Understanding the behavior of materials under extreme conditions—high pressure, temperature, and strain rate—is fundamental to fields ranging from planetary geophysics to defense engineering. This article provides a detailed review of the equation of state (EOS) and strength properties of selected materials, including metals (copper, tantalum), ceramics (alumina, silicon carbide), and geological reference materials (quartz, halite). We discuss the theoretical frameworks (Mie-Grüneisen, Birch-Murnaghan, and Johnson-Cook models) and experimental validation techniques (diamond anvil cells, gas guns, and laser-driven shocks). The coupling between EOS (compressibility, thermal expansion) and strength (yield stress, hardening, spall strength) is critical for accurate material modeling in extreme environments.
[ P = \frac3K_02 \left[ \left(\fracVV_0\right)^-7/3 - \left(\fracVV_0\right)^-5/3 \right] \cdot \left 1 + \frac34(K_0' - 4)\left[\left(\fracVV_0\right)^-2/3 - 1\right] \right ] equation of state and strength properties of selected
