## 1 Introduction  
The material constitutive relationship is not only the conclusion of some regulations summarized from experimental data, but also plays an important role in numerical simulations. It reflects the realistic physical and mechanical properties of materials as much as possible to improve the accuracy of numerical results. At present, various kinds of constitutive models for materials are being developed and being optimized constantly along with an increasing need for numerical simulations. Especially for those materials under the loading conditions of large strains, high strain rates, and high pressures (LHH), dynamic constitutive models usually contain more complicated parameters of physical properties and some sensitive coefficients such as various rate effects [1; 2; 3; 4; 5] and strength coefficients [6; 7; 8], so that the parameter determination becomes an increasingly difficult problem. Therefore, accurate parameter determination for material constitutive models, which may directly affect the reliability and validity of the analytical results in numerical simulations, has become a significant task [9], and a growing number of researchers have devoted themselves to this work [10; 11; 12]. In computational constitutive models for materials subjected to LHH, [PERSON], [PERSON], and [PERSON] et al. contributed significantly to research on a wide variety of materials in the past 30 years. Initially, [PERSON] and [PERSON] [1] reported a constitutive model and experimental data for metals including copper, brass, nickel, iron, etc., under LHH conditions. Later, the Johnson-Holmquist-Ceramics (JH-1) constitutive model was first presented by [PERSON] and [PERSON] [2] to study the mechanical behavior of brittle materials subjected to LHH. Afterwards, a corrected constitutive model named the Johnson-Holmquist-2(JH-2) model [3] was presented based on the JH-1 model considering the softening property for some brittle materials such as boron carbide (B\({}_{4}\)C). Further studies were performed for the high strain rate properties and constitutive modeling of glass [13] and the response of B\({}_{4}\)C [4] subjected to severe loading conditions with LHH based on the JH-2 model, and subsequently a variety of impact and penetration problems were illustrated using the methods of Lagrangian finite element and Eulerian finite difference computations. During the same period, another constitutive model was developed for concrete subjected to LHH [14], called \"HJC\", derived from the \"Holmquist-Johnson-Cook\" constitutive model [15; 16]. Subsequently, [PERSON] et al. [17] and [PERSON] et al. [5] expanded the application to aluminum nitride subjected to LHH using the JH-2 model. Different from the general brittle material, however, phase change is not considered in the previous JH-2 model, but is a new feature in their corrected constitutive model so that the embryonic form of the Johnson-Holmquist-Beissel (JHB) model was developed [5]. Additionally, [PERSON] and [PERSON] [18; 19] redressed the response of B\({}_{4}\)C to high-velocity impact adopting optimized experimental data, and then the JHB constitutive model was used to simulate the material behavior under penetration, which illustrated the importance of the material parameters for the accuracy of simulations. Recently, a corrected computational constitutive model was presented based on the JHB model for glass subjected to LHH, and the effect of the third invariant was also included [20]. Apart from the JH-series constitutive models mentioned above, some novel constitutive models have also appeared considering different aspects, e.g., discontinuous deformation analysis (DDA) contact constitutive model [21], statistical damage constitutive model [22; 23; 24], average strain energy density (ASED) criterion for brittle and quasi-brittle materials [25], local and nonlocal damage models [6], frictional sliding crack model, and the strain energy density factor approach [7].