On irreversibility and dissipation in hyperelasticity with softening

Bulk and interface material failures are often modeled via hyperelastic stored energy functions incorporating softening behavior. The softening is reversible due to the hyperelastic nature of the constitutive law and material can "heal" under unloading. To prevent this healing, special numerical procedures (like finite element deletion) are usually used in computer simulations. In the present work, we suggest an alternative: very simple analytical formulation, which makes failure irreversible when a critical stored energy is reached. This new notion is directly incorporated into the constitutive equations, consequently, relieving the need for preliminary discretization of the boundary-value problem.