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Calculus of the square root of a positive definite symmetrical linear mapping by solely determining a rotation

type de publication      communication internationale avec actes publiés
date de publication 2001
auteur(s) Vallee Claude; Pietraszkiewicz W.; Bouby Céline; Fortuné Danielle
conférence 5th International Seminar on Geometry, Continua and Microstructures
     dates de 26-09-2001 à 28-09-2001
     lieu Sinaia, Romania
     nom des actes Proceedings of the 5th International Seminar on Geometry, Continua and Microstructures
pages 255 – 263
ISBN / ISSN 973-27-0880-8
résumé Given a positive definite symmetrical mapping such that the right Cauchy-Green strain tensor C of 3-dimensional continuum mechanics, we prove that it can be regarded as the composition of a somewhat artificial deformation gradient with its adjoint. Using the result that the polar decomposition of this deformation gradient can be managed starting by the determination of the rotation, we prove that the square root of C can also obtained by worrying only with rotations. We end by generalizing to every finite dimension greater than 3.
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