A Geometrically Regularized Gradient‐Damage Model With Orthogonality‐Based Energy Split for Dynamic Anisotropic Compression‐Shear Fracture

ABSTRACT

This study proposes a novel geometrically regularized gradient‐damage model for simulating dynamic mixed‐mode fracture in orthotropic materials with tension–compression asymmetry. In this model, a thermodynamic framework is formulated by incorporating damage dissipation into internal energy evolution, from which the constitutive relation and the damage energy release rate are derived. The geometry of sharp cracks is regularized using a functional of crack surface density, resulting in a volumetric expression for the Griffith‐type crack dissipation energy. By enforcing energetic equivalence between the crack dissipation energy and the damage dissipation energy, a gradient damage evolution law is obtained. An orthotropic Helmholtz free energy decomposed by an orthogonality‐based volumetric–deviatoric–spectral split operator is introduced to consider the material anisotropy and tension‐compression asymmetry. A hybrid driving force for unified modelling of mixed‐mode fracture, is then proposed by combining the decomposed free energy with the Mohr–Coulomb criterion and three mode‐dependent fracture energies. The resultant governing equations are discretized within the finite element framework and solved via an alternate minimization Newton–Raphson algorithm. Its accuracy and robustness are verified through three benchmark problems of 2D and 3D dynamic fracture. The results demonstrate the proposed method is powerful in modelling complex dynamic anisotropic mixed‐mode fracture.