Modeling Anisotropic Hyperelastic Behavior of Soft Tissues Using the Smoothed Particle Hydrodynamics Method

Modeling the mechanical behavior of many soft tissues and certain man-made synthetic materials requires accurate representation of their complex and anisotropic nature. In this research, we implement the anisotropic hyperelastic Holzapfel-Gasser-Ogden (HGO) model using the meshless smoothed particle hydrodynamics (SPH) method. To overcome the challenges of incompressibility, inherent in this class of materials and the associated difficulties of the numerical solution, mixed formulations are employed. Accordingly, the SPH model is developed within a total Lagrangian framework, utilizing first-order conservation laws for linear momentum, the deformation gradient tensor, surface mapping and volume mapping. The accuracy of the implementation is demonstrated by solving several well-known benchmarks in the dynamic behavior of solids undergoing large deformations. Additionally, the results of the hyperelastic model are compared with those obtained from the finite element software Abaqus. Furthermore, the behavior of human skin as an anisotropic soft tissue reinforced with collagen fibers is simulated and compared with available experimental results. The comparisons show that the SPH model effectively simulates the anisotropic behavior of soft tissues under large deformations. The findings of this research indicate that the meshless SPH method can be utilized as a framework for modeling the behavior of soft tissues with complex deformations.