“…fibres, vir fl , in the virgin sate, then the equation in the virgin state is rewritten as Similarly, the Cauchy stress components in the tissue are divided into three parts: the first part is the stress in the matrix vir m due to vir m , the second part is the stress in the circumferential fibres vir fc and the third part is the stress in the longitudinal fibres vir fl , i.e. Likewise, the circumferential Young's moduli in total, in the matrix and in the fibres E dam c , E dam mc and E dam fc as well as the longitudinal Young's moduli in total, in the matrix and in the fibre E dam l , E dam ml and E dam fl are expressed asFor linear materials, the damage variable is related to the ratio of the Young's modulus in the damaged state to the modulus in the virgin state,[3,8,9,16,17,30,31], and written mathematically as For anisotropic, nonlinear GB walls, it is supposed that this definition is held for each pair of Young's moduli in Eq. (9) in the damaged state and those in Eq (12).…”