Damage-induced Stress-softening Effects in Elastomeric and Biological Membranes

The two-dimensional finite strain constitutive model for membranes is presented; it incorporates stress-softening behaviour typically observed in elastomeric and natural or biologically-derived soft membranes subjected to severe deformations. It is assumed that the experimentally observed progressive degradation of a membrane stiffness under monotonous and cycling loading can macroscopically be modelled by a scalar damage variable. The evolution of this variable during the deformation process is specified by the kinetic law of damage growth, which together with the constitutive equation for the surface stress tensor and the damage criteria completely determines the presented constitutive model. It is shown that the general constitutive model can be specified for particular classes of problems under certain additional assumptions. In particular, a remarkable simplification of the model is achieved assuming that the state of strain at membrane points can be characterised by a single scalar variable, the so-called effective (equivalent) strain. This assumption is combined with the hypothesis of maximum strain according to which the stress softening in the membrane depends only on the maximum previous strain experienced during deformation history. Within these two hypotheses the progressive degradation of membrane stiffness is completely described by a softening function which determines the current value of damage variable in terms of maximum equivalent strain. Various specific forms of such a softening function as well as different definitions of the effective strain are considered.