A complementary energy-based constitutive model for the Mullins effect

A phenomenological pseudo-elastic model for isotropically elastic, incompressible materials exhibiting Mullins-type dissipation has been developed using a complementary energy-based approach. The work-conjugate constitutive variables in the inverse stress-strain relations are the Hencky logarithmic strain tensor and the Cauchy stress tensor. The thermo-mechanically consistent pseudo-elastic model is derived by applying the dissipation inequality in terms of complementary energy. The basic constitutive model for the virgin material is described by a complementary energy potential, which is assumed to be a power-law function of the second and third invariants of the deviatoric Cauchy stress tensor. The scalar measure of the maximum load is chosen to be the basic complementary energy. The virgin state variable describes the amplification of the logarithmic strain and behaves monotonically with respect to the Cauchy stress along the secondary loading paths. The applicability and efficacy of the model are demonstrated for uniaxial tension problems. The basic model contains three fitting parameters, and the monotonic amplification of the logarithmic strain is described by one additional fitting parameter. The predictive capability of this four-parameter pseudo-elastic model is validated through parameter fitting procedures using three different sets of experimental data from the open literature.