An exact solution to the Lame problem for a hollow sphere for new types of nonlinear elastic materials in the case of large deformations

被引：8
作者：
Levin, V. A. [1 ]
Podladchikov, Y. Y. [1 ,2 ]
Zingerman, K. M. [1 ,3 ,4 ]
机构：
[1] Lomonosov Moscow State Univ, Dept Mech & Math, Moscow 119991, Russia
[2] Univ Lausanne, Inst Earth Sci, CH-1015 Lausanne, Switzerland
[3] Tver State Univ, Dept Appl Math & Cybernet, Tver 170100, Russia
[4] Natl Res Nucl Univ MEPhI, Div Nucl Phys & Technol, Moscow 115409, Russia
来源：
EUROPEAN JOURNAL OF MECHANICS A-SOLIDS | 2021年 / 90卷
基金：
俄罗斯科学基金会;
关键词：
Lame  problem; Finite strain; Murnaghan's equation of state; Nonlinear elasticity; Exact solutions; STRONG ELLIPTICITY; INCLUSION; PRESSURE; EQUILIBRIA;
D O I：
10.1016/j.euromechsol.2021.104345
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
Constitutive relations of two classes are proposed for nonlinear elastic isotropic materials, which, in case of purely volumetric deformation, are reduced to the Murnaghan's equation of state. Exact analytical solution of the Lame problem of the radially symmetric deformation of a hollow sphere is obtained for one of these material classes. Nonlinear effects are studied. The non-uniqueness of solution is obtained for the case in which the sphere radii are specified in the initial configuration. It is shown for this case that there is a limiting pressure, above which the problem has no solution. The strong ellipticity conditions are tested. The obtained results can be used in geomechanics for modeling the recrystallization of metamorphic rocks.
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页数：7
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