caa a22 4500 475840046 CHVBK 20180406123859.0 cr unu---uuuuu 170329e20000201xx s 000 0 eng 10.1023/A:1004734311626 doi (NATIONALLICENCE)springer-10.1023/A:1004734311626 An extension of Key's principle to nonlinear elasticity [Elektronische Daten] [M. Shariff, D. Parker] A variational principle for finite isothermal deformations of anisotropic compressible and nearly incompressible hyperelastic materials is presented. It is equivalent to the nonlinear elastic field (Lagrangian) equations expressed in terms of the displacement field and a scalar function associated with the hydrostatic mean stress. The formulation for incompressible materials is recovered from the compressible one simply as a limit. The principle is particularly useful in the development of finite element analysis of nearly incompressible and of incompressible materials and is general in the sense that it uses a general form of constitutive equation. It can be considered as an extension of Key's principle to nonlinear elasticity. Various numerical implementations are used to illustrate the efficiency of the proposed formulation and to show the convergence behaviour for different types of elements. These numerical tests suggest that the formulation gives results which change smoothly as the material varies from compressible to incompressible. Kluwer Academic Publishers, 2000 nonlinear elasticity nationallicence near incompressibility nationallicence variational formulation nationallicence finite deformations nationallicence finite elements nationallicence Shariff M. School of Computing and Mathematics, University of Teesside, TS1 3BA, Middlesborough, Cleveland, U.K. aut Parker D. Department of Mathematics and Statistics, University of Edinburgh, The King's Buildings, EH9 3JZ, Edinburgh, U.K. aut Journal of Engineering Mathematics Kluwer Academic Publishers 37/1-3(2000-02-01), 171-190 0022-0833 37:1-3<171 2000 37 10665 https://doi.org/10.1023/A:1004734311626 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1004734311626 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Shariff M. School of Computing and Mathematics, University of Teesside, TS1 3BA, Middlesborough, Cleveland, U.K aut NATIONALLICENCE 700 1- Parker D. Department of Mathematics and Statistics, University of Edinburgh, The King's Buildings, EH9 3JZ, Edinburgh, U.K aut NATIONALLICENCE 773 0- Journal of Engineering Mathematics Kluwer Academic Publishers 37/1-3(2000-02-01), 171-190 0022-0833 37:1-3<171 2000 37 10665 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer