Review of mathematical models and methods to research the explosive loads propagation in continuous environments

Design calculations in building and structure engineering are inextricably linked to the analysis of strength, stability, and the stress-strain state (SSS) of structural elements. Today, the importance of assessing structures under special loads and impacts has significantly increased. However, such analyses are often complicated due to the underdevelopment of the mathematical framework and insufficient understanding of the nature and propagation characteristics of such loads. As a result, the creation of adequate computational models becomes nearly impossible. A distinct category among special load analyses is dynamic assessment under seismic, impulsive, and impact loads, including explosive effects. The current state of the problem of constructing blast loads waves propagation mathematical models and approaches to study the dynamic response of structures and buildings under their influence is considered. The classification of different intensity dynamic processes in relation to the deformation rate is given and recommendations for choosing the most effective methods for integrating the computational equations of motion in the time coordinate are given. A review of works on the study of dynamic waves in anisotropic and isotropic environments and soil masses is conducted. The aim of this series of studies is to develop new effective models, methods, and algorithms for analyzing the propagation of shock stress waves in continuous media using the finite element method (FEM). Based on this, the goal is to create numerical tools capable of providing rapid assessments of the impact of extreme transient loads of impulsive or explosive nature on aboveground and underground civil and engineering structures.