Fracture simulation in hyperelastic materials and soft tissues by a novel finite strain smoothing gradient damage approach

Fracture of hyperelastic materials and load-bearing soft tissues is particularly important to various biomechanical applications. The underlying knowledge and mechanisms associated with the initiation and evolution of crack, leading to (bio)material failure, have not been fully understood. We present a novel finite strain smoothing gradient-enhanced damage approach for modeling complicated fracture processes in isotropic/anisotropic hyperelastic materials, in particular, in rubber-like materials and aortic walls. Our recently developed smoothing gradient-enhanced damage model (SGDM), which owns several desirable features for modeling complicated fracture phenomena like crack-branching and mixed mode failure in brittle/quasi-brittle materials, is significantly extended to finite strain with a suitable constitutive model to capture the fracture in hyperelastic materials. For crack growth in arterial walls, the damage model accounts for both the elastin matrix and the anisotropy of the collagen fibers. Numerically, a second-order structural tensor that represents the orientation of collagen fibers is incorporated into the finite strain SGDM framework. The strain energy density is also mathematically augmented with a description of fibers, enabling a thorough investigation of anisotropic soft tissues. Numerical simulations of damage growth in rubber-like and aortic walls using the developed approach, are presented and analyzed. The computed results are thus compared with reference experimental and numerical solutions to show the accuracy and performance of the developed finite strain damage model.