Orthotropic cyclic stress-softening model for pure shear during repeated loading and unloading

Rickaby, Stephen R. and Scott, Nigel H. (2014) Orthotropic cyclic stress-softening model for pure shear during repeated loading and unloading. IMA Journal of Applied Mathematics, 79 (5). pp. 869-888. ISSN 0272-4960

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Abstract

We derive an orthotropic model to describe the cyclic stress softening of a carbon-filled rubber vulcanizate through multiple stress-strain cycles with increasing values of the maximum strain. We specialize the deformation to pure shear loading. As a result of strain-induced anisotropy following on from initial primary loading, the material may subsequently be described as orthotropic because in pure shear there are three different principal stretches so that the strain-induced anisotropy of the stress response is different in each of these three directions. We derive non-linear orthotropic models for the elastic response, stress relaxation and residual strain to model accurately the inelastic features associated with cyclic stress softening. We then develop an orthotropic version of the Arruda-Boyce eight-chain model of elasticity and then combine it with the ideas previously developed in this paper to produce an orthotropic constitutive relation for the cyclic stress softening of a carbon-filled rubber vulcanizate. The model developed here includes the widely occurring effects of hysteresis, stress-relaxation and residual strain. The model is found to compare well with experimental data.

Item Type: Article
Uncontrolled Keywords: hysteresis,mullins effect,orthotropy,residual strain,stress-relaxation
Faculty \ School:
Faculty of Science > School of Mathematics
Related URLs:
Depositing User: Pure Connector
Date Deposited: 08 Apr 2016 11:48
Last Modified: 22 Apr 2020 01:15
URI: https://ueaeprints.uea.ac.uk/id/eprint/58174
DOI: 10.1093/imamat/hxu021

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