Dynamic crushing of cellular materials: A unique dynamic stress–strain state curve

• Dynamic stress–strain behavior is analyzed with the wave propagation technique.
• Local stress–strain history curves under different loading rates are obtained.
• A unique dynamic stress–strain state curve of cellular material is obtained.
• The loading-rate and strain-rate effects of cellular materials are investigated.

Cellular materials under high loading rates have typical features of deformation localization and stress enhancement, which have been well characterized by one-dimensional shock wave models. However, under moderate loading rates, the local stress–strain curves and dynamic response of cellular materials are still unclear. In this paper, the dynamic stress–strain response of cellular materials is investigated by using the wave propagation technique, of which the main advantage is that no pre-assumed constitutive relationship is required. Based on virtual Taylor tests, a series of local dynamic stress–strain history curves under different loading rates are obtained by Lagrangian analysis method. The plastic stage of local stress-strain history curve under a moderate loading rate presents a crooked evolution process, which demonstrates the dynamic behavior of cellular materials under moderate loading rates cannot be characterized by a shock model. A unique dynamic stress–strain state curve of the cellular material is summarized by extracting the critical stress–strain points just before the unloading stage on the local dynamic stress–strain history curves. The result shows that the dynamic stress–strain states of cellular materials are independent of the initial loading velocity but deformation-mode dependent. The dynamic stress–strain states present an obvious nonlinear plastic hardening effect and they are quite different from those under quasi-static compression. Finally, the loading-rate and strain-rate effects of cellular materials are investigated. It is concluded that the initial crushing stress is mainly controlled by the strain-rate effect, but the dynamic densification behavior is velocity-dependent.