Quadtree SBFEM-based nonlocal damage analysis for soft biological tissues with interval parameters

The interval model, which requires less prior information than probabilistic and fuzzy models, is used to describe the uncertainty of the material and geometric parameters of soft biological tissues. A quadtree scaled boundary finite element method (quadtree SBFEM) and an optimization-based numerical algorithm are developed for the interval damage analysis of soft biological tissues. The material is hyperelastic, and the damage behavior is described by a gradient-enhanced damage model without mesh dependence. The deterministic problem is solved by the image-based quadtree SBFEM, and the interval problem is solved via an optimization based bounds estimation, which is reliable and insensitive to the scale of the intervals. A Legendre polynomial surrogate (LPS) is constructed to approximate the SBFEM-based deterministic solutions to reduce the computational cost of the optimization process. Numerical examples are presented to illustrate the effectiveness of the proposed approaches, and the uncertain behavior of the Cauchy stress and damage function.