A 3D brittle fracture model with effect of microstructure, strain gradient and strain rate

Based on the two-scale asymptotic expansion theory, we establish a dynamic fracture model for 3D micro-cracked materials which extends the previous 2D results presented by the authors in Rao (2022); Rao et al. (2023). Using the two-scale theory for 3D problems, an analytical formulation of dynamic energy release rate is obtained that includes additive contributions of macroscopic strain, strain gradient and strain rate. The coefficients of the strain, strain gradient and strain rate are related to the microstructural size and derivatives of the homogenized (effective) elastodynamics moduli, which are determined by solutions of elementary elastodynamics problems defined in a reference unit cell. The microdamage evolution equation is developed by combining the analytical formulation of dynamic energy release rate with the Griffith fracture law. In contrast to the two-dimensional case where the normalized microcrack length is used as the measure of microdamage, in the three-dimensional case, the normalized microcrack area is used as the measure of microdamage, and then, the dynamic evolution equation of the microdamage variable for 3D problems has the same form as that for 2D cases. We analyze the properties of the homogenized elastodynamics moduli and compare them with those in the 2D cases. The coupling of microstructure size, strain gradient and strain rate are analyzed by examining local material responses and spallation experiment. The finite element simulations based on the model are well validated against available experimental results and previous reports.