Damage functions of the internal variables for soft biological fibred tissues

Several typical equations for damage variables are proposed in the literature in the context of Continuum Damage Mechanics for fibred materials such as soft biological tissues. All these proposed functions are defined for the same or similar soft tissues. The applicability of some of them, however, is not clear. The paper compares a series of damage functions given in the literature for the description of softening in soft biological tissues. In addition, a new damage function is introduced. The difference in the response of this function compared to those previously proposed in the literature is that the first derivative is zero at the initial damage state. This represents a potential advantage with respect to numerical calculations since smooth derivatives are obtained.