<p>Constitutive models for engineering materials exhibit significant differences under varying strain rate conditions, necessitating improved quantitative descriptions of strain rate effects. This study examines experimental data for three categories of engineering materials—metals, brittle materials, and plastics—across low, medium, and high strain rates. The results reveal that material strength or yield stress is insensitive to strain rate in both the low and high strain rate conditions (corresponding to the weakly sensitive and saturation zones, respectively), while showing high sensitivity at medium strain rates (strongly sensitive zone). The classical Johnson–Cook constitutive model fails to accurately capture this phenomenon due to limitations in its strain rate effect term formulation. Building upon the Johnson–Cook constitutive model, this study proposes a unified phenomenological constitutive model applicable across different engineering materials, effectively characterizing the weakly sensitive, strongly sensitive, and saturation zones of strain rate effects on material strength or yield stress. The fitted curves using this model align well with experimental data.</p>