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Derivatives and Rates of the Stretch and Rotation Tensors

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Abstract

General expressions for the derivatives and rates of the stretch and rotation tensors with respect to the deformation gradient are derived. They are both specialized to some of the formulas already available in the literature and used to derive some new ones, in three and two dimensions. Essential ingredients of the treatment are basic elements of differential calculus for tensor valued functions of tensors and recently derived results on the solution of the tensor equation A X + XA= H in the unknown X.

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Authors and Affiliations

  1. Dipartimento di Scienza delle Costruzioni, Università di Napoli “Federico II”, via Claudio 21, 80124, Napoli, Italy. E-mail

    Luciano Rosati

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  1. Luciano Rosati
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Rosati, L. Derivatives and Rates of the Stretch and Rotation Tensors. Journal of Elasticity 56, 213–230 (1999). https://doi.org/10.1023/A:1007663620943

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