Micromechanical modeling of rubber-like materials based on analytical network averaging

Abstract eng:
In this contribution, a micromechanical model is proposed to capture quasi-static response of all types of rubber-like materials. Accordingly, the rubber composite is decomposed into a pure rubber network considered to contribute to the deformation-induced network rearrangement, and a polymer particle network in charge of the network damage. The numerical integration over the unit sphere is avoided by using a generalized analytical network-averaging concept. The free energy of polymer chains is developed on the basis of a closed-form of Rayleigh’s exact non-Gaussian distribution function. The inelastic effects in filled rubbers are elucidated by three deformation-induced mechanisms: network damage, network recovery, and network rearrangement. The proposed model includes very few physically motivated material constants and demonstrates good agreement with multi-dimensional experimental data of both unfilled and filled rubbers. The result confirms that the concept of numerical integration over the unit sphere is not crucial for both isotropic and anisotropic constitutive modeling.

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