A physically-based damage model for soft elastomeric materials with anisotropic Mullins effect

In this paper, we develop a new physically-based damage model to describe the anisotropic Mullins effect of elastomeric materials. The damage model is based on our previous hyperelastic model (Xiang et al., 2018), which has a strain energy density function composed of the crosslinked part and the entangled part. We describe the damage of the crosslinked network using a network alteration theory. Chains along various directions suffer from different degrees of damage and thus cause the anisotropy. The irreversible degradation on constraints for entanglement leads to the reduction of the entangled modulus with the increasing of historical maximal stretch. This model can well capture the stress-softening, anisotropy and residual deformation (permanent set) with only five parameters that have definite physical meanings. It also predicts the damage behaviors under various states of deformation, for both unfilled and filled elastomers. We use the model to fit the experiment data of VHB 4905, silicon rubber, carbon-black filled styrene butadiene rubber (SBR) and carbon-black filled nature rubber (NR). The damage induced anisotropy, which is validated by directional loading experiments of silicon rubber and carbon-black filled NR, can be characterized. We compare this model with other existing similar ones, and show its competitive advantages in characterizing the comprehensive Mullins effect with concise and explicit mathematical expression and physical meaning.