Modeling And Constitutive Relationship Of Metallic Foams Considering Geometric Irregularity

Metallic foams are new engineering materials with many mechanical and physicalproperties in combination, which have metals and pore as the composite phases. Comparedwith conventional metal materials, metallic foams have such excellent mechanical propertiesas super light, high specific stiffness and high specific strength and other characteristics likethermostability, shock-absorbing, denoising, et al. For those reasons, metallic foams are moreand more widely used in the fields of aerospace, transport industry, civil engineeringtelecommunications and biomedical. The meso-structure of metallic foams performs stronggeometrical inhomogeneity, whose effects on the mechanical properties are still not wellunderstood. And it brings the obstacles for the prediction and optimization of the mechanicalproperties of metallic foams. By means of analytical analysis and numerical simulation, thispaper studied the numerical simulation rationality, on which basis we proposed a more precisedescription of the meso-structure of metallic foams and gave qualitative analysis of its effectson the macroscopic compressive mechanical behavior. Further, we developed aphenomenological constitutive model applicable to metallic foams considering themeso-structure, and thus established the internal connection between the mechanical responseof metallic foams on the macro-scale and meso-scale.First of all, we constructed a3D closed-cell metallic foam model based on the3DVoronoi technique and discussed the influence of various parameters involved in the finiteelement simulation of the quasi-static compression of metallic foams, including the modelsize, element type, element size, mass scaling and loading rate. It was shown that that elementmesh size has a significant influence on the accuracy of finite element simulation and reducedintegration shell elements would be more reasonable than full integration shell elements. Onthe other hand, the loading rate and mass scaling will affect the inertial effects, therebyaffecting the quasi-static loading requirements. The simulation results also showed that thereexists the size effect of the metallic foams when the number of cells is insufficient, whichessentially reflects the interference of an unstable state. And by the above analysis, weguaranteed the validity of the finite element models.Definitions of size irregularity and shape irregularity based on2D Voronoi polygons and3D Voronoi polyhedral were introduced to more precisely give a quantitative description ofthe meso-structure of metallic foams. Also, the effects of cell irregularity on the compressionbehavior of metallic foams were investigated. The results suggested that mesoscopicgeometrical irregularity has a great effect on compressive mechanical properties of metallic foams. The foams with smaller size irregularity and shape irregularity are anticipated topossess higher elastic modulus and plateau strength. And through further analysis, we foundthat the size irregularity has an negligible effect on the compression behavior of metallicfoams and the different performance among the closed-cell metallic foams with differentmeso-structure are mainly caused by the size irregularity.The quasi-static compression results of models with different cell sizes showed that, inthe case of avoiding the size effect, the effect of average cell s ize on compressive mechanicalproperties of metallic foams is unapparent. And the compressive mechanical properties ofmetallic foams are mainly affected by the metal-base material, relative density and cell shapeirregularity. On this basis, the functional forms of such mechanical characteristic parametersas elastic modulus, yield strength and plateau stress, in terms of metal-base material property,relative density and shape irregularity were developed, which further were identified by fittingthe available simulation data from models with distinct relative density and shape irregularity.Finally, a phenomenological constitutive model applicable to metallic foams considering themesoscopic geometry irregularity was proposed, which was well proved to capt ure thecompressive stress-strain response of metallic foams.