The Pseudo-Elastic Response of Rubberlike Solids

Particle-reinforced rubbers exhibit a marked hysteretic response during unloading after loading in uniaxial tension, compression or shear, for example, i.e. the stress on unloading is significantly less than that on loading at the same strain. The difference in the stresses corresponding to the same strain level under loading and retraction depends primarily on the proportion of filler in the rubber compound; for unfilled rubber the difference is negligible but it becomes very marked for elastomers with high carbon black content. The stress difference is greatest during the first loading-unloading cycle and approaches a fixed (strain-dependent) value after a number of cycles. This hysteretic behavior is not accounted for when the mechanical properties are represented in terms of a strain-energy function, i.e. if the material is modeled as hyperelastic. This project is concerned with the formulation of constitutive models to capture certain inelastic effects in particle-reinforced rubbers subjected to loading-unloading cycles. As a basis for the modeling we use some recently obtained experimental data.

Figure1: Pre-conditioning of a particle-reinforced dumbbell specimen with 1 phr of carbon black with maximum stretch λ = 3.

Figure 2: Pre-conditioning of a particle-reinforced dumbbell specimen with 20 phr of carbon black with maximum stretch λ = 3.

Figure3: Pre-conditioning of a particle-reinforced dumbbell specimen with 60 phr of carbon black with maximum stretch λ = 3.

Publications:

Dorfmann A., Ogden R.W.: A Constitutive Model for the Mullins Effect with Permanent Set in Particle-Reinforced Rubber, International Journal of Solids and Structures 41 (2004), 1855-1878.

Dorfmann A.: Stress Softening of Elastomers in Hydrostatic Tension, Acta Mechanica 165 (2003), 117-137.

Dorfmann A., Ogden R.W.: A Pseudo-Elastic Model for Loading, Partial Unloading and Reloading of Particle-Reinforced Rubber, International Journal of Solids and Structures 40 (2003), 2699-2714.

Drozdov A.D., Dorfmann A.: A Micromechanical Model for the Response of Filled Elastomers at Finite Strains, International Journal of Plasticity 19 (2003), 1037-1067.

Drozdov A.D., Dorfmann A.: Stress-strain Relations in Finite Viscoelastoplasticity of Rigid-Rod Networks: Applications to the Mullins Effect, Continuum Mechanics and Thermodynamic 13 (2001), 183-205.