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Abstract.Exact explicit expressions are obtained for an isotropic tensor-valued function of a nonsymmetric second-order tensor, and its derivative, without resort to eigenvector calculations.These are then used to derive explicit expressions for the material time derivative of the general strain measures in terms of the deformation rate tensor. Introduction.Isotropic tensor-valued functions of symmetric second-order tensors are used to express various strain measures in the kinematics of finite deformation. These strain measures are often expressed in a spectral form with respect to the principal triad of the right stretch tensor (left stretch tensor, if the strain measure is Eulerian)\ Hill [5]. Using the Hamilton-Cayley theorem, a strain measure of this kind can be represented in the coordinate-invariant form. Ting [14] obtains closed-form expressions for the general isotropic functions of a symmetric second-order tensor. Among the various strain measures, logarithmic strain is considered to have certain advantages in constitutive modeling; Hill [6]. However, the relation between the rate of stretch (or deformation rate) and the material time derivative of the logarithmic strain is very complicated. Hill [6] obtains this relation in component form with respect to the principal triad of the right stretch tensor. Later, Hill [7] obtains a relation between the deformation rate and

Herein, acid functionalized carbon nanotubes (FCNTs) reinforced epoxidized natural rubber (ENR 25) composites with 25% epoxidation are studied with particular reference to the effect of FCNTs on microstructural development along with their effect on thermo-mechanical and gas barrier properties. Excellent improvement in tensile strength, that is, 128% and 118%, was observed with the addition 1 and 2 wt% of FCNTs, respectively, without compromising the elongation at break. A 76% improvement in oxygen impermeability was found for 2 wt% of FCNTs. Chemical interactions among FCNTs and ENR 25 altered the composite morphology and led to good dispersion, both of which contribute to the excellent thermo-mechanical and gas barrier properties of the composites. The distribution of the filler inside ENR 25 has been characterized with scanning electron microscopy, which unveiled segregated FCNTs. The obtained experimental gas permeability values were correlated with the well-known Bharadwaj model. The fabricated functional composites could find applications in automobiles, packaging, and other demanding engineering sectors.

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