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Remarks on the Behavior of Simple Directionally Reinforced Incompressible Nonlinearly Elastic Solids

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Abstract

The effect of directional reinforcing in generating qualitative changes in the mechanical response of a base neo-Hookean material is examined in the context of homogenous deformation. Single axis reinforcing giving transverse isotropy is the major focus, in which case a standard reinforcing model is characterized by a single constitutive reinforcing parameter. Various qualitative changes in the mechanical response ensue as the reinforcing parameter increases from the zero-value associated with neo-Hookean response. These include (in order): the existence of a limiting contractive stretch for transverse-axis tensile load; loss of monotonicity in off-axis simple shear; loss of monotonicity in on-axis compression; loss of positivity in the stress-shear product in off-axis simple shear; and loss of monotonicity for plane strain in on-axis compression. The qualitative changes in the simple shear response are associated with stretch relaxation in the reinforcing direction due to finite rotation.

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Authors and Affiliations

  1. Department of Materials Science and Mechanics, Michigan State University, East Lansing, MI, 48824-1226, U.S.A

    G.Y. Qiu & T.J. Pence

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  1. G.Y. Qiu
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  2. T.J. Pence
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Qiu, G., Pence, T. Remarks on the Behavior of Simple Directionally Reinforced Incompressible Nonlinearly Elastic Solids. Journal of Elasticity 49, 1–30 (1997). https://doi.org/10.1023/A:1007410321319

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  • DOI: https://doi.org/10.1023/A:1007410321319

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