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On the Dirichlet problem for incompressible elastic materials

✍ Scribed by M. Hayes; C. O. Horgan

Publisher
Springer Netherlands
Year
1974
Tongue
English
Weight
502 KB
Volume
4
Category
Article
ISSN
0374-3535

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✦ Synopsis

The linearized equations governing the deformations of incompressible elastic bodies are discussed. The Dirichlet problem is formulated for this system of equations using the theory of elliptic systems due to Douglis and Nirenberg. A uniqueness theorem is proved. Necessary and sufficient conditions for uniqueness of solution to the Dirichlet problem are obtained for small deformations of a Mooney-Rivlin material which has been subjected to a finite homogeneous biaxial deformation.

RI~SUMI~

Le but de cet essai est d'analyser les ~quations linearis6es en relation avec les d6formations des corps 61astiques incompressibles. Le probl6me de Dirichlet est formul6 en vue de ce syst6me d'6quations utilisant la theorie des syst6mes elliptiques de Douglis et Nirenberg. Un th6or6me d'uaicit6 est 6tabli. Les conditions n6cessaires et suffisantes pour l'unicit6 de la solution au probl6me de Dirichlet sont obtenues darts le cas de d6formations mineures Ii6es ~ des mat~riaux Mooney-Rivlin qui ont ~t6 sujets/l une d6formation finie et homogSne, ~gale dans les deux directions.

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