A dynamic damage constitutive model and three-dimensional internal crack propagation of rock-like materials in bond-based peridynamic

The original bond-based peridynamic model addresses brittle fracture rather than progressive fracture. It also does not account for the impact of strain rate on bond strength and fails to incorporate the impact of internal length on non-local long-range forces. As a result, it is inadequate for simulating the dynamic failure of rock-like materials under impact loading. To address these limitations, a new approach involves a sextic polynomial attenuation function. This function captures the impact of internal length on non-local long-range forces and leads to the derivation of a corresponding micro-modulus expression. A damage function and a new failure criterion are integrated to describe the nonlinear mechanical behavior and progressive failure of rock-like materials. The influence of strain rate on bond dynamic strength is considered to reflect the strain rate effect in rock materials. The outcome is a newly proposed dynamic damage constitutive model that overcomes the three shortcomings of the original bond-based peridynamic model when simulating the dynamic failure of rock-like materials. Numerical examples are simulated based on this model, and their results are compared with the experimental data. This comparison allows further exploration of the volumetric fracturing behavior and mechanical properties of rock specimens with internal flaws in three dimensions when subjected to impact loading. The findings demonstrate the effectiveness of the proposed model in accurately simulating crack propagation and mechanical properties across varying strain rates in rock-like materials. Notably, the internal flaw's depth significantly influences the specimen's mechanical properties and energy utilization efficiency at a specific flaw angle alpha = 90. Complex three-dimensional cracks, consisting of shell-like, wing, anti-wing, and shear cracks, emerge due to the interconnection of various crack types. The shape of these cracks is intricately linked to the flaw angle and depth. Ultimately, this model solves the challenge of capturing internal crack growth during dynamic impact processes that are often difficult to observe in experimental tests.