A hyperelastic-damage model based on the strain invariants

We develop a unified framework to describe the hyperelastic and damage behaviors of soft materials. The free energy density consists of both the crosslinked part of Langevin chains and the entanglement part described by a tube model. The micro–macro transition is obtained by using the averaging value over a microsphere. Consequently, the free energy density only depends on the strain invariants. The damage mechanism is then incorporated via the network alteration theory for the crosslinked part, while the deformation can also induce dilation of the tube and subsequent a decrease in the modulus for the entangled part. The hyperelastic model captures the Mooney Rivlin plot with a first decrease in the small deformation regime and then an increase in the large deformation region. The hyperelastic model can also accurately reproduce the stress–strain relationships in the uniaxial and biaxial loading conditions for various elastomer systems. The damage model can describe the stress response of filled rubbers in uniaxial and biaxial loading conditions, which shows a considerable improvement compared with the damage model without the entanglement effect. Since the model only depends on the strain invariants, the model can be easily implemented into the commercial finite element software Abaqus through a UHYPER. The finite element model can accurately reproduce the experimentally measured strain distribution of filled rubbers with complex geometry in the loading process. These results clearly show that the hyperelastic-damage model developed in this work has strong potentials to predict the mechanical responses of soft materials for practical applications.