ZerilliArmstrong

Zerilli-Armstrong is a family of phenomenological constitutive models used to describe the plastic flow of metals under a range of temperatures and strain rates. It expresses the yield or flow stress as a function of equivalent plastic strain, strain rate, and temperature, with separate formulations for body-centered cubic (bcc) and face-centered cubic (fcc) metals. The model was developed in the early 1980s by Ferdinando Zerilli and J. W. Armstrong to capture the behavior of metals under high strain-rate loading where conventional models may fail to predict dynamic response reliably.

Mechanistically, the Zerilli-Armstrong formulation treats flow stress as comprising a baseline component and a thermally activated, rate-sensitive component, with strain-hardening supported by additional terms. The baseline terms and exponents are material constants determined by fitting experimental data across temperature and strain-rate ranges. The temperature dependence often reflects lattice friction and dislocation mechanisms, while the rate dependence reflects thermally activated processes that vary with strain rate. The model is designed to be calibrated from laboratory tests such as tension, compression, and torsion experiments over the intended service envelope.

Usage and scope: Zerilli-Armstrong is widely used in finite element analysis of metal forming, impact, and ballistic problems. Material databases implement it as a material model in codes such as ABAQUS, LS-DYNA, and ANSYS. Typical calibration materials include steels, aluminum alloys, titanium alloys, and other metals with available high-strain-rate data.

Limitations: The model is empirical and relies on experimental calibration; extrapolation beyond calibrated ranges can be unreliable and it may not capture phase transformations or complex microstructural changes. Variants exist to address specific materials or to incorporate pressure effects and dynamic loading considerations.