Over the past few decades, dynamic fracture theory, rooted in energy balance and crack propagation, has laid a fundamental groundwork for analyzing fracture phenomena in various ballistic applications. This paper systematically reviews several classical models that characterize the compressive failure behavior of brittle materials. Models based on energy conversion principles posit that the total energy of a fracturing body splits into the kinetic energy of expanding fragments and the fracture energy—the latter theoretically derived from changes in the system’s free energy during fracture. In contrast, models centered on crack propagation explore key phenomena such as elastic modulus degradation, dilatancy, pressure sensitivity, and strain-rate dependent yielding. Additionally, a range of models have been effectively developed for numerical simulations. Among these, the DP and JH-2 models describe the constitutive and failure behavior of brittle solids by incorporating pressure dependence and stress-strain relationships, while the DFH model employs a probabilistic framework based on Weibull statistics to represent the fracture states of brittle materials. Through a detailed analysis of these classical frameworks, this review provides critical insights that support the advancement and refined modeling of compressive fracture in brittle solids.
Minghui et al. (2025) studied this question.