Non-elliptic elastic materials and the modeling of dissipative mechanical behavior: An example. (English) Zbl 0626.73011
The authors describe the modelling of dissipative mechanical behavior in non-elliptic solids. The theory is based upon the principles of finite elasticity. It predicts mechanical response similar to that associated with the pseudo-elastic effect found in shape memory alloys.
The paper is long, containing much information. Although quite specialized, it should be useful to theoreticians working in finite elasticity.
The paper is long, containing much information. Although quite specialized, it should be useful to theoreticians working in finite elasticity.
Reviewer: R.L.Huston
MSC:
| 74B20 | Nonlinear elasticity |
Keywords:
equilibrium theory; large strains; quasi-static motions; discontinuous displacement gradients; internal variable formalism; macroscopic plastic behavior; microstructural effects; dissipative mechanical behavior; non- elliptic solids; pseudo-elastic effect; shape memory alloysReferences:
| [1] | R. Abeyaratne, Discontinuous deformation gradients in plane finite elastostatics of incompressible materials,Journal of Elasticity 10 (1980) 255-293. · Zbl 0486.73031 · doi:10.1007/BF00127451 |
| [2] | R. Abeyaratne, Discontinuous deformation gradients in the finite twisting of an incompressible elastic tube,Journal of Elasticity 11 (1980) 43-80. · Zbl 0511.73035 · doi:10.1007/BF00042481 |
| [3] | J.L. Ericksen, Equilibrium of bars,Journal of Elasticity 5 (1975) 191-201. · Zbl 0324.73067 · doi:10.1007/BF00126984 |
| [4] | R.L. Fosdick and R.D. James, The elastica and the problem of pure bending for a non-convex stored energy function,Journal of Elasticity 11 (1981) 165-186. · Zbl 0481.73018 · doi:10.1007/BF00043858 |
| [5] | R.L. Rosdick and G. MacSithigh, Helical shear of an elastic, circular tube with a nonconvex stored energy,Archive for Rational Mechanics and Analysis 84 (1983) 31-53. · Zbl 0529.73007 |
| [6] | M.E. Gurtin, Two-phase deformations of elastic solids,Archive for Rational Mechanics and Analysis 84 (1983) 1-29. · Zbl 0525.73054 · doi:10.1007/BF00251547 |
| [7] | R.D. James, Finite deformation by mechanical twinning,Archive for Rational Mechanics and Analysis 77 (1981) 143-176. · Zbl 0537.73031 · doi:10.1007/BF00250621 |
| [8] | R.D. James, Co-existent phases in the one-dimensional static theory of elastic bars,Archive for Rational Mechanics and Analysis 72: (1979) 99-140. · Zbl 0429.73001 · doi:10.1007/BF00249360 |
| [9] | R.D. James, The equilibrium and post-buckling behavior of an elastic curve governed by a non-convex energy,Journal of Elasticity 11 (1981) 239-269. · Zbl 0514.73029 · doi:10.1007/BF00041939 |
| [10] | R.D. James, On the stability of phases,International Journal of Engineering Science 22 (1984) 1193-1197. · Zbl 0588.73024 · doi:10.1016/0020-7225(84)90122-8 |
| [11] | R.D. James, Displacive phase transformations in solids,Journal of the Mechanics and Physics of Solids 34 (1986) 359-394. · Zbl 0585.73198 · doi:10.1016/0022-5096(86)90008-6 |
| [12] | J.K. Knowles, On the dissipation associated with equilibrium shocks in finite elasticity,Journal of Elasticity 9 (1979) 131-158. · Zbl 0407.73037 · doi:10.1007/BF00041322 |
| [13] | J.K. Knowles and E. Sternberg, On the failure of ellipticity and the emergence of discontinuous deformation gradients in plane finite elastostatics,Journal of Elasticity 8 (1978) 329-379. · Zbl 0422.73038 · doi:10.1007/BF00049187 |
| [14] | M.E. Gurtin, The linear theory of elasticity, inHandbuch der Physik, vol. VI a/2 (S. Flügge, ed.), pp. 1-295, Springer-Verlag, Berlin, 1972. |
| [15] | J.R. Rice, Continuum mechanics and thermodynamics of plasticity in relation to microscale deformation mechanisms, inConstitutive equations in plasticity, (A.S. Argon, ed.), pp. 23-79, MIT Press, Cambridge, Mass., 1975. |
| [16] | J.R. Rice, Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticity,Journal of the Mechanics and Physics of Solids 19: (1971) 433-455. · Zbl 0235.73002 · doi:10.1016/0022-5096(71)90010-X |
| [17] | J.R. Rice, On the structure of stress-strain relations for time dependent plastic deformation in metals,Journal of Applied Mechanics 37 (1970) 728-737. · doi:10.1115/1.3408603 |
| [18] | R. Hill and J.R. Rice, Elastic potentials and the structure of inelastic constitutive laws,SIAM Journal on Applied Mathematics 25 (1973) 448-461. · Zbl 0275.73028 · doi:10.1137/0125045 |
| [19] | J.B. Martin,Plasticity: Fundamentals and General Results, MIT Press, Cambridge, 1975. |
| [20] | L.D. Landau and E.M. Lifshitz,Fluid Mechanics, volume 6 ofCourse of Theoretical Physics, Pergamon, New York, 1959. |
| [21] | R. Courant and K.O. Friedrichs,Supersonic Flow and Shock Waves, Interscience, New York, 1948. · Zbl 0041.11302 |
| [22] | A.J.M. Spencer,Continuum Mechanics, Longman, London, 1980. · Zbl 0427.73001 |
| [23] | L.R.G. Treloar, The photoelastic properties of rubber II. Double refraction and crystallisation in stretched vulcanized rubber,Transactions of the Faraday Society (London) 43 (1947) 284-293. · doi:10.1039/tf9474300284 |
| [24] | L. Delaey, R.V. Krishman, H. Tas, H. Warlimont, Review: Thermoelasticity, pseudoelasticity and the memory effects associated with martensitic transformations,Journal of Materials Science 9 (1974) 1521-1555. · doi:10.1007/BF00552939 |
| [25] | J. Lubliner, A maximum-dissipation principle in generalized plasticity,Acta Mechanica 52 (1984) 225-237. · Zbl 0572.73043 · doi:10.1007/BF01179618 |
| [26] | R. Abeyaratne, An admissibility condition for equilibrium shocks in finite elasticity,Journal of Elasticity 13 (1983) 175-184. · Zbl 0545.73032 · doi:10.1007/BF00041234 |
| [27] | R. Abeyaratne and J.K. Knowles, Non-elliptic elastic materials and the modeling of elastic-plastic behavior for finite deformation,Journal of the Mechanics and Physics of Solids 35 (1987) 343-365. · Zbl 0608.73044 · doi:10.1016/0022-5096(87)90012-3 |
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