Fung's model of arterial wall enhanced with a failure description

One of the seminal contributions of Y.C. Fung to biomechanics of soft tissue is the introduction of the models of arterial deformation based on the exponential stored energy functions, which are successfully used in various applications. The Fung energy functions, however, explain behavior of intact arteries and do not include a description of arterial failure. The latter is done in the present work where Fung's model is enhanced with a failure description. The description is based on the introduction of a limiter for the stored energy - the average energy of chemical bonds, which can be interpreted as a failure constant characterizing the material 'toughness'. The limiting failure energy controls materials softening, which indicates the onset of failure. We demonstrate the efficiency of the enhanced Fung formulation on a problem of the arterial inflation under internal pressure. We show, particularly, that residual stresses delay the onset of failure. The considered softening hyperelasticity approach is an alternative to the simplistic pointwise failure criteria of strength of materials on the one hand and the sophisticated approach of damage mechanics involving internal variables on the other hand.