Quadtree SBFEM and MSPM Based Uncertain Damage Analysis With Random Field Model for Soft Biological Tissues

This paper presents a numerical model for damage problems in soft biological tissues with random fields, integrating the advantages of the modified stochastic perturbation method (MSPM) and quadtree scaled boundary finite element method (quadtree SBFEM). The anisotropic hyperelastic constitutive model is used, and the damage behavior is described by a gradient-enhanced damage model without mesh dependence. The deterministic problem is formulated by the quadtree SBFEM with the benefit of convenient mesh regeneration directly from images. In order to describe spatial heterogeneous soft biological tissues, the constitutive parameters are assumed by the random field model, which is given by Karhunen-Loève (K-L) expansion. The stochastic responses of structures are solved by MSPM, for which the derivatives of the system matrices are not required. Numerical examples are conducted to verify the accuracy and efficiency of the proposed approaches and to obtain the mean values and standard deviations of the random response of spatial heterogeneous soft biological tissues damage problems, including the calculation of the probability of failure (PoF) of arterial wall during atherosclerosis in angioplasty.