| Автор | Martins, L., C. |
| Автор | Duda, F., P. |
| Дата выпуска | 1998 |
| dc.description | The determination of static fields that are producible in every isotropic, homogeneous, incompressible, elastic body under the sole action of surface traction is known as Ericksen's problem. In this paper, the authors consider a family of isotropic constraints including incompressibility, and for each class in the family, they obtain the complete set of plane deformations with uniform transverse stretch that are universal; that is, producible in any elastic body of the particular class under the sole action of surface traction. In fact, in the case where the plane stretches are not constant, the authors distinguish the class they consider only in the last step of their construction of a solution, and this renders possible a general analysis of the problem. The authors stress the singular aspects of nonhomogeneous solutions for which all stretches are constant, showing that for nearly all constraints, they are universal. |
| Издатель | Sage Publications |
| Название | Constrained Elastic Bodies and Universal Solutions in the Class of Plane Deformations with Uniform Transverse Stretch |
| Тип | Journal Article |
| DOI | 10.1177/108128659800300106 |
| Print ISSN | 1081-2865 |
| Журнал | Mathematics and Mechanics of Solids |
| Том | 3 |
| Первая страница | 91 |
| Последняя страница | 106 |
| Аффилиация | Duda, F., P., COPPE-Universidade Federal do Rio de Janeiro, C.P. 68503, 21945-970, Rio de Janeiro, RJ, Brazil |
| Выпуск | 1 |
| Библиографическая ссылка | [1] Antman, S. S.: Nonlinear Problems of Elasticity, Springer-Verlag, New York, 1995. |
| Библиографическая ссылка | [2] Beatty, M. F.: Topics in finite elasticity: Hyperelasticity of rubber, elastomers, and biological tissues-with examples. Appl. Mech. Rev., 40, 1699-1734 (1987). |
| Библиографическая ссылка | [3] Beatty, M. F. and Hayes, M. A.: Deformations of an elastic, internally constrained material-Part 1: Homogeneous deformations. J. Elasticity, 29, 1-84 (1992). |
| Библиографическая ссылка | [4] Beatty, M. F. and Hayes, M. A.: Deformations of an elastic, internally constrained material-Part 2: Nonhomogeneous deformations. Q. J. Mech. Appl. Math., 45, 663-709 (1992). |
| Библиографическая ссылка | [5] Bell, J. F.: Contemporary perspectives in finite strain plasticity. Int. J. Plasticity, 1, 3-27 (1985). |
| Библиографическая ссылка | [6] Duda, F. P. and Martins, L. C.: Compatibility conditions for the Cauchy-Green strain fields: Solutions for the plane case. J. Elasticity, 39, 247-264 (1995). |
| Библиографическая ссылка | [7] Duda, F. P. and Martins, L. C.: Plane deformations with constant strain invariants, Internal Report of the Mechanical Engineering Department, COPPE-Universidade Federal do Rio de Janeiro, Brazil. |
| Библиографическая ссылка | [8] Ericksen, J. E.: Deformations possible in every compressible, perfectly elastic material. J. Math. Phys., 34, 126-128 (1955). |
| Библиографическая ссылка | [9] Ericksen, J. E.: Deformations possible in every isotropic incompressible, perfect elastic material body. Z. Angew. Math. Phys., 5, 466-489 (1954). |
| Библиографическая ссылка | [10] Ericksen, J. E.: Constitutive theory for some constrained elastic cristals. Int. J. Solids Structures, 22, 951-964 (1986). |
| Библиографическая ссылка | [11] Fosdick, R. L.: Remarks on compatibility, in Developments in Mechanics of Continua, pp. 109-127, Academic Press, New York, 1966. |
| Библиографическая ссылка | [12] Fosdick, R. L. and Schuler, K W.: On Ericksen's problem for plane deformations with uniform transverse stretch. Int. J. Eng. Sci., 7, 217-233 (1969). |
| Библиографическая ссылка | [13] Gurtin, M. E.: An Introduction to Continuum Mechanics, Academic Press, New York, 1981. |
| Библиографическая ссылка | [14] Klingbeil, W. and Shield, R. T.: On a class of solutions in plane finite elasticity. Z. Angew. Math. Phys., 17, 489-501 (1966). |
| Библиографическая ссылка | [15] Pucci, E. and Saccomandi, G.: Some universal solutions for totally inextensible isotropic elastic materials. Q. J. Mech Appl. Math., 49, 147-162 (1996). |
| Библиографическая ссылка | [16] Pucci, E. and Saccomandi, G.: Universal relations in constrained elasticity. Math. Mech. Solids, 1, 207-217 (1996). |
| Библиографическая ссылка | [17] Rivlin, R. S. and Saunders, D. W.: Large elastic deformations of isotropic materials, VII. Experiments on the deformation of rubber. Philosophical Trans. Roy. Soc., A243, 251-288 (1951). |
| Библиографическая ссылка | [18] Singh, M. and Pipkin, A. C.: Note on Ericksen's problem. Z. Angew. Math. Phys., 16, 706-709 (1965). |
