Constitutive law of healthy gallbladder walls in passive state with damage effect

Biomechanical properties of human gallbladder (GB) wall in passive state can be valuable to diagnosis of GB diseases. In the article, an approach for identifying damage effect in GB walls during uniaxial tensile test was proposed and a strain energy function with the damage effect was devised as a constitutive law phenomenologically. Scalar damage variables were introduced respectively into the matrix and two families of fibres to assess the damage degree in GB walls. The parameters in the constitutive law with the damage effect were determined with a custom MATLAB code based on two sets of existing uniaxial tensile test data on human and porcine GB walls in passive state. It turned out that the uniaxial tensile test data for GB walls could not be fitted properly by using the existing strain energy function without the damage effect, but could be done by means of the proposed strain energy function with the damage effect involved. The stresses and Young moduli developed in two families of fibres were more than thousands higher than the stresses and Young's moduli in the matrix. According to the damage variables estimated, the damage effect occurred in two families of fibres only. Once the damage occurs, the value of the strain energy function will decrease. The proposed constitutive laws are meaningful for finite element analysis on human GB walls.