New multi-axial constitutive models for large elastic deformation behaviors of soft solids up to breaking

A hyperelastic model is proposed to characterize large elastic deformation behaviors of soft solids. Novelties in four respects are incorporated in this model, namely, (i) general compressible deformations may be treated and, accordingly, the usually-assumed incompressibility constraint and associated issues may be bypassed; (ii) applicability for all kinds of material samples may be automatically ensured, in the sense that any given test data for three deformation modes may be exactly fitted, including uniaxial, equi-biaxial and plane-strain extension; (iii) model parameters of direct physical meanings may be provided to characterize both strain-stiffening and softening effects; and (iv) breaking behavior may be simulated. Numerical results for model validation are in good agreement with Treloar's classic data for rubbers and with extensive data for various kinds of polymer gels.