Modeling the damage-induced softening behavior of brain white matter using a coupled hyperelasticty-damage model

White matter in the brain is structurally anisotropic consisting of large bundle of aligned axonal fibers. Hyperelastic, transversely isotropic constitutive models are typically used in the modeling and simulation of such tissues. However, most studies constrain the material models to describe the mechanical behavior of white matter in the limit of small deformation, without considering the experimentally observed damage initiation and damage-induced material softening in large strain regime. In this study, we extend a previously developed transversely isotropic hyperelasticity model for white matter by coupling it with damage equations within the framework of thermodynamics and using continuum damage mechanics method. Two homogeneous deformation cases are used to demonstrate the proposed model's capability in capturing the damage-induced softening behaviors of white matter under uniaxial loading and simple shear, along with the investigation of fiber orientation effect on such behaviors and material stiffness. As a demonstration case of inhomogeneous deformation, the proposed model is also implemented into finite element codes to reproduce the experimental data (nonlinear material behavior and damage initiation) from an indentation configuration of porcine white matter. Good agreement between numerical results and experimental data is achieved indicating the potential of the proposed model in characterizing the mechanical behaviors of white matter considering damage at large strain.