Multi-scale Analysis And Characterization Of Dynamic And Quasi-static Mechanical Properties Of Cellular Materials

Cellular materials have typical multi-scale features and exhibit excellent mechanical properties for the existence of complicated meso-structures,such as lightweight,high specific strength and good impact resistance.They have been widely used in the fields of automobile,aerospace and military,etc,especially for the design of energy absorption structures.The diversity of meso-structures makes it promising to design of cellular materials or multifunctional structures,to expand the space of material properties,to broaden the engineering applications and to develop constitutive relation of cellular materials.However,it is still unclear of the determined relation between the meso-structural parameters and the dynamic mechanical properties of cellular materials.In this study,we adopt the cell-based Voronoi model and the analysis method based on velocity distribution to investigate the dynamic behaviors of cellular material and the dependence of dynamic responses on meso-structural parameters,which may be helpful to guide crashworthiness design of cellular materials and structures.Three dimensional meso-structural finite element model of cellular material is constructed based on Voronoi technique with modular modeling ideology in this study.Cell walls are meshed with the structured grid template method and are further optimized with proper transformation of the original meshing region.The implementation of numerical simulations indicates that random shear bands are raised in cellular material during quasi-static crushing and the rate-independent,rigid-plastic hardening(R-PH)idealisation,which contains only two material parameters,could well characterize the quasi-static behaviors of cellular material.The initial crush stress and the strain hardening parameter of R-PH are determined as power-law relation with relative densities.Under impact loading,the layer-wise collapse feature is usually characterized by a shock wave propagating through this kind of material.Investigation of the asymptotic behavior of shock wave speed and impact velocity shows that the difference between the shock wave speed and the impact velocity is asymptotic to a constant when the impact velocity is high enough.The dependence of the dynamic material parameter on meso-structural parameters and base material properties is determined with dimensional analysis and a determined relation between the dynamic material parameter and relative density is established.Based on the dynamic rigid-plastic hardening(D-R-PH)shock model and conservation relations across shock front,the specific internal energy during crushing is determined,which reveals the mechanism of energy dissipation across the shock front and could guide the optimization design for meso-structures of cellular materials.Besides,the dynamic material parameter that characterizes the hardening behaviors of cellular material also exhibits the nearly linear relation with the strain hardening parameter,strain rate-hardening parameter of cell-wall material and the gas pressure within cells while the initial crushing stress is independent of strain hardening of cell-wall material and the gas pressure within cells but increases linearly with strain rate-hardening parameter of cell-wall material.Actually,the crushing band happens within a finite width and is not a first-order singular surface under dynamic loading.The continuous velocity distribution is applied to study the local dynamic responses of cellular material during crushing.Results show that densification strain approachs to the critical value that corresponds to fully densification state with impact velocity.Under high-velocity impact,the local strain rate is up to a certain magnitude and varies within a small range.Consequently,the initial crushing stress does not change significantly and is treated as a constant of cellular materials under high-velocity loading.Since the stress of the region behind crushing band is almost uniform,dynamic stress is mainly dominated by inertia effect,which behaves as velocity-dependence.Compared with quasi-static stress-strain curve of cellular material,dynamic stress-strain state exhibits obviously loading-rate sensitivity,i.e.deformation-mode dependent feature,which is attributed to the interactions among crushing bands for different deformation modes.Fused deposition modeling is used to fabricate the closed-cells Voronoi specimen as the preliminary application of three dimensional printing technology to meso-structural design of cellular materials.The dependences of mechanical properties of polylactide(PLA)foams on layer deposition orientations during printing,relative density and meso-structures are investigated experimentally.It is demonstrated that cell walls of PLA foam are ruptured more easily along the bond adjoining filaments and obvious lateral expansion is observed when the layer deposition orientation is parallel to the loading direction.For a given Voronoi structure,the initial crushing stress and plateau stress of PLA foams have power-law tendenies with increase of relative densities which are determined by the cell-wall thickness.Moreover,PLA foams with random and tetrakaidecahedron cells exhibit better performance in specific energy absorption,stress undulation and deformation stability.Finally,a statistical constitutive model for the macroscopic mechanical behaviors of random PLA foams is proposed by considering the meso-structural characteristics in cell scale.The statistical model establishes the relation between meso-structures and macro-mechanical responses of cellular materials and provides an idea to study such trans-scale problem raised in cellular materials.This meso-statistical model fits the experimental results of random PLA foams well and the whole deformation process is accurately captured.In particular,the model is capable of capturing the peak stress at the onset of plastic collapse and subsequent stress drop of cellular materials.The dependence of the six parameters in the model on the relative density is analyzed and the corresponding quantitative statistical relation is determined for the random PLA foams used.