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Some Effects of Fiber Dispersion on the Mechanical Response of Incompressible Soft Solids

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Abstract

Many soft tissue materials consist of an isotropic ground matrix which is reinforced by fibers that are dispersed about a mean orientation. In this work, we attempt to examine how fiber dispersion affects the mechanical response of a base Neo-Hookean material subjected to a few simple deformations. We find that the composite which consists of a highly dispersed fiber assembly exhibits large resistance to compressive loads along the mean fiber direction. It is an established fact that for a unidirectionally reinforced base material, fiber compression leads to material instability and loss of ellipticity of governing equations primarily due to fiber kinking. We observe that reinforcement by means of dispersed fibers improves material stability against kinking in planar deformations. We present results for two particular fiber strain energy densities, namely, the standard reinforcing model and the exponential model and employ the rotationally symmetric von-Mises distribution function to incorporate fiber dispersion. It is expected that the results qualitatively depict the general response of a Neo-Hookean solid that is reinforced by fibers with a convex strain energy function and which are dispersed with rotational symmetry about a preferred direction.

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Acknowledgements

The author wishes to thank Prof. Biswanath Banerjee for helpful discussions on nonlinear elasticity, and Prof. Arghya Deb for insightful discussions and for help in revising an earlier version of this article. Thanks are due to the anonymous reviewers for their constructive comments that have helped in improving this study.

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  1. Department of Civil Engineering, Indian Institute of Technology, Kharagpur, 721302, West Bengal, India

    Shashwati Sen

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Sen, S. Some Effects of Fiber Dispersion on the Mechanical Response of Incompressible Soft Solids. J Elast 150, 119–149 (2022). https://doi.org/10.1007/s10659-022-09901-8

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