Local Stress Calculation Method In Cell-based Finite Element Model Of Cellular Materials And Its Application

Cellular material is a kind material which is composed of a certain cell structure and has a number of voids interiorly. It has obvious multi-scale characteristic. It has high specific stiffness and strength, which is widely used as lightweight structure in the field of shock resistant and energy absorption. Stress enhancement and deformation localization are two typical features of cellular materials under dynamic crushing. The continuum-based macroscopic nominal stress-strain curves lose the physical meaning and cannot describe the constitutive behavior of cellular materials under dynamic impact. Due to the stress enhancement at the impact end, the nominal stress based on the end face can not reflect the true state of stress in the material. In the case of high-velocity impact, the deformation is concentrated on the impact and propagates like a shock wave. In order to describe this characteristic, a series of shock wave models have been proposed in the literature, such as the classical R-PP-L (rate independent, rigid-perfectly plastic-locking) model and R-PH (rate independent, rigid-plastic hardening) model. However, these models are based on the quasi-static stress-strain curves, so it is necessary to study the stress-strain relationship of cellular materials under dynamic impact. In order to obtain the local stress information of cellular materials under dynamic crushing, we have developed a method to calculate the cross-sectional engineering stress based on the Lagrangian position. This method is then applied to study the stress distribution information and dynamic stress-strain behavior of cellular materials together with the local strain field calculation method.A cross-sectional engineering stress method based on the mesoscale finite element model is proposed in this paper to obtain local stress information in cellular materials. The cross-sectional engineering stress is defined at the Lagrangian position,which is composed of two parts, namely, the node-transitive stress and the contact-induced stress. The node-transitive stress is caused by the nodal force transmitted by the matrix material element, and the contact-induced stress is caused by the contact between the cell walls. In the initial stage of the impact, the contact-induced stress is almost zero, and node-transitive stress is equal to the cross-sectional stress. After the onset of contact, the node-transitive stress seldom changes. The contact-induced stress increases sharply, which is almost equal to the cross-sectional stress. The contact-induced stress is dominant for the stress enhancement.The stress history and stress distribution of homogeneous honeycomb under constant-velocity compression are studied by the cross-sectional stress calculation method. The stress-strain history curves at different impact velocities are obtained by combining the stress history and local strain history. At a low impact velocity, the stress-strain relationship is almost coincident with the quasi-static stress-strain curve.But at a moderate and high impact velocity, stress and strain changes from the initial crushing state ahead of the shock front to the compacted state along a plastic crushing stage. The stress-strain history curve contains the Rayleigh line process. The slope of the Rayleigh curve increases with the increase of the impact velocity, which means that the shock wave speed increases with the impact velocity. The stress-strain state points behind the shock wave are all located on the right side of the quasi-static stress-strain curve, i.e.,the dynamic densification strain is larger than the quasi-static one for a same stress. The propagation of the plastic shock wave in the specimen is confirmed by the stress distribution. The relation between the shock wave velocity and the impact velocity is obtained, which is later compared to the shock models. A piecewise model is proposed based on the relationship between shock wave velocity and impact velocity together with the one-dimensional shock wave theory. A rate-independent constitutive model of the homogeneous honeycomb under dynamic impact is derived based on the piecewise model.The introduction of gradient makes the cellular materials exhibit different mechanical properties. The stress distribution of density-graded honeycombs under constant-velocity compression is studied. The single and double wave propagation modes are observed in the gradient honeycomb directly through the stress distribution.Theoretical models of single wave and double wave propagation based on the R-PP-L and R-PH idealizations are derived and verified by the cross-sectional stress calculation method. The R-PP-L model is confirmed to be improper to characterize the mechanical behavior of cellular materials under dynamic crushing. The stress distribution and the shock wave velocity obtained by the R-PH model are similar to the finite element results.The seemingly contradictory understandings on the initial crush stress of cellular materials under dynamic loadings exist in the literature and a comprehensive analysis of this issue is carried out with using direct information of local stress and strain.Local stress/strain calculation methods are applied to determine the initial crush stresses and the strain rates at initial crush from a cell-based finite element model of irregular honeycomb under dynamic loadings. The initial crush stress under constant-velocity compression is identical to the quasi-static one but less than the one under direct impact, i.e. the initial crush stresses under different dynamic loadings could be very different even though there is no strain-rate effect of matrix material. A power-law relation between the initial crush stress and the strain rate is explored to describe the strain-rate effect on the initial crush stress of irregular honeycomb when the local strain rate exceeds a critical value, below which there is no strain-rate effect of irregular honeycomb. Deformation mechanisms of the initial crush behavior under dynamic loadings are also explored. The deformation modes of the initial crush region in the front of plastic compaction wave are different under different dynamic loadings.