocal Continuum Mechanics Part II: Structure, Asymptotics, and Computations
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OpenAlex topics: Elasticity and Wave Propagation
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References (23)
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1. H. Attouch, Variational convergence for functions and operators. Appl. Math. Series, Pitman Adv. Publ. Program, 1984.
2. J.M. Ball, A version of the fundamental theorem of Young measure. In: Partial Differential Equations and Continuum Models of Phase Transitions, M. Rascle, D. Serre, and M. Slemrod (eds), Lecture Notes in Physics 344, 207–215. Springer-Verlag, 1989.
3. J.M. Ball and R.D. James, Proposed experimental tests of a theory of fine microstructure and the two well problem. Phil. Trans. R. Soc. Lond. A, 338 (1992) 389–450.10.1098/rsta.1992.0013 ↗
4. J.F. Blowey, and C.M. Elliot, The Cahn-Hilliard gradient theory for phase separation with nonsmooth free energy, Part I: Mathematical analysis. Euro. J. of Appl. Math. 2 (1991) 233–279.10.1017/S095679250000053X ↗
5. V. Bongiorno, and H.T. Davis, Modified van der Waals theory of fluid interfaces. Phys. Rev. A, 12 (1975) 2213–2224.10.1103/PhysRevA.12.2213 ↗
6. D. Brandon, T. Lin, and R.C. Rogers, Phase transitions and hysteresis in nonlocal and order-parameter models. ICAM Report, Virginia Polytechnic Institute, Department of Mathematics, 6 October, 1994.
7. J. Carr, M.E. Gurtin and M. Slemrod, Structured phase transitions on a finite interval. Arch. Rational Mech. Anal. 86 (1984) 317–351.10.1007/BF00280031 ↗
8. J.E. Dunn, and R.L. Fosdick, The morphology and stability of material phases. Arch. Rational Mech. Anal. 74 (1980) 1–99.10.1007/BF00250831 ↗
9. J.L. Ericksen, Equilibrium of bars. J. Elasticity 5 (1975) 191–201.10.1007/BF00126984 ↗
10. R.L. Fosdick and D.E. Mason, Single phase energy minimizers for materials with nonlocal spatial dependence. Quart. Appl. Math 54 (1996) 161–195.10.1090/qam/1373845 ↗
11. R.L. Fosdick and D.E. Mason, Nonlocal continuum mechanics, Part I: Existence and regularity. SIAM J. Appl. Math. To appear.
12. R.L. Fosdick and D.E. Mason, Apriori Geometric Conditions for the Existence of Stable Coexistent Phase Fields in a Theory of Nonlocal Mechanics. Forthcoming.
13. R.L. Fosdick and Y. Zhang, A structured phase transition for the anti-plane shear of an elastic circular tube. Quart. J. Mech. and Appl. Math. 48 (1995) 189–210.10.1093/qjmam/48.2.189 ↗
14. J.W. Gibbs, On the equilibrium of heterogeneous substances. Transactions of the Connecticut Academy, III. 108–248, Oct. 1875–May, 1876 and 343–524, May, 1877–July, 1878.
15. M.E. Gurtin, On a theory of phase transitions with interfacial energy. Arch. Rational Mech. Anal. 87 (1985) 187–212.10.1007/BF00250724 ↗
16. D.E. Mason, Phase transitions in nonlocal continuum mechanics., Ph.D. Thesis, University of Minnesota, Dept. of Aerospace Engineering and Mechanics, 1996.
17. L. Modica, Gradient theory of phase transitions and minimal interface criterion. Arch. Rational Mech. Anal. 98,No. 2 (1987) 123–142.10.1007/BF00251230 ↗
18. L. Modica, Gradient theory of phase transitions with boundary contact energy. Ann. Inst. Henri Poincaré 4 (1987) 487–512.10.1016/s0294-1449(16)30360-2 ↗
19. S. Müller, Singular perturbations as a selection criterion for periodic minimizing sequences. Calculus of Variations 1 (1993) 169–204.
20. R.C. Rogers, Some remarks on nonlocal interactions and hysteresis in phase transitions. Continuum Mech. Thermodyn. 8 (1996) 65–73.10.1007/s001610050029 ↗
21. P. Sternberg, The effect of a singular perturbation on nonconvex variational problems. Arch. Rational Mech. Anal. 101 (1988) 209–260.10.1007/BF00253122 ↗
22. J.D. van der Waals, The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density. (In Dutch), Verhandel. Konink. Akad. Weten. Amsterdam (Sect. 1) 1,No. 8 (1893).
23. J.W. Walter, On a nonlocal model of fluid phases, Ph.D. Thesis, University of Minnesota, Dept. of Aerospace Engineering and Mechanics, 1985.