Simulation of finite deformation failure in soft biological tissues by a mixed local and nonlocal gradient damage approach.

Abstract

This study introduces an anisotropic energy limiter-based gradient damage framework designed to predict the failure of soft biological tissues under finite deformations. Traditional damage models often struggle with these materials due to their complex, anisotropic microstructures and highly nonlinear behavior. The proposed framework addresses these challenges by incorporating an anisotropic energy limiter function to control local damage evolution and a gradient-enhanced formulation that ensures mesh-independent results through a rate-dependent damage evolution law that accounts for the loading-rate sensitivity of soft biological tissues. A significant theoretical contribution of this work is the derivation of closed-form analytical solutions for anisotropic damage, which are used to verify numerical outcomes and facilitate model parameter fitting. To enhance computational performance, the authors also introduce a simplified plane stress version of the Holzapfel-Gasser-Ogden (HGO) model, which improves numerical efficiency and stability while mitigating locking issues during finite element method (FEM) simulations. The framework was validated through comparisons with experimental data from aortic specimens, analytical solutions, and published numerical benchmarks across 2D and 3D structures. The results show good agreement with the reference solutions and experimental observations, demonstrating that the model effectively captures progressive failure, strain softening, and anisotropic damage evolution, thereby providing an effective computational framework for the biomechanical simulation of soft tissue failure.